case study of statistical process control

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• Volume 16, Issue 5
• Application of statistical process control in healthcare improvement: systematic review
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• Johan Thor ,
• Jonas Lundberg ,
• Jakob Ask ,
• Jesper Olsson ,
• Cheryl Carli ,
• Karin Pukk Härenstam ,
• Mats Brommels
• Medical Management Centre, Karolinska Institutet, Stockholm, Sweden
• Correspondence to:
 Dr Johan Thor
 Medical Management Centre, Berzelius väg 3, 5th floor, Karolinska Institutet, S-171 77 Stockholm, Sweden; johan.thor{at}ki.se

Objective: To systematically review the literature regarding how statistical process control—with control charts as a core tool—has been applied to healthcare quality improvement, and to examine the benefits, limitations, barriers and facilitating factors related to such application.

Data sources: Original articles found in relevant databases, including Web of Science and Medline, covering the period 1966 to June 2004.

Study selection: From 311 articles, 57 empirical studies, published between 1990 and 2004, met the inclusion criteria.

Methods: A standardised data abstraction form was used for extracting data relevant to the review questions, and the data were analysed thematically.

Results: Statistical process control was applied in a wide range of settings and specialties, at diverse levels of organisation and directly by patients, using 97 different variables. The review revealed 12 categories of benefits, 6 categories of limitations, 10 categories of barriers, and 23 factors that facilitate its application and all are fully referenced in this report. Statistical process control helped different actors manage change and improve healthcare processes. It also enabled patients with, for example asthma or diabetes mellitus, to manage their own health, and thus has therapeutic qualities. Its power hinges on correct and smart application, which is not necessarily a trivial task. This review catalogues 11 approaches to such smart application, including risk adjustment and data stratification.

Conclusion: Statistical process control is a versatile tool which can help diverse stakeholders to manage change in healthcare and improve patients’ health.

• MRSA, methicillin resistant Staphylococcus aureus
• PEFR, peak expiratory flow rate
• QI, quality improvement
• RCT, randomised controlled trial
• SPC, statistical process control

https://doi.org/10.1136/qshc.2006.022194

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Quality improvement (QI) practices represent a leading approach to the essential, and often challenging, task of managing organisational change. 1 Statistical process control (SPC) is, in turn, a key approach to QI. 2 SPC was developed in the 1920s by the physicist Walter Shewhart to improve industrial manufacturing. It migrated to healthcare, first in laboratory settings (eg, Fisher and Humphries 3 ) and then into direct patient care applications, along with other approaches to QI. Before we report on our systematic review of the literature on how SPC has been applied to QI in healthcare, there is a need to define SPC and its role in QI.


 “Statistical process control (SPC) is a philosophy, a strategy, and a set of methods for ongoing improvement of systems, processes, and outcomes. The SPC approach is based on learning through data and has its foundation in the theory of variation (understanding common and special causes). The SPC strategy incorporates the concepts of an analytic study, process thinking, prevention, stratification, stability, capability, and prediction. SPC incorporates measurement, data collection methods, and planned experimentation. Graphical methods, such as Shewhart charts (more commonly called ‘control charts’), run charts, frequency plots, histograms, Pareto analysis, scatter diagrams, and flow diagrams are the primary tools used in SPC.” (Carey 4 , p xviii)

The terms “statistical process control” and “statistical quality control” are often used interchangeably, 5 although sometimes the latter is used to describe a broader organisational approach to quality management that evolved into the concept of total quality management. 6

One of the tenets of QI is that to improve healthcare performance we must change our way of working. 7 But change does not always mean improvement. To discriminate between changes that yield improvement and those that do not, relevant aspects of performance need to be measured. In addition, measurement guides decisions about where improvement efforts should be focused in the first place. SPC may facilitate such decision making. Control charts, central to SPC, are used to visualise and analyse the performance of a process—including biological processes such as blood pressure homoeostasis or organisational processes such as patient care in a hospital—over time, sometimes in real time. Statistically derived decision rules help users to determine whether the performance of a process is stable and predictable or whether there is variation in the performance that makes the process unstable and unpredictable. One source of such variation can be a successful intervention aimed at improvement that changes performance for the better. If the improvement is maintained, the process will stabilise again at its new level of performance. All of this can be easily determined by using SPC. 4

Although there are theoretical propositions that SPC can facilitate decision making and QI in healthcare (eg, Berwick, 8 Benneyan et al , 9 Plsek 10 ) it is not clear what empirical support there is in the literature for such a position 11 :


 “The techniques of statistical process control, which have proved to be invaluable in other settings, appear not to have realised their potential in health care. ... Is this because they are, as yet, rarely used in this way in health care? Is it because they are unsuccessful when used in this way and thus not published (publication bias)? Or is it that they are being successfully used but not by people who have the inclination to share their experience in academic journals?” (p 200)

The present systematic review aimed to answer these questions. We examined the literature for how and where SPC has been applied in QI of clinical/patient care processes and the benefits, limitations, barriers and facilitating factors related to such application.

MATERIALS AND METHODS

Drawing on the principles and procedures for systematic review of QI interventions 12 we searched for articles on the application of SPC in healthcare QI published between 1966 and June 2004 (see appendix A) in the following databases: Web of Science, Ovid Medline(R), EMBASE, CINAHL (Cumulative Index to Nursing and Allied Health Literature), PsycInfo, and the Centre for Reviews and Dissemination databases. We also included articles found by searching reference lists or from elsewhere which we were aware of, if they met our inclusion criteria: original empirical studies of SPC application in improvement of clinical/patient care processes in healthcare organisations, published in English. We excluded articles dealing with application of SPC in laboratory or technical processes (eg, film processing) and in surveillance/monitoring (unless they also contained empirical data about improvement efforts), as well as tutorials (unless they contained empirical case studies), letters, book reviews and dissertations.

We reviewed abstracts, when available, or else other information about the publication provided in the database (eg, publication type such as letters, book reviews or original articles). Articles that did not meet the inclusion criterion were excluded. We retrieved and read the full text of the remaining articles, again excluding the articles that did not meet the inclusion criterion.

We developed, pilot tested and modified a data abstraction form which we then used to consistently capture information of relevance to our review questions on reading the full text articles. The information recorded was: whether and how the article met the inclusion criterion; study objective(s); study design; whether the study empirically compared application of SPC with any other method for process data display and analysis; reported benefits, limitations, barriers and facilitating factors related to SPC; organisational setting; country where study was conducted; clinical specialty; unit of analysis; variables for SPC analysis; and other observations. Some questions in the form required a yes/no or brief response (eg, country where study was conducted) and others required answers in the form of direct quotes from the article or the a summary of the article written by the reviewer. Each article was read and data abstracted by one member of the review team (the coauthors of this review). Following this, all the data abstraction forms were reviewed by the first author, who solicited clarification and checked for any missing or incomplete data to ensure consistency in reporting across all articles reviewed. He also conducted the initial data synthesis, which was then reviewed by the entire team.

We determined the study design for each article and whether the investigators intended to test the utility of SPC application, alone or in combination with other interventions. In several articles, the study design or study objectives were not explicitly stated. Our determination of such intention in such cases was based on our reading of the full text papers.

Simple descriptive statistics—for example, the number of publications per year of publication or per country—were used to characterise the included studies. The qualitative nature of our research questions and of the abstracted data shaped our analysis and synthesis of findings regarding benefits, limitations, SPC variables, etc. 13 The abstracted data was reviewed one question at a time and data from each article was classified into one or more thematic categories, each with a descriptive heading. Informed by our present understanding of QI and healthcare, we developed these categories as we reviewed the data, rather than using categories derived a priori from theory. For data that did not fit into an existing category, we developed a new one. Thus the categories emerged as we synthesised the data. We report the categorised data in tabular form, illustrated with examples, and give the references of all the source studies.

To strengthen our review through investigator triangulation, 14 we sought feedback on an earlier version of this manuscript from two SPC experts: one was the most frequent coauthor in the included studies and the other was an expert on SPC application also in settings other than healthcare. Their comments helped us refine our data synthesis and distil our findings.

