CUSUM Schemes for Monitoring Prespecified Changes in Linear Profiles

Abstract

Because of the characteristics of a system or process, several prespecified changes may happen in some statistical process control applications. Thus, one possible and challenging problem in profile monitoring is detecting changes away from the ‘normal’ profile toward one of several prespecified ‘bad’ profiles. In this article, to monitor the prespecified changes in linear profiles, two two‐sided cumulative sum (CUSUM) schemes are proposed based on Student's t‐statistic, which use two separate statistics and a single statistic, respectively. Simulation results show that the CUSUM scheme with a single statistic uniformly outperforms that with two separate statistics. Besides, both CUSUM schemes perform better than alternative methods in detecting small shifts in prespecified changes, and become comparable on detecting moderate or large shifts when the number of observations in each profile is large. To overcome the weakness in the proposed CUSUM methods, two modified CUSUM schemes are developed using z‐statistic and studied when the in‐control parameters are estimated. Simulation results indicate that the modified CUSUM chart with a single charting statistic slightly outperforms that with two separate statistics in terms of the average run length and its standard deviation. Finally, illustrative examples indicate that the CUSUM schemes are effective. Copyright © 2016 John Wiley & Sons, Ltd.

A new Bayesian multivariate exponentially weighted moving average control chart for phase II monitoring of multivariate multiple linear profiles

“…The above simulations results, for both control charts (C_MEWMA and B_MEWMA), were obtained under the assumption that the true profile parameters (eg, B and Σ ε ) are known. This has been a common assumption in most of the related studies; see, for example, Abbas et al, [48][49][50] Eyvazian et al, 40 Kamranrad and Amiