ENBIS-16 in Sheffield

11 – 15 September 2016; Sheffield Abstract submission: 20 March – 4 July 2016

What Statistical Handbooks do not Teach about Shewhart Control Charts?

14 September 2016, 09:20 – 09:40

Abstract

Submitted by
Vladimir Shper
Authors
Vladimir Shper (Moscow Institute of Steel & Alloys), Yuri Adler (Moscow Institute of Steel & Alloys)
Abstract
In this paper we’d like to discuss some questions about the application of Shewhart Control Charts (ShCC) in real life. Such application is based on the information one gets out of ShCC. This information may be divided into two groups: about the values of the process under study and about the structure which these values elucidate. Which group of information is more important for right interpretation of ShCC – is the goal of our discussion. In fact we discuss the process of transmission from Phase I of preliminary analysis in order to design the control chart to Phase II of using the designed chart for process monitoring and improving. Our approach begs a simple but interesting question: does the order of statistics sampled from the process under study matter or not? Or another question closely connected with the advices given by many textbooks about comparative performance of different types of ShCC. Such comparison is often based on the simulation of real processes (for example, Average Run Length studies) so one may ask: when a statistician is simulating a process by taking random values from an appropriate distribution and neglecting the order of points - at what degree he/she may hope to get the copy close enough to the original? Our answer is obviously very predictable: it depends! But we are going to move further than that. Our paper discusses the conditions when it is reasonable to think that traditional way of designing a control chart is appropriate, and when the tacit assumption that the order of points does not matter is unrealistic. Examples from real processes and some results of simulations are presented as well.
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