The database searches yielded 311 references. The initial review (abstracts etc.) yielded 100 articles which we read in full text form. Of these, 57 articles met the inclusion criteria and have been included in the review. 15– 71 To characterise the body of liferature, figure 1 shows the year of publication and whether the studies were conducted in USA or elsewhere (further specified below); table 1 gives the study designs and objectives—whether or not to test SPC utility.

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 Study design and objectives of the studies included in the systematic review*

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 The number of included articles by year of publication. (A total of 55 articles were published in 1990–2003; the two articles from 2004 are not included in this graph since the database searches were conducted in June 2004.) Black bars: studies conducted in the USA; grey bars: studies conducted outside the USA.

Most of the articles (45/57) concerned application of SPC in healthcare improvement in the USA. 15– 35, 37– 40, 42, 43, 45, 47, 49– 56, 59, 60, 63, 67– 71 While the first US-based article was published in 1990, the non-US articles were published between 1998 and 2003: three articles were from the UK, 61, 62, 66 three were from Switzerland, 36, 41, 46 and one each were from Australia, 58 Finland, 65 France, 57 Indonesia, 44 Norway 64 and Spain. 48 The intention to test the utility of SPC is exemplified by a study aiming to reduce the rate of acquisition of methicillin-resistant Staphylococcus aureus (MRSA) on wards and units at Glasgow Royal Infirmary hospitals. 61 Annotated control charts displaying data on MRSA acquisition were fed back monthly to medical staff, managers and hotel services. Sustained reductions in the rate of acquisition from the baseline, which could not otherwise be accounted for, started 2 months later. In contrast, investigators at a paediatric emergency department used SPC to demonstrate a decline in the rate of contamination following the introduction of a new approach to drawing blood for culture specimens, 68 but the study had no intention to test the utility of SPC per se.

To characterise the content of the articles, we first present how and where SPC has been applied to healthcare QI. Tables 2–4 present the study settings (ie, hospital etc. where SPC was applied; table 2), the field of healthcare (ie, specialties or forms of care; table 3), and the units of analysis (table 4). Table 5 enlists the 97 distinct SPC variables that have been reported. Tables 6–9 convey our synthesis of the reported benefits, limitations, barriers and facilitating factors related to SPC application. For each category, we have given explanations or examples and references to the source articles.

 How and where SPC was applied: study settings*

 How and where SPC was applied: fields of healthcare*

 How and where SPC was applied: units of analysis*

 SPC variables*

 Benefits of using SPC to improve clinical processes*

SPC has been applied to healthcare improvement in a wide range of settings and specialties, at diverse levels of organisations and directly by patients, using many types of variables (fig 1, tables 2–5). We found reports of substantial benefits of SPC application, as well as important limitations of, barriers to and factors that facilitate SPC application (tables 6–9). These findings indicate that SPC can indeed be a powerful and versatile tool for managing changes in healthcare through QI. Besides helping diverse stakeholders manage and improve healthcare processes, SPC can also help clinicians and patients understand and improve patients’ health when applied directly to health indicators such as PEFR in asthma or blood sugar concentrations in diabetes. In healthcare, the “study subject” can thus also be an active agent in the process, as when patients apply SPC to their own health. Several studies indicated the empowering effects this may have on patients. 35, 38, 40, 50 SPC application thus has therapeutic potential as it can help patients manage their own health. We agree with Alemi and Neuhauser 70 that this potential merits further investigation.

Most of the included articles concerned application of SPC in healthcare improvement in the USA. Articles from other countries appeared only towards the end of the study period (fig 1). We have no explanation for this finding, but we speculate that it is related to differences between US and other healthcare systems with regard to QI awareness and implementation. 73

Only 22 studies included in the review were intended to test the utility of SPC (table 1). Of the four controlled studies, only one included a control chart in the intervention (as a minor component which did not fully exploit the features of SPC). In 35 articles we did not find an intention to test the utility of SPC application. In those cases, SPC was applied for other reasons (ie, to evaluate the impact of other interventions). Even though many articles thus did not address the utility of SPC, all studies offered information—to varying degrees—relevant to our review’s question of how SPC has been applied to healthcare. The utility of SPC is reflected in benefits reported regarding SPC application (table 6).

SPC has been applied in over 20 specialties or fields of healthcare, at a wide range of levels (tables 3 and 4), suggesting that SPC has broad applicability in healthcare. The dominance of anaesthesia and intensive care can be explained in large part by the fact that many studies included their services in conjunction with other specialties. This reflects the way in which anaesthesia has a vital supporting role in many clinical care processes. The 97 SPC variables reported (table 5) demonstrate a diversity of situations in which SPC has been applied, ranging from process indicators of patients’ health to health outcomes and many aspects of healthcare processes and organisational performance. This indicates that SPC is a versatile QI tool.

The benefits of SPC application (table 6) mirror those given in books and tutorials on SPC (exemplified by the quote in the Introduction to this review). As noted in a report from a top-ranked healthcare system which has applied SPC widely:


 “Among the most powerful quality management tools that IHC [Intermountain Health Care, USA] has applied is statistical process control, SPC. Most notable among those tools are control charts. Under optimal conditions, these graphical depictions of process performance allow participants to know what is happening within their processes as ‘real time’ data enable them to make appropriate decisions. The capability of truly understanding processes and variation in a timely manner has resulted in the most dramatic, immediate, and ongoing improvements of any management technique applied at IHC.” (Shaha, 26 p 22)

The limitations of SPC application (table 7) identified by this review are important, and yet perhaps less emphasised than the benefits in books and tutorials on SPC. SPC cannot solve all problems and must be applied wisely. There are many opportunities to “go wrong”, as illustrated by the case where incorrect application was highlighted by other authors (limitation number 5 in table 7). In several cases, our own understanding of SPC suggested that investigators had not used it correctly or fully (eg, standard decision rules to detect special causes were not applied to identify process changes). In the worst case scenario, incorrect application of SPC could lead to erroneous conclusions about process performance and waste time, effort and spirit and even contribute to patient harm. In the more authoritative studies we reviewed, co-investigators included experts in industrial engineering or statistics or authors who otherwise had developed considerable expertise in SPC methodology. On the basis of these observations, we conclude that although SPC charts may be easy to use even for patients, clinicians or managers without extensive SPC training, they may not be equally simple to construct correctly. To apply SPC is, paradoxically, both simple and difficult at the same time. Its power hinges on correct and smart application, which is not necessarily a trivial task. The key, then, is to develop or recruit the expertise necessary to use SPC correctly and fully and to make SPC easy for non-experts to use, before using it widely.

 Limitations of SPC application in improvement of clinical processes*

Autocorrelation is another limitation of SPC highlighted by this review. Our review, and published books, offer limited advice on how to manage it:


 “There is no single acceptable way of dealing with autocorrelation. Some would say simply to ignore it. [Others] would disagree and suggest various measures to deal with the phenomenon. One way is to avoid the autocorrelation by sampling less frequently. ... Others argue against plotting autocorrelated data on control charts and recommend that the data be plotted on a line chart (without any centerline or control limits).” (Carey, 4 p 68)

Just over a quarter of the articles reported barriers to SPC application (table 8). The three broad divisions of barriers—people, data and chart construction, and IT—indicate where extra care should be taken when introducing SPC in a healthcare organisation. Ideas on how to manage the limitations of and barriers to SPC application can be found among the factors reported to facilitate SPC application (table 9). They deal with, and go beyond, the areas of barriers we found. We noted the prominence of learning and also of focusing on topics of interest to clinicians and patients. The 11 categories under the heading “Smart application of SPC can be helpful” contain valuable approaches that can be used to improve SPC application. Examples include risk adjustment 51, 52, 71 and stratification 30, 37, 59 to enable correct SPC analysis of data from heterogeneous populations of patients (or organisational units). Basic understanding of SPC must be taught to stakeholders and substantial skill and experience is required to set up successful SPC application. Experts, or facilitators, in healthcare organisations can help, as indicated in table 9, and as we have described for other QI methods. 74

