Actually, stratification is a strategy that is used throughout the rest of the seven basic quality tools, and in the application of any other statistical technique in quality control. For example, it was stratification what we did when designing the check sheet to gather information by supplier. Stratification can also be applied to histograms, scatter plots, or Pareto charts. We will see in Chapter6 that stratified sampling is also a way to improve our estimations and predictions about the process. The seven basic quality tools is a topic covered by a number of authors, as it is an effective and easy to implement problem-solving technique, even being included in the Project Management Base of Knowledge (PMBoK) [20]. In this regard, most of the lists keep the six previous tools. However, some of them replace “stratification” by “run chart” or “flow chart.” A run chart is actually a simplified version of the control chart, where data points are plotted sequentially. Flow charts and similar diagrams such as process maps are in fact a previous-to-stratification step. Those problem-structuring tools allow to divide the process into steps or sub-processes, and identify the different factors that could influence the output, thereby defining the groups in which perform the stratified analysis. A detailed explanation of process maps and how to get them with R can be found in [3].
3.9
ISO Standards for the Seven Basic Quality Control Tools
The cause-and-effect diagram is one of the tools in the Six Sigma quality improvement methodology. There is a subcommittee devoted to this methodology within the ISO/TC 69 that has developed the ISO 13053 Series, Quantitative methods in process improvement – Six Sigma. According to part 1 of ISO 13053, DMAIC methodology [17], the cause-and-effect diagram should be one of the
Fig. 3.16 Stratified box plots. Box plots by groups provide quick insights about the differences between groups, regarding both central tendency and variability
A B C 10.6 10.7 10.8 10.9 11.0 11.1
Box plots by supplier
Supplier
Density (
g
cm
outputs in the Analyze phase of the DMAIC5 methodology. In this part, the cause- and-effect diagram is also included in the typical training agendas for both SixSigma black belts and green belts, see [2] for a brief introduction on the Six Sigma methodology. On the other hand, in part 2 of ISO 13053, Tools and techniques [18], a complete factsheet for the tool can be found, pointing to [6] as a key reference. This standard relates the cause-and-effect diagram with the brainstorming tool as a possible input. On the other hand, ISO/IEC 31010 [7], Risk management – Risk assessment techniques, includes the cause-and-effect diagram as one of the tools to be used in root cause analysis (RCA), as well as in the cause-and-effect analysis, both of them being part of the risk assessment techniques covered by that standard. Regarding check sheets, they should be part of the Data collection plan, also included in ISO 13053-2 [18] as a DMAIC methodology tool. You could also check clause 7 (data collection) of ISO/IEC 19795-1 [8]. Pareto charts and Pareto analysis are also included as Six Sigma tools in ISO 13053 series.
Histograms are defined in ISO 3534-1 [9], Statistics – Vocabulary and symbols – Part 1: General statistical terms and terms used in probability. This standard “defines general statistical terms and terms used in probability which may be used in the drafting of other International Standards. In addition, it defines symbols for a limited number of those terms”.
There is a series of standards for control charts, developed by ISO/TC 69 SC 4. The following parts have been already published at the time this is written6: • ISO 7870-1:2014 [15], Control charts – Part 1: General guidelines. It presents
key elements and philosophy of the control chart approach;
• ISO 7870-2:2013 [14], Control charts – Part 2: Shewhart control charts. It is a guide to the use and understanding of the Shewhart control chart approach to processes’ statistical control;
• ISO 7870-3:2012 [13], Control charts – Part 3: Acceptance control charts. This part gives guidance on the uses of acceptance control charts and establishes general procedures for determining sample sizes, action limits and decision criteria;
• ISO 7870-4:2011 [12], Control charts – Part 4: Cumulative sum charts. This part provides statistical procedures for setting up cumulative sum (cusum) schemes for process and quality control using variables (measured) and attribute data; • ISO 7870-5:2014 [16], Control charts – Part 5: Specialized control charts.
Specialized control charts should be used in situations where commonly used Shewhart control chart approach to the methods of statistical control of a process may either be not applicable or less efficient in detecting unnatural patterns of variation of the process;
5Define, Measure, Analyze, Improve, and Control.
References 117
Part 6 of the 7870 series is in preparation for Exponentially Weighted Moving Average (EWMA) control charts, which will be likely already published when you are reading this chapter.7
Stratification is defined in ISO 3534-1 [9], and then this definition is used in other ones to bound the use of some techniques such as sampling, e.g. in ISO 3534-4, Survey Sampling [10]. As a crossing topic, stratification can also appear in different ISO standards to apply in other tools and techniques. For example, in ISO 13053-2 [18], stratified data collection is needed, and descriptive statistics visualization may involve stratifying by levels of a factor.
Finally, ISO 11462-2 [11] is a catalogue of tools and techniques for Statistical Process Control (SPC) that includes all the 7 basic quality control tools in such a catalogue. There you can find a short description, application, and references (including related ISO Standards).
