Shewhart Control Chart: Long-Term Data Analysis Tool with High Development Capacity

*Vladimir Shper, Elena Khunuzidi, Svetlana Sheremetyeva and Vladimir Smelov*

*Useful application of control charts starts and ends with education*

 *Kaoru Ishikawa*

#### **Abstract**

This chapter suggests some of the ways in which we can enrich our understanding of the theory of variability when we extend our attention to a gap between the real problems any practitioner may encounter and the traditional theory of control charts stated in textbooks, guides, standards, etc. The benefits are about more than just covering additional ground, for this expanded focus also provides insights into how many real problems are being ignored, many new types of charts turn out to be excessively difficult for engineers, many tacit assumptions that traditional theory is based on stay not being understood by practitioners. We are going to consider the impact of different types of process instability, data homogeneity, nonnormality, and nonrandomness on the right application of Shewhart control charts. We also propose the recommendations to practitioners on how to avoid the above-mentioned problems and improve data-based decision-making.

**Keywords:** exploratory data analysis, shewhart control chart, process stability, assignable causes of variation, nonhomogeneity, nonrandomness, capability indices

#### **1. Introduction**

On 16 May 2024, the World will be celebrating the 100th anniversary of the Shewhart Control Chart (ShCC) – the most essential tool of process stability analysis used successfully in practically all areas of human activity. This 100-year-old tool of exploratory data analysis is described in many old and new books (see, e.g., [1–11], to name a few), and there are international standards devoted to control charting [12] as well as numerous sites on the Internet. On the other hand, most quality professionals, managers and engineers, CEOs, and even not a small amount of statisticians either are not familiar with this tool of data analysis or have just very superficial understanding of it [13]. Almost 30 years ago, R. Hoyer and W. Ellis claimed this thought in their

paper ([14], *63*) 1 in the following form: "… our experience indicated that a sizable majority of quality professionals are not knowledgeable about basic issues of statistics and Statistical Process Control (SPC). Our instructional activities in a broad range of academic, industrial, and service delivery environments have convinced us that there are many individuals who are "doing SPC" without understanding what it is about". Then they made a conclusion (*ibid*): "Although it is disappointing that the technical content of the quality improvement discipline has progressed so little during the past 65 years, that is probably not the most significant problem facing process control initiatives during the next decade. Instead, there is every reason to be concerned that many quality professionals are directing continuous process improvement activities without a sound understanding of the basic issues". We are sure that this situation has not changed notably since those times [13], but this chapter is devoted just to "the technical content of the quality improvement discipline". It is noteworthy that such prominent experts in Statistical Process Control (SPC) area as Lloyd Nelson and William Woodall argued emphatically [15] against the assertion of Hoyer and Ellis that "the technology of the quality science has been intellectually dormant for the past 65 years" ([16], *73*). The authors of [14] agreed with the experts that many interesting issues have been going on in the research journals devoted to quality improvement. "But, unfortunately, it appears to be primarily academics… and there are many realworld settings in which these results are only marginally useful" ([15], *93*). That is just what our paper is focused on. We will discuss several traditional assumptions that cover a minuscule part of reality and lead to many gaps between real process behavior and corresponding math models. Moreover, there are many practical questions that are not being discussed in the current literature at all, and have not been ever discussed in the past. In Section 2, we will give a brief survey of the problems that seem to be the most important to us. Then, Section 3 is devoted to the ambiguity in the notion of assignable causes of variation – one of the basic ideas of SPC. In Section 4, we will present our considerations on the data nonrandomness. Then, in Section 5, we will discuss the issues of highly skewed processes. Section 6 contains some examples revealing the limitation of current theory of ShCCs. Finally, in Section 7, we will share our concerns about the interaction between SPC and metrology, SPC and management. Our proposals for further research are given in conclusion.