 Barriers to SPC application*

 Factors or conditions facilitating application of SPC*

We found more information on SPC benefits and facilitating factors than on limitations and barriers, and this may represent a form of publication bias, as indicated by the quote in the Introduction. 11 We did not find any study that reported failed SPC application. We can speculate that there have been situations when SPC application failed, just as there must be many cases of successful SPC application that have not been reported in the literature. Studies of failed SPC application efforts, as well as studies designed to identify successful ways to apply SPC to manage change, would help inform future SPC application efforts. On the basis of this review, we agree with the argument that “medical quality improvement will not reach its full potential unless accurate and transparent reports of improvement work are published frequently and widely (p 319),” 75 and also that the way forward is to strengthen QI research rather than to lower the bar for publication. 76

Methodological considerations regarding the included studies

None of the studies we found was designed to evaluate the effectiveness quantitatively—that is, the magnitude of benefits—of SPC application. This would have required other study designs such as cluster randomised trials or quasi-experimental studies. 12 Although the “methods of evaluating complex interventions such as quality improvement interventions are less well described [than those to evaluate less complex interventions such as drugs]”, Eccles et al argue that the “general principle underlying the choice of evaluative design is ... simple—those conducting such evaluations should use the most robust design possible to minimise bias and maximise generalisability. [The] design and conduct of quantitative evaluative studies should build upon the findings of other quality improvement research (p 47).” 77 This review can provide such a foundation for future evaluative studies.

An important distinction is warranted here: we believe that SPC rests on a solid theoretical, statistical foundation and is a highly robust method for analysing process performance. The designs of the studies included in this systematic review were, however, not particularly robust with regard to evaluating the effectiveness of SPC application, and that was not their objective. This does not mean that SPC is not a useful tool for QI in healthcare, only that the studies reviewed here were more vulnerable to bias than more robust study designs, even if they do indicate many clear benefits of SPC application (table 6). Despite the studies not being designed to evaluate the effectiveness of SPC, many used SPC to effectively show the impact of QI or other change initiatives. In this way, SPC analysis can be just as powerful and robust as study designs often deemed superior, such as randomised controlled trials (RCTs). 77 The key to this power is the statistical and practical ability to detect significant changes over time in process performance when applying SPC. 9 On the basis of a theoretical comparison between control charts and RCTs, Solodky et al 38 argue that control charts can complement RCTs, and sometimes even be preferable to RCTs, since they are so robust and enable replication—“the gold standard” for research quality—at much lower cost than do RCTs. These points have been further elaborated in subsequent work. 78, 79

A curious methodological wrinkle in our review is: can you evaluate the application of a method (eg, SPC) using that same method for the evaluation? Several of the included studies used SPC both as (part of) an intervention and as a method to evaluate the impact of that intervention. For example, Curran et al used annotated control charts to feed information on MRSA acquisition rates back to stakeholders and used these same control charts to show the effectiveness of the feedback programme. 61

Relationship between monitoring and improvement

When SPC is applied for monitoring, rather than for managing change, the aims are different—for example, to detect even small but clinically important deviations in performance—as are the methodological challenges. 80, 81 This review focused on the latter. Thus although studies on SPC application for monitoring healthcare performance were excluded from this review, we recognise the importance of such monitoring. The demarcation between monitoring and improvement is not absolute. Indeed, there are important connections between measurement, monitoring and improvement, even if improvement does not follow automatically from indications of dissatisfactory performance. “To improve performance, organizations and individuals need the capability to control, improve, and design processes, and then to monitor the effects of this improvement work on the results. Measurement alone will not suffice (pp 1–35).” 82

Monitoring performance by way of control charts has been suggested as a better approach to clinical governance in the British National Health Service. Through six case studies, Mohammed et al demonstrate how control chart monitoring of performance can distinguish normal performance from performance that is either substandard or better than usual care. “These case studies illustrate an important role for Shewhart’s approach to understanding and reducing variation. They demonstrate the simplicity and power of control charts at guiding their users towards appropriate action for improvement (p 466).” 83

Comments on the review methodology

No search strategy is perfect, and we may well have missed some studies where SPC was applied to healthcare QI. There are no SPC specific keywords (eg, Medical Subject Headings, MeSH) so we had to rely on text words. Studies not containing our search terms in the title or abstract could still be of potential interest although presumably we found most of the articles where SPC application was a central element. We believe the risk that we systematically missed relevant studies to be small. Therefore, our findings would probably not have changed much due to such studies that we might have missed.

The review draws on our reading, interpretation and selection of predominantly qualitative data—in the form of text and figures—in the included articles to answer the questions in our data abstraction form. The questions we addressed, the answers we derived from the studies, and the ways we synthesised the findings are not the only ways to approach this dataset. Furthermore, each member of the review team brought different knowledge and experiences of relevance to the review, potentially challenging the reliability of our analysis. An attempt was made to reduce that risk by having one investigator read all data abstraction forms, and obtain clarifications or additional data from the original articles when needed. That investigator also conducted the initial data synthesis, which was then reviewed by the entire team and the two outside experts. Although other interpretations and syntheses of these data are possible, we believe that ours are plausible and hope they are useful.

The methods for reviewing studies based primarily on qualitative data in healthcare are less well developed than the more established methods for quantitative systematic reviews, and they are in a phase of development and diversification. 13, 84, 85 Among the different methods for synthesising evidence, our approach is best characterised as an interpretive (rather than integrative) review applying thematic analysis—it “involves the identification of prominent or recurrent themes in the literature, and summarising the findings of different studies under thematic headings”. 86 There is no gold standard for how to conduct reviews of primarily qualitative studies. Our response to this uncertainty has been to use the best ideas we could find, and to be explicit about our approach to allow readers to assess the findings and their provenance.

The main limitation of this review is the uncertainty regarding the methodological quality of many of the primary studies. Assessment of quality of qualitative studies is still under debate, and there is no consensus on whether at all, or, if so, how to conduct such assessments. 84 We reviewed all the studies that satisfied our inclusion criteria and made no further quality assessment. Therefore our findings should be considered as tentative indications of benefits, limitations, etc to be corroborated, or rejected, by future research. The main strength of this review is our systematic and explicit approach to searching and including studies for review, and to data abstraction using a standardised form. It has helped generate an overview of how SPC has been applied to healthcare QI with both breadth and depth—similar to the benefits of thematic analysis reported by investigators reviewing young people’s views on health and health behaviour. 87

In conclusion, this review indicates how SPC has been applied to healthcare QI with substantial benefits to diverse stakeholders. Although there are important limitations and barriers regarding its application, when applied correctly SPC is a versatile tool which can enable stakeholders to manage change in healthcare and improve patients’ health.

Database search strategy

Web of Science (1986 – 11 June 2004)

TS [topic search]  =  ((statistical process control or statistical quality control or control chart* or (design of experiment and doe)) and (medical or nurs* or patient* or clinic* or healthcare or health care))

We limited the search to articles in English only which reduced the number of hits from 167 to 159. We saved these 159 titles with abstracts in an EndNote library. Using a similar strategy, we searched the following databases through Ovid:

Ovid MEDLINE(R) (1966 to week 1, June 2004)

EMBASE (1988 to week 24, 2004)

CINAHL (1982 to week 1, June 2004)

PsycINFO (1985 to week 5, May 2004)

This yielded 287 hits, including many duplicates, which we saved in the same EndNote library as above.

Centre for Reviews and Dissemination (CRD)

We searched all CRD databases and found two articles which we also added to our EndNote library.

Acknowledgments

We thank Ms Christine Wickman, Information Specialist at the Karolinska Institutet Library, for expert assistance in conducting the database searches. We also acknowledge the pilot work conducted by Ms Miia Maunuaho as a student project at Helsinki University, supervised by Professor Brommels, which provided a starting point for this study. We thank Professor Duncan Neuhauser, Case Western Reserve University, Cleveland, Ohio, USA, and Professor Bo Bergman, Chalmers University of Technology, Gothenburg, Sweden, for their helpful comments on an earlier version of this manuscript. We thank Dr Rebecca Popenoe for her editorial assistance.

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Funding: No dedicated funding was received for this study. All coauthors were supported by their respective employers in conducting this research as part of their work.

Competing interests: None.