References
1. Anhoej, J.: Qicharts: quality improvement charts, url http://CRAN.R-project.org/package= qicharts. R package version 0.2.0 (2015)
2. Cano, E.L., Moguerza, J.M., Redchuk, A.: Six sigma in a nutshell. In: Six Sigma with R, Use R!, vol. 36, pp. 3–13. Springer, New York (2012). doi:10.1007/978-1-4614-3652-2_1. urlhttp://dx.doi.org/10.1007/978-1-4614-3652-2_1
3. Cano, E.L., Moguerza, J.M., Redchuk, A.: Six sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York (2012). urlhttp://www.springer. com/statistics/book/978-1-4614-3651-5
4. Dahl, D.B.: Xtable: export tables to LaTeX or HTML, urlhttp://CRAN.R-project.org/package= xtable. R package version 1.7-4 (2014)
5. Ishikawa, K.: What is total quality control? The Japanese way. Prentice Hall Business Classics. Prentice-Hall, Englewood Cliffs (1985)
6. Ishikawa, K.: Guide to Quality Control. Asian Productivity Organisation, Tokyo (1991) 7. ISO: ISO/IEC 31010:2009, Risk management – Risk assessment techniques. International
standard (2010)
8. ISO: ISO/IEC 19795-1:2006, Information technology – Biometric performance testing and reporting – Part 1: Principles and framework. International standard (2016)
9. ISO TC69/SC1–Terminology and Symbols: ISO 3534-1:2006 - Statistics – Vocabulary and symbols – Part 1: General statistical terms and terms used in probability. Published standard (2010). urlhttp://www.iso.org/iso/catalogue_detail.htm?csnumber=40145
10. ISO TC69/SC1–Terminology and Symbols: ISO 3534-4:2014 - Statistics – Vocabulary and symbols – Part 4: Survey sampling. Published standard (2014). urlhttp://www.iso.org/iso/ catalogue_detail.htm?csnumber=56154
11. ISO TC69/SC4–Applications of statistical methods in process management: ISO 11462-1:2010 - Guidelines for implementation of statistical process control (SPC) – Part 2: Catalogue of tools and techniques. Published standard (2010). urlhttp://www.iso.org/iso/home/store/catalogue_ tc/catalogue_detail.htm?csnumber=42719
7At the time of writing, the development stage is Final Draft International Standard (FDIS), see Chapter4to find out more about standards development stages.
12. ISO TC69/SC4–Applications of statistical methods in process management: ISO 7870-4:2011 - Control charts – Part 4: Cumulative sum charts. Published standard (2011). urlhttp://www. iso.org/iso/catalogue_detail.htm?csnumber=40176
13. ISO TC69/SC4–Applications of statistical methods in process management: ISO 7870-3:2012 - Control charts – Part 3: Acceptance control charts. Published standard (2012). urlhttp://www. iso.org/iso/catalogue_detail.htm?csnumber=40175
14. ISO TC69/SC4–Applications of statistical methods in process management: ISO 7870-2:2013 - Control charts – Part 2: Shewhart control charts. Published standard (2013). urlhttp://www. iso.org/iso/catalogue_detail.htm?csnumber=40174
15. ISO TC69/SC4–Applications of statistical methods in process management: ISO 7870-1:2014 - Control charts – Part 1: General guidelines. Published standard (2014). urlhttp://www.iso. org/iso/catalogue_detail.htm?csnumber=62649
16. ISO TC69/SC4–Applications of statistical methods in process management: ISO 7870-5:2014 - Control charts – Part 5: Specialized control charts. Published standard (2014). urlhttp://www. iso.org/iso/catalogue_detail.htm?csnumber=40177
17. ISO TC69/SC7–Applications of statistical and related techniques for the implementation of Six Sigma: ISO 13053-1:2011 - Quantitative methods in process improvement – Six Sigma – Part 1: DMAIC methodology. Published standard (2011). urlhttp://www.iso.org/iso/catalogue_ detail.htm?csnumber=52901
18. ISO TC69/SC7–Applications of statistical and related techniques for the implementation of Six Sigma: ISO 13053-2:2011 - Quantitative methods in process improvement – Six Sigma – Part 2: Tools and techniques. Published standard (2011). urlhttp://www.iso.org/iso/catalogue_ detail.htm?csnumber=52902
19. Kume, H.: Statistical Methods for Quality Improvement. The Association for Overseas Technical Scholarships, Tokyo (1985)
20. PMI: A guide to the projet management body of knowledge. Project Management Institute (PMI), Newton Square (2013)
21. Roth, T.: Qualitytools: Statistics in Quality Science, url http://www.r-qualitytools.org. R package version 1.54 (2012)
22. Sarkar, D.: Lattice: Multivariate Data Visualization with R. Springer, New York (2008). urlhttp://lmdvr.r-forge.r-project.org. ISBN 978-0-387-75968-5
23. Scrucca, L.: Qcc: an R package for quality control charting and statistical process control. R News 4/1, 11–17 (2004). urlhttp://CRAN.R-project.org/doc/Rnews/
24. Wickham, H.: Ggplot2: Elegant Graphics for Data Analysis. Use R!. Springer, New York (2009)
Chapter 4
R and the ISO Standards for Quality Control
Abstract This chapter details the way ISO international standards for quality
control are developed. Quality Control starts with Quality, and standardization is crucial to deliver products and services where quality satisfies final users, whatever they are customers, organizations, or public bodies. The development process, carried out by Technical Committees (TCs), entails a kind of path until the standard is finally adopted, including several types of intermediate deliverables. The work of such TCs is outlined along with the general structure of ISO, and with a focus on the TC in charge of statistical methods. Finally, the current and potential role that R can play, not only as statistical software, but also as programming language, is shown.