Title
Design of variance control charts with estimated parameters: A head to head comparison between two perspectives
Date Issued
01 January 2022
Access level
metadata only access
Resource Type
journal article
Author(s)
Jardim F.S.
Chakraborti S.
Epprecht E.K.
Publisher(s)
Taylor and Francis Ltd.
Abstract
Since parameter estimation degrades chart performance, it is important to design a control chart correctly, that is, taking account of the estimation effects. To this end, two perspectives are available in the literature: the unconditional, which focuses on the unconditional in-control (IC) average run length ((Formula presented.)), and the conditional, which focuses on the IC run-length distribution conditioned on the parameter estimates and the exceedance probability criterion (EPC). Much of the literature on this topic is in the context of monitoring the mean. However, monitoring the variance is important in the larger monitoring context, not only per se, but also because a reliable and stable estimate of the process variance is required in the first place for setting up the control chart for the mean. With this in mind, and given that a recent paper studied the design of the (Formula presented.) chart, here we consider the S 2 chart and examine the effects of each perspective on the design and IC performance. To this end, we first compare the required number of Phase I samples and the control limit adjustments in two cases: the upper one-sided chart and the equal-tailed two-sided chart. Second, we examine the performance of each chart, designed according to one perspective, under the other perspective. Results show major differences in the impact and consequences of the adopted chart design perspective on chart performance. An illustration with a real dataset is provided. Finally, an overall summary and some conclusions are presented.
Start page
249
End page
268
Volume
54
Issue
3
Language
English
OCDE Knowledge area
Otras ingenierías y tecnologías Ingeniería, Tecnología
Scopus EID
2-s2.0-85096854351
Source
Journal of Quality Technology
ISSN of the container
00224065
Sponsor(s)
This work was financially supported by the Scientific Research Institute (IDIC) of the University of Lima, Peru and in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brasil (CAPES) - Finance Code 001 for the first author, by CNPq (Brazilian Council for Scientific and Technological Development) through postdoctoral grant (number 153183/2018-7 for the second author) and project numbers 401523/2014-4 (for the third author) and 308677/2015-3 (for the fourth author). The authors are thankful to the anonymous reviewers and the Editor for their insightful comments and suggestions which have improved the paper.
Sources of information: Directorio de Producción Científica Scopus