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• Guide: Statistical Process Control (SPC)

Daniel Croft

Daniel Croft is an experienced continuous improvement manager with a Lean Six Sigma Black Belt and a Bachelor's degree in Business Management. With more than ten years of experience applying his skills across various industries, Daniel specializes in optimizing processes and improving efficiency. His approach combines practical experience with a deep understanding of business fundamentals to drive meaningful change.

• Last Updated: March 24, 2024
• Learn Lean Sigma

Statistical Process Control is a key method used in making sure products are made to specification and efficiently, especially in making expensive products like cars or electronics where margins can be low and the cost of defects can eliminate profitaility. It uses a detailed, numbers-based way to monitor, manage, and improve processes where product are made or services are provided.

SPC focuses on carefully examining data to help businesses understand problems or issues in how they make products or provide services. It’s all about making decisions based on solid evidence rather than guesses or feelings, with the goal of finding and fixing any changes in the process that could affect the quality of the product.

Table of Contents

What is statistical process control.

Statistical Proces Control is a key method used in quality control, and Lean Six Sigma used to maintain and improve product quality and efficiency. It is used in various industries but is primarily used in manufacturing as a systematic, data-driven approach to uses statistical methods to monitor, control, and improve processes and process performance. 

SPC is a data-driven methodology that relies heavily on data to analyze process performance. By collecting and analyzing data from various stages of a manufacturing or service process, SPC enables organizations to identify trends, patterns, and anomalies. This data-driven approach helps in making informed decisions rather than relying on assumptions or estimations.

The main aim of SPC is to detect and reduce process variability. Variability is a natural aspect of any process, but excessive variability can lead to defects, inefficiency, and reduced product quality. By understanding and controlling this variability, organizations can ensure that their processes consistently produce items within desired specifications. SPC involves continuous monitoring of the process to quickly identify deviations from the norm. This systematic approach ensures that problems are detected early and can be rectified before they result in significant quality issues or production waste.

History and Background of the Development of SPC

Walter shewhart and control charts.

The foundations of SPC were laid in the early 20th century by Walter Shewhart working at Bell Laboratories. Shewhart’s primary contribution was the development of the control chart , a tool that graphically displays process data over time and helps in distinguishing between normal process variation and variation that signifies a problem. The control chart remains a cornerstone of SPC and is widely used in various industries to monitor process performance.

W. Edwards Deming and Post-War Japan

After World War II, W. Edwards Deming brought the concepts of SPC to Japan, where they played a key role in the country’s post-war industrial rebirth. Deming’s teachings emphasized not only statistical methods but also a broader philosophical approach to quality. He advocated for continuous improvement ( Kaizen ) and total quality management , integrating SPC into a more comprehensive quality management system.

Impact on Manufacturing and Beyond

The implementation of SPC led to significant improvements in manufacturing quality and efficiency. It allowed companies to produce goods more consistently and with fewer defects. The principles of SPC have since been adopted in various sectors beyond manufacturing, including healthcare, finance, and service industries, demonstrating its versatility and effectiveness in process improvement.

Fundamental Concepts of SPC

To understand and read what control charts are telling you it is first important to understand how variation and how it might be displayed on the chart. In everything, there is always a level of variation relative to what is being measured. But we must identify what acceptable variation and what is a variation that needs to be explored and addressed.

Understanding Process Variation

In SPC, process variation is categorized into two types: common causes and special causes.

• Common Cause Variation: These are inherent variations that occur naturally within a process. They are predictable and consistent over time. In the image below common cause variation is the variation within the control limits
• Special Cause Variation: These variations are due to external factors and are not part of the normal process. They are unpredictable and can indicate that the process is out of control. In the image below, the special cause variation is the data point outside the upper control limit 

Control Charts

Control charts are essential tools in SPC, used to monitor whether a process is in control.

• Graphical Representation: They graphically represent data over time, providing a visual means to monitor process performance.
• Control Limits: Control charts use upper and lower control limits, which are statistically derived boundaries. They help in distinguishing between normal process variation (within limits) and variations that require attention (outside limits).

Types of Control Charts

After understanding the types of variation you might find on a control chat, it is important to understand the types of control charts in SPC. This is crucial for effectively monitoring and improving various processes. These charts are broadly categorized based on the type of data they handle: variable data and attribute data. Additionally, the implementation of SPC in a process, from data collection to continuous improvement, is a systematic approach that requires diligence and precision. Let’s explore these aspects in more detail.

Variable Data Control Charts

Variable data control charts are used for data that can be measured on a continuous scale. This includes characteristics like weight, length, or time.

X-bar and R Chart

• Purpose: Used to monitor the mean (average) and range of a process.
• Application: Ideal for situations where sample measurements are taken at regular intervals and the mean and variability of the process need to be controlled.
• Structure: The X-bar chart shows how the mean changes over time, while the R chart displays the range (difference between the highest and lowest values) within each sample.

Individual-Moving Range (I-MR) Chart

• Purpose: Monitors individual observations and the moving range between observations.
• Application: Useful when measurements are not made in subgroups but as individual data points.
• Structure: The I chart tracks each individual data point, and the MR chart shows the range between consecutive measurements.

Attribute Data Control Charts

Attribute data control charts are used for data that are counted, such as defects or defective items.

P-chart (Proportion Chart)

• Purpose: Monitors the proportion of defective items in a sample.
• Application: Ideal for quality characteristics that are categorical (e.g., defective vs. non-defective) and when the sample size varies.
• Structure: It plots the proportion of defectives in each sample over time.

C-chart (Count Chart)

• Purpose: Tracks the count of defects per unit or item.
• Application: Used when the number of opportunities for defects is constant, and defects are counted per item or unit.
• Structure: It plots the number of defects in samples of a constant size.

Implementing SPC in a Process

Implementing SPC in a process is a structured approach that involves several key steps: data collection, establishing control limits, monitoring and interpretation, and continuous improvement. Each of these steps is critical to the successful application of SPC. Let’s explore these steps in more detail.

Step 1: Data Collection

First, data must be collected systematically to ensure it accurately represents the process. This involves deciding what data to collect, how often to collect it, and the methods used for collection. The selection of data is important. It should be relevant to the quality characteristics you want to control. For example, in a manufacturing process, this might include measurements of product dimensions, the time taken for a process step, or the number of defects.

The data should be representative of the actual operating conditions of the process. It means collecting data under various operating conditions and over a sufficient period.

The sample size and frequency of data collection should be adequate to capture the variability of the process. It’s a balance between collecting enough data for reliability and the practicality of data collection.

Step 2: Establishing Control Limits

Control limits are calculated using historical process data. They are statistical representations of the process variability and are usually set at ±3 standard deviations from the process mean.

These limits reflect what the process can achieve under current operating conditions.

To help you calculate your data control limits, you can use our Control Limits Calculator.

Control limits are not fixed forever. As process improvements are made, these limits may be recalculated to reflect the new level of process performance.

When significant changes are made to a process (like new machinery, materials, or methods), it might be necessary to recalculate the control limits based on new performance data.

Step 3: Monitoring and Interpretation

Regularly reviewing control charts is essential for timely detection of out-of-control conditions. Apart from individual points, it’s crucial to look for patterns or trends in the data, which could indicate potential issues.

When data points fall outside the control limits or exhibit non-random patterns, it triggers a need for investigation. The goal is to identify the root cause of the variation, whether it’s a common cause that requires a process change, or a special cause that might be addressed more immediately.

Step 4: Continuous Improvement

SPC is not just about maintaining control; it’s about continuous improvement. The insights gained from SPC should drive ongoing efforts to enhance process performance.

Based on SPC data, processes can be adjusted, improved, and refined over time. This might involve changes to equipment, materials, methods, or training.

In conclusion, SPC is a key tool in the aim for quality control and process improvement. Its strength lies in its ability to make process variability visible and manageable. From the seminal contributions of Walter Shewhart and W. Edwards Deming, SPC has evolved into a comprehensive approach that integrates seamlessly with various quality management systems.

By continuously monitoring processes through control charts and adapting to the insights these charts provide, SPC empowers organizations to maintain control over their processes and pursue relentless improvement. Thus, SPC not only sustains but also elevates the standards of quality, efficiency, and customer satisfaction in diverse industrial landscapes.

• Madanhire, I. and Mbohwa, C., 2016. Application of statistical process control (SPC) in manufacturing industry in a developing country .  Procedia Cirp ,  40 , pp.580-583.
• Gérard, K., Grandhaye, J.P., Marchesi, V., Kafrouni, H., Husson, F. and Aletti, P., 2009. A comprehensive analysis of the IMRT dose delivery process using statistical process control (SPC).   Medical physics ,  36 (4), pp.1275-1285.

Q: What is Statistical Process Control?

A : SPC is a method used to monitor, control, and improve processes by analyzing performance data to identify and eliminate unwanted variations.

Q: Why is SPC important?

A : SPC helps ensure processes are consistent and predictable. It aids in early detection of issues, reducing defects, and improving overall product or service quality.

Q: What is a control chart?

A : A control chart is a graphical representation used in SPC to plot process data over time, with control limits that help distinguish between common and special cause variations.

Q: How are control limits determined?

A : Control limits are typically set at three standard deviations above and below the process mean, based on historical data. However, these limits can be adjusted depending on the specific chart type and industry standards.

Q: What's the difference between common cause and special cause variation?

A : Common cause variation is the inherent variability in a process, while special cause variation arises from specific, unusual events and is not part of the normal process.

Daniel Croft is a seasoned continuous improvement manager with a Black Belt in Lean Six Sigma. With over 10 years of real-world application experience across diverse sectors, Daniel has a passion for optimizing processes and fostering a culture of efficiency. He's not just a practitioner but also an avid learner, constantly seeking to expand his knowledge. Outside of his professional life, Daniel has a keen Investing, statistics and knowledge-sharing, which led him to create the website learnleansigma.com, a platform dedicated to Lean Six Sigma and process improvement insights.

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Statistical Process Control for Autocorrelated Processes: A Case-Study

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Statistical control charts are usually designed to monitor independently distributed observations, typically subject to a normal distribution. For many industrial processes the normal distribution may indeed provide an adequate description of data. When production is in discrete items, the assumption of independence may often be reasonable, whereas many chemical and environmental processes show an inherent dynamical variation with the implication that successive observations are (strongly) correlated.

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Control Charts with R

The generally weighted moving average control chart for monitoring the process mean of autocorrelated observations

Statistical Process Control

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Iwersen, J. (1997). Statistical Process Control for Autocorrelated Processes: A Case-Study. In: Lenz, HJ., Wilrich, PT. (eds) Frontiers in Statistical Quality Control. Frontiers in Statistical Quality Control, vol 5. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-59239-3_11

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Statistical Process Control for the Food Industry by Sarina A. Lim, Jiju Antony

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10 Case Studies

This chapter disclosed the case studies gathered from research and literature. Each case study is described in brief, focusing on the application of the specific expediting process control approach it illustrates, including the approach to choose pilot projects, the control of key quality of the process attributes, and the application of various type of control charts served for different types of data. This chapter displays how SPC has been successfully applied in several different situations.

The details and situation of the cases are varied, however in general each will provide the background of the cases, the data and suitable type of charts. The charts are interpreted, and interesting points are discussed in the case study. It is not necessarily to understand the calculation and detail calculations to benefit from this book. Implementing SPC in the organisation, it only requires a few number staff to understand the theory and formulae on the calculations of control charts.

10.1 Application of the Control Charts in the Industries

Control charts are typically taught in the classes and mostly when teaching the theory of SPC it is understandable to find the data for the control chart are the easiest to be understood. Theoretically, normality is expected in the food processing data; however, this is rarely the case in the food industry. In the real‐world data, neither SPC nor any other technique is the solution for all problems, where other quality tools may ...

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A statistical process control case study

Affiliation.

• 1 Department of Health Services and Information Management, School of Allied Health Sciences, East Carolina University, Greenville, NC 27858, USA. [email protected]
• PMID: 17047496
• DOI: 10.1097/00019514-200610000-00004

Statistical process control (SPC) charts can be applied to a wide number of health care applications, yet widespread use has not occurred. The greatest obstacle preventing wider use is the lack of quality management training that health care workers receive. The technical nature of the SPC guarantees that without explicit instruction this technique will not come into widespread use. Reviews of health care quality management texts inform the reader that SPC charts should be used to improve delivery processes and outcomes often without discussing how they are created. Conversely, medical research frequently reports the improved outcomes achieved after analyzing SPC charts. This article is targeted between these 2 positions: it reviews the SPC technique and presents a tool and data so readers can construct SPC charts. After tackling the case, it is hoped that the readers will collect their own data and apply the same technique to improve processes in their own organization.

• Data Interpretation, Statistical*
• Diffusion of Innovation*
• Efficiency, Organizational* / statistics & numerical data
• Health Facilities
• Outcome and Process Assessment, Health Care / methods*
• Outcome and Process Assessment, Health Care / statistics & numerical data
• Total Quality Management / methods
• Total Quality Management / statistics & numerical data*
• United States

A practical application of statistical process control to evaluate the performance rate of academic programmes: implications and suggestions

Quality Assurance in Education

ISSN : 0968-4883

Article publication date: 22 August 2022

Issue publication date: 28 September 2022

This study aims to properly and objectively assess the students’ study progress in bachelor programmes by applying statistical process control (SPC). Specifically, the authors focused their analysis on the variation in performance rates in business studies courses taught at a Spanish University.

Design/methodology/approach

A qualitative methodology was used, using an action-based case study developed in a public university. Previous research and theoretical issues related to quality indicators of the training programmes were discussed, followed by the application of SPC to assess these outputs.

The evaluation of the performance rate of the courses that comprised the training programs through the SPC revealed significant differences with respect to the evaluations obtained through traditional evaluation procedures. Similarly, the results show differences in the control parameters (central line and control interval), depending on the adopted approach (by programmes, by academic year and by department).

Research limitations/implications

This study has inherent limitations linked to both the methodology and selection of data sources.

Practical implications

The SPC approach provides a framework to properly and objectively assess the quality indicators involved in quality assurance processes in higher education.

Originality/value

This paper contributes to the discourse on the importance of a robust and effective assessment of quality indicators of the academic curriculum in the higher education context through the application of quality control tools such as SPC.

• Quality assurance
• Higher education
• Statistical process control
• Performance rate
• Evaluation process
• Academic programme

Gessa, A. , Marin, E. and Sancha, P. (2022), "A practical application of statistical process control to evaluate the performance rate of academic programmes: implications and suggestions", Quality Assurance in Education , Vol. 30 No. 4, pp. 571-588. https://doi.org/10.1108/QAE-03-2022-0065

Emerald Publishing Limited

Copyright © 2022, Ana Gessa, Eyda Marin and Pilar Sancha.

Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial & non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode

Introduction

The need to advance the modernisation of universities is a key element in developing a knowledge-based society and a more competitive economy. In this context, it is not surprising that quality assurance, has become one of the cornerstones for policy and decision makers in higher education institutions in the European Higher Education Area (EHEA) ( Curaj et al. , 2015 ).

Quality assurance in higher education has two primary functions. First, it establishes the legitimacy of an institution and the academic programmes it offers. Second, it informs the institutions’ stakeholders about program objectives and outcomes and the fulfilment of the expected quality standards ( Kinser, 2014 ).

In the European Union, national accreditation and quality assurance agencies play a key role, as they are in charge of quality management through evaluation, certification and accreditation of programmes, professors and universities. They design different programmes to guarantee internal and external quality, following the Standards and Guidelines for Quality Assurance in the EHEA (ESG), adopted by the European Association for Quality Assurance in Higher Education (ENQA) (2015) .

Under ENQA’s umbrella, universities apply procedures that facilitate both the improvement of the quality of their degrees and the external evaluation processes conducted by the corresponding competent institutions. In this sense, the indicators used for the evaluation of the academic curriculum performance constitute a key element for accountability and transparency.

Despite the experience accumulated over more than a decade in university degree programme evaluation processes, criticisms of approaches to definition and to operationalisation is recurrent in the literature ( Hanna et al. , 2012 ; Strang et al. , 2016 ). The main concerns across agencies relate, among others, to the consolidation of good practices and appropriate statistical principles when evaluating and analysing performance indicators.

subjectivity about what should be considered excellent, acceptable, or insufficient prevails in the analysis;

the lack of approaches that consider the context of universities, faculties, departments and even courses;

the ignorance of uncontrollable factors that underline the inherent variability in the educational processes; and

more importantly – the extended practice of comparing performance with averages or the use of arbitrary cut-off numbers without taking into consideration that educational processes have an inherent variability ( Bi, 2018 ).

An alternative approach to overcome these shortcomings and remove the barriers is the application of statistical process control (SPC), something which has been widely and successfully used for decades in the manufacturing industry, and later more slowly introduced in the service sector, in general and in the educative sector in particular ( MacCarthy and Wasusri, 2002 ; Sulek, 2004 ; Suman and Prajapati, 2018 ; Utley and May, 2009 ; Yang et al. , 2012 ). Contrary to the classical statistical methods that are developed for fixed populations and not for processes, SPC can be very effective in detecting process shifts and the dynamics of the process itself. Moreover, it enables hidden problems to be revealed therefore indicating the actions necessary for continuous improvement.

In any process, a certain amount of inherent or natural variability will always exist due to the cumulative effect of unavoidable causes. These sources of variability are called “chance causes” ( Montgomery, 2009 ). SPC helps to assess the variability of the educational processes, distinguishing between assignable (inappropriate educational resources and methodology; ineffective curriculum, etc). and random (student profile, family context, etc). causes ( Daneshmandi et al. , 2020 ; Nikolaidis and Dimitriadis, 2014 ).

This work aims to contribute to understanding the usefulness of the application of SPC, in the processes of accreditation and monitoring of university degrees, through the analysis of the variability of the performance rate associated with the procedures that constitute the quality assurance system (QAS). Specifically, the authors focussed their analysis on the variation in performance rates in business studies taught at a Spanish University. Based on this goal, the following research question is suggested: Are there any significant differences between the results obtained with a standard statistical analysis and the results obtained through the SPC application?

For this purpose, the next section outlines the theoretical framework of this study. Subsequently, the paper presents the methodology and results. The last section discusses the conclusions.

Theoretical framework

Quality assurance in spanish higher education systems.

Quality assurance has become one of the key issues for higher education systems (HES) around the world. The changes that have arisen in the European education area have forced university institutions to adopt new management models, with a priority being to guarantee the quality of the studies, as a contributing factor to the development of the economy and society [Red Iberoamericana para la Acreditación de la Calidad de la Educación Superior (RIACES), 2007]. The comparability and recognition of degrees from the perspective of quality management, strengthened by evaluation and assurance mechanisms and quality of higher education qualifications and certifications, has undoubtedly made the EHEA possible. The key instrument to make it possible was the ESG [ European Association for Quality Assurance in Higher Education (ENQA), 2015 ]. Specifically:

[…] they set a common framework for quality assurance systems for learning and teaching at European, national and institutional level; they enable the assurance and improvement of the quality of higher education in the EHEA; they support mutual trust, thus facilitating recognition and mobility within and across national borders; and they provide information on quality assurance in the EHEA [ European Association for Quality Assurance in Higher Education (ENQA), 2015 , p. 7].

“Higher education institutions have primary responsibility for the quality of their provision and its assurance;

quality assurance responds to the diversity of HES, institutions, programmes and students;

quality assurance supports the development of a quality of culture; and

quality assurance takes into account the needs and expectations of students, and other stakeholders and society” [ European Association for Quality Assurance in Higher Education (ENQA), 2015 , p. 8].

European agencies vary in their approaches to the implementation and adaptation of the ESG ( Alzafari and Ursin, 2019 ; Kohoutek et al. , 2018 ; Nascimbeni, 2015 ; Manatos and Huisman, 2020 ). In Spain, the National Agency for Quality Assessment and Accreditation (ANECA) has developed a set of programmes to conduct its activities of evaluation, certification and accreditation of teaching staff, universities and degrees ( Table 1 ). These programmes constitute a framework that makes it easier for universities to implement their internal QAS as well as the external evaluation processes conducted by the responsible regional agencies and universities.

performance rate in the qualification;

dropout rate;

efficiency rate; and

graduation rate.

The reports also include global data regarding the qualification and an analysis of the adequacy of the evolution of the indicators and their consistency with the target established in the qualification verification report.

The usual practice of universities and evaluation agencies when analysing these indicators is limited to the application of conventional descriptive statistics methods that involves the analysis of variation through measures such as mean, standard deviation, median etc. As a result, the analysis seems subjective, decontextualized and unsound, as it focusses on the evaluation of the outcomes of the educational processes and their comparison with outdated fixed reference values ( Andreani et al. , 2020 ; Klasik and Hutt, 2019 ). Therefore, this practice does not enable us to identify whether the process is under control and if it is not, to identify if this status is due to causes attributable to the processes themselves or to random causes, depending, in turn, on factors such as the branch of study, the type of centre, the university and the region ( Bi, 2018 ; Hanna et al. , 2012 ; Kember and Leung, 2011 ). An alternative practice to overcome this limitation could be the application of SPC charts, which have become a useful tool with which to achieve stability and improvement in the quality of educational service delivery by monitoring certain variables or attributes over time, such as the previously mentioned performance indicators. The application of SPC in an educational context is already a reality, and it is increasing, as shown in the next section. This will allow the progressive implementation of typical practices of quality management in the field of education, within the general framework of the continuous improvement of processes.

Statistical control of processes in education services

SPC allows the identification of different sources of variation and also enables detection of an “out of control” status ( Besterfield, 1995 ; Shewhart, 1936 ). A control chart “shows the value of the quality characteristics of interest as a function of time or sample number” ( Montgomery, 2009 ). Thus, the variability of a quality characteristic should be based on output, which involves estimating its statistical distribution and parameters ( Juran and Gryna, 1988 ).

The standard control chart shows a central line (CL), which is the mean of the variable being monitored, the upper control limit (UCL) and the lower control limit (LCL), which are typically set at  ± 3 standard deviations of the CL and its graphic representation is shown in Figure 1 .

When a plot violates a control limit, which is when some of the plot points fall outside the three-sigma limits (Zone B), it should be treated as a special cause of variation, attributable to the system. If special causes are present, it is said that the process is out of control. The zone between the UCL and the LCL (Zone A) shows the expected normal (common cause) plot point variation. Unlike special causes of variability, common causes are also called “natural” or “random variability” and are due to a large number of small sources of variation that are not easily identifiable. If assignable or special causes of variation are removed, characteristic parameters such as the mean, standard deviation and probability distribution are constant and process behaviour is predictable; the system is said to be “in a state of statistical control” or simply “under control”. However, certain abnormal patterns (trends, sudden shifts, systematic variation, cycles and mixtures) may alert one to the existence of special causes.

There are a great variety of quality control charts, depending on the type of quality characteristic to control (variable or attributes) and the number of variables to control (univariate or multivariate) ( Montgomery, 2009 ).

controlling student achievement;

monitoring the effectiveness of the teaching–learning process;

evaluating student satisfaction; and

identification abnormal patterns in certain educational processes.

Statistical process control charts to control students’ achievements

Objective and quantitative measures such as examination scores or grade point averages (GPAs) to monitor learning performance have been used to conduct numerous studies, under different approaches and educational levels. Thus, for example, Schafer et al. (2011) , in their work, used traditional Shewhart X-R charts to follow the performance of primary and secondary students in large-scale assessment programmes. In a similar way, Bakir and McNeal (2010) and Bakir et al. (2015) designed a non-parametric control chart based on the sign statistic to detect statistically significant shifts in students’ GPAs from a desired level. Milosavljevic et al. (2018) used attribute charts from the perspective of the number of passing exams. Other studies following a similar framework include Peterson (2015) , Zolkepley et al. (2018) , Hrynkevych (2017) , Aldowaisan and Allahverdi (2016) , Mazumder (2014) , Djauhari et al. (2017) , Cervetti et al. (2012) and Hanna et al. (2012) .

SPC charts have also been applied to monitor the consistency of scale scores or ratings over time. Lee and von Davier (2013) used cumulative sum charts (CUSUM) in a study conducted with data from 72 countries to detect changes in a measurement process of rating performance items in operational assessments. Omar (2010) proposed X-S charts to monitor the consistency of the scores in a co-assessment process. SPC charts that have also been applied in similar frameworks are Beshah (2012) , Edwards et al. (2007) and Savic (2006) .

Monitoring the effectiveness of the teaching–learning process

Another line of research aims to measure both teachers’ contributions to increasing student knowledge and student’s learning outcomes. The technique usually applied for this purpose consists of administering to students, prior to a lecture, a test known as the Background Knowledge Probe (BKP), which contains questions about concepts covered during the lecture, and after the lecture students have to answer the same questions. Rather than grading the students’ outcomes, the BKP should be understood as a resource to measure student’s gain. This would enable an improvement in the teaching programmes by virtue of detecting the student’s mistakes and gaps in knowledge transfer. Thus, Green et al. (2012) used traditional mean graphics (Graph X), whereas Agrawal and Khan (2008) , Grygoryev and Karapetrovic (2005a , 2005b ), Karapetrovic and Rajamani (1998) and Pierre and Mathios (1995) used graphics of non-conformity attributes ( p graphics).

Evaluating students’ satisfaction

SPC chart techniques have also been used to monitor and evaluate the level of student satisfaction regarding the quality of faculty members’ teaching and university service operation. Thus, Jensen and Markland (1996) published one of the first studies in this field, reporting the use of a Hotelling’s T multivariate control chart to detect shifts in satisfactory and unsatisfactory perceptions of computer services at a large university institution. Debnath and Shankar (2014) proposed the use of attribute control charts ( c -charts and u -charts) to evaluate the level of student satisfaction with their academic process. In their study, students were asked to provide information about various parameters, such as the grievance-handling process with respect to students’ admissions and results, facilities, practical orientation process.

On the other hand, it is worth mentioning works that, under the controversial field of Student Evaluation of Instruction, are addressed from the perspective of SPC, bringing a new approach that focusses not on educational outputs and outcomes, but on the quality of the underlying educational processes. Bi (2018) and Nikolaidis and Dimitriadis (2014) used X-S charts; Cadden et al. (2008) and Marks and O'Connel (2003) used X charts; Manguad (2006) , proposed the use of X-R charts; Ding et al. (2006) and Carlucci et al. (2019) applied attributes control chart ( p and u charts, respectively). Finally, Sivena and Nikolaidis (2019) through simulation, evaluate several popular types of control charts, identifying the most suitable among them.

Identification of abnormal patterns in certain educational processes

Another segment of this body of research has looked at the use of CUSUM charts to detect known items and outliers in computer adaptive testing ( Meijer, 2002 ; Veerkamp and Glas, 2000 ). This instrument allows the level of acquisition of different skills (linguistic, professional accreditations, etc). to be detected in the context of item response theory.

Given the aforementioned considerations, three facts have motivated this research. First, the existence of inadequate statistical approaches that university institutions have traditionally used to assess certain outcomes of educational processes. Second, the potential of SPC to assess different quality characteristics for higher education institutions has been demonstrated in the literature review. Third, the authors of this paper are active members of the Board for the Monitoring and Accreditation of Qualifications at a business faculty at a Spanish University. Moreover, some of the authors teach courses related to quality management. They share the aforementioned concerns and for the sake of “practice as they preach”, they advocate that some successfully industrial quality management techniques such as SPC which is occasionally taught in their courses, should be incorporated to assess and analyse the variation related to educative performance indicators. This application would improve the assessment of the quality of educative processes so that root causes can be detected and corrective actions can be taken by those who supervise instruction Hanna et al. (2012) .

Materials and method

Research context.

The study was conducted at the Faculty of Business Sciences and Tourism (FBST) of the University of Huelva (Spain). The FBST offers three bachelor’s programmes: Bachelor in Business Management (BM), Bachelor in Finance and Accounting (F&A) and Bachelor in Tourism. Table 2 shows the main characteristics of the study context.

Design of the study

The method adopted for this study is the action-based case study approach conducted at FBST. Previous research and theoretical issues related to SPC implementation and quality indicators of the training programmes proposed in Protocol for the Monitoring and Renewal of the Accreditation for Official University Qualifications were discussed. Then the authors built a conceptual framework that provided a step-by-step approach to SPC implementation as illustrated in Figure 2 .

In this first approach applying the SPC to assess the variability of progress indicators, we only focus on the performance rate.

Applied at course level and by academic year, the performance is indicated by relationship in the total number of ordinary credits passed by the students in a particular academic year and the total number of ordinary credits in which they are enrolled [ University Commission for the Regulation of Monitoring and Accreditation (UCRMA), 2010 ].

This rate provides a snapshot of the proportion of students passing a course in an academic year. Analysis of this rate, with the help of SPC charts, helps to identify root causes such as unmotivated students to further take actions such as monitoring the enrolment process.

For this purpose, the performance rates of the courses taught at the FBST of the University of Huelva between the years 2014 and 2020 were collected from reports on the QAS of the FBST.

To avoid skewing the results, the last academic year of the degrees was excluded from the study due to the type of courses taught. It included elective courses and credits given to students for the completion of curricular internships and the final degree project.

Applying statistical process control

To apply SPC, we followed a standard set of guidelines for setting up an SPC charting scheme, illustrated in Figure 2 .

As our main goal was to monitor the effectiveness of undergraduate academic programmes at faculty level, we chose an X-R chart and the quality characteristic to control was the performance rate of the courses in a given academic year for each programme taught at the FBST As already mentioned, to draw an X-R chart, it was necessary to calculate the CL, UCL and LCL ( Table 3 ).

To achieve the proposed goal, we used Minitab 17 statistical software.

Results and discussion

Bearing in mind the inherent variability of the educational processes, we are able to identify: first, courses that fall below the LCL underperform (Zone B, Figure 1 ), i.e. the percentage of students who passed the course was worryingly low. Second, courses that fall above the UCL (Zone B, Figure 1 ) indicate that the percentage of students who passed the course was extraordinarily high. Finally, courses that fall within the three-sigma limits had more stable performances, meaning that only common causes explain the variability presented between the control limits (Zone A, Figure 1 ).

In this work, several sets of X-R graphs are presented in which the parameters were calculated by programme, by academic year in which the courses were taught and by department. They were completed with a comparative analysis.

Control by academic programme

In Figure 3 , we provide the results of X-bar charts that plot the variability of the performance rate of the courses for the years 2014–2020, for each of the three programmes analysed, considering the courses within the programme grouped by academic year.

The graphs show similar behaviours for the BM and F&A programmes, with a similar under control performance average (60.54% and 59.49%, respectively). In addition, by academic year, the courses with a low performance rate, e.g. below the lower control limits, were concentrated in the first year and those with a high performance rate, e.g. above the LCS, were concentrated in the third year. The performance rates of the second-year courses are considered to be normal, as they were located within the control interval zone.

The performance rate of the courses within the Tourism Degree is 79.93%, which is substantially higher than the BM and F&A ratio. It is worth noting that the distance to the LCL of the out-of-control courses is much greater for the Degree in Tourism than for the BM and the F&A.

Rather than a particular high or low value for the performance rate, the wide range in the proportions observed between degrees and as shown in the graphs, evidences that while F&A show more stability in the proportion of students passing the courses, a worrying lack of stability is a common factor for B&M and Tourism.

This suggests that higher ratings are not necessarily better, and for this reason it is very important to contextualize the analysis. Because the correct application of X chart formulas requires that all performance ratings contribute to determining the three-sigma limits, the previous analysis lacks subjectivity when it categorizes performance ratings into three groups: high, normal and low.

Surprisingly, for the BM and the F&A, the means of the performance ratios calculated using the traditional approach are higher than those estimated applying SPC: 64.67 > 60.54 and 65.14 > 59.49, respectively. By contrast, the traditional mean of the Degree in Tourism (71.39), is lower than the mean calculated under statistic control (75.93) ( Table 2 ).

The differences pointed out above highlight the need to review the procedures for evaluating the results of the degree study programs, promoting methods such as SPC that allow a contextualized, robust and unbiased analysis.

However, it is important to bear in mind that the analysis could change if control chart parameters were calculated using the programme mean, the department mean or the programme year mean. Thus, to complement the SPC study, in the following sections we present the results according to academic year and department.

Control by academic year

Figure 4 shows the results of SPC application conducted independently for each of the academic years that make up each degree, and not in an aggregated form approach as in the previous section.

The results show differences in the control parameters (CL and control interval), depending on the programme itself and the academic year in which the courses were taught. As an example, the central values for the first year and the second year of BM and F&A were very similar (50.55% and 51.84%; 58.81% and 57.98%, respectively). However, these values increased significantly for courses taught in the third year and differed considerably between programmes (BM 79.19%, F&A 67.72%) ( Figure 4 ). Notably, the three programmes present an overall upward trend in the under control performance rate associated with the sequence of the courses within a structured curricular of the program and the wide range in the academic year to year performance ratio observed ( Table 4 ). This finding is consistent with the results of Hanna et al. (2012) who found a similar trend in a study of the proportion of students passing the class analysed by course and using p -charts. Taken together, these findings would suggest the need to identify the root causes of this trend such as the necessity to revise admission standards. Regarding possible reasons behind the high performance ratios values of the courses located in the second and third academic year of the program we suggest three possibilities. First, it is possible that the faculty and the administration were aware of the presence of special reasons behind the variation and responded by improving teaching strategies. Second, it is also possible that those students lacking motivation and ability were filtered out and did not pass to the subsequent academic year, thereby increasing student performance for higher courses. Third, a low performance rate in the first academic year coupled with a high dropout rate would have had the effect of lowering the standards for the high level courses.

Under this independent analysis, the results also show that the courses taught in the second year of BM and F&A were under statistical control as they were in the aggregate analysis, but with a lower average performance rate (58.81 and 57.98% versus 60.54 and 59.49% of BM and F&A, respectively). Surprisingly, for the courses that were out of control in BM and F&A, those of the first year were above the UCL limit, whereas for the third year, they were located below the LCL in clear contrast to what occurred in the aggregate analysis of the programme described in the previous section. In the case of the tourism degree, the courses outside the control interval were mainly concentrated in the last year, unlike the results obtained in the joint analysis, which were concentrated in the other years. In general, a progressive increase in the value of the CL (under control) of the performance rate was observed, to the extent that the courses were taught in higher academic years. This year-by-year contextualized analysis applying SPC demonstrates the usefulness of this approach by revealing hidden problems that affect variability, such as the profile of students who enrol in a degree for the first time or how students adapt to their university studies over time.

Finally, the use of the three-sigma limits also shows important differences with the results of the traditional evaluation (mean of the academic program) ( Table 4 ). This reinforces the argument previously made in the analysis by academic programs with SPC.

Control by department

Bearing in mind that the courses taught in the different degrees were assigned to different departments, in this section, we present the CL for the courses, grouping them by departments with the highest teaching load for each degree. Table 5 shows the results.

These new parameters imply changes with respect to those obtained in the previous applications. For example, courses which in the control graph built by the programme were under control, were out of control with this new parameterisation and vice versa. Figure 5 shows differences of under control means (CL) between the two departments with the highest teaching load allocation for each degree.

As a summary of the results, and for comparative purposes, Figure 6 shows the performance under control of the courses, grouped by program, academic year and department, comparing them in turn with the mean performance rate, which was precisely the one traditionally used to monitor the performance rate.

Conclusions

The results of this study show significant differences in the analysis of the variability of the performance rate between the scenarios described (degree, year and department), depending on the reference parameters (CL, UCL, LCL), focussing the analyses on the process itself rather than the result.

Similarly, in the analysis of the variability of the processes, the SPC approach does not only allow hidden problems to be revealed and their causes to be determined so that corrective actions can be taken to reduce oscillations and therefore improve the stability of the educational processes. Once SPC has been incorporated as an assessment tool to measure the variation relating to academic performance ratios, better information would be available to establish more suitable target goals.

The main conclusion of this study is that the traditional analysis which compares performance ratings with means of the degrees or arbitrary cut-off numbers overlooks the inherent variability of the educative processes. In addition to being useless for comparative purposes, this traditional approach lacks the objectivity and robustness necessary for its application in decision-making, in the accreditation and monitoring processes in which this work is framed.

By contrast, SPC allows a contextualized, robust and unbiased analysis of the variability of quality indicators involved in the accreditation and monitoring processes, providing valuable information for decision making to administrators, teachers and other stakeholders in HE.

This study is a first approach to SPC application for monitoring the control indicators proposed in the ESG [ European Association for Quality Assurance in Higher Education (ENQA), 2015 ]. However, the results are focussed on the analysis of just three programmes in a Spanish University, and thus should be interpreted with caution. In future studies, we will explore the application of multivariable charts and capability analysis, the inclusion of other programmes and time horizons, thereby widening the scope of this study.

Conventional control chart for monitoring the variability of a process

Application of the SPC in the scope of the study

Control results by academic programmes (2014–2020)

Control results by academic year

Results by departments (CL)

Comparative analysis related to performance rate

Evaluation programmes of Spanish University

Control parameters by departments

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Further reading

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Minitab Inc ( 2014 ), Minitab Statistical Software Version 17 , Minitab Inc. , State College, PA , available at: www.minitab.com

Acknowledgements

Funding : This study was supported by the University of Huelva (Spain) – Andalusia Consortium (CBUA).

Corresponding author

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Quality America Inc.

SPC defined

Control Chart Properties

Rational Subgroups

Distributions

Defining Control Limits

Short Run Techniques

Interpretation & Calculations

Attributes Charts

Pareto Charts

X-Bar / Range Charts

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SPC to Improve Quality, Reduce Cost

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Use Of SPC To Detect Process Manipulation

Using Data Mining and Knowledge Discovery With SPC

Case Study: SPC to Improve Quality and Reduce Cost

One company that has been able to improve quality and reduce costs through the use of a computer based Statistical Process Control (SPC) software pro duct is Green Bay Packaging Inc. The Green Bay Packaging Inc. plant in Tulsa, Oklahoma, a corrugated shipping container manufacturer, has been using SPC for years. Recently, customers are requesting statistical reports to be forwarded to them in an ongoin g and timely manner. Initially, they responded by using handwritten control charts. This took additional time to perform and was a drain on their resources. It also did not allow them to perform alternate data analysis in a cost effective or timely basis.

G reen Bay Packaging Inc. quickly saw the need for SPC software and chose SPC-PC IV from Quality America, Inc. They found the product to have all the charting tools they needed as well as the flexibility and ease of use their employees demanded. SPC-PC IV i s now used in many divisions of the company. Not only are manufacturing plants utilizing the product, but the corporate quality staff uses SPC-PC IV to analyze monthly reports sent electronically by several divisions.

Green Bay Packaging Inc. then went one step further with SPC-PC IV and utilized its Real Time Gage Module to accept readings directly from gages. Prior to using the Real Time Module, they were recording measurements manually. They realized that this process can lead to a higher possibility of e rrors in reading the measurement from the gage, transcribing the measurements to paper, and entering the data into a computer. Besides reducing the possibility of errors, Green Bay Packaging Inc. main goal in reading measurements in real time was to provi d e immediate analysis and reduce data entry time.

They found that by using SPC-PC IV in real time they are now able to quickly and efficiently analyze the data using different tools. Green Bay Packaging Inc. is able to visualize the data in the form of hist ograms, something that they were unable to do consistently through their manual process. In addition, ability of SPC-PC IV to display their specification limits directly onto a histogram allows them to easily visualize their process in relation to specific ations. Green Bay Packaging also stores assignable causes directly in the software to perform Pareto analysis to determine what areas of their process they need to focus on. This is something that was extremely difficult to do with paper records.

Through t he use of SPC-PC IV, Green Bay Packaging has been able to monitor their process more effectively. This has lead to reductions in process variability, scrap material, and costs.

Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller , in his online SPC Concepts short course (only $39 ), or his online SPC certification course ( $350 ) or online Green Belt certification course ( $499 ).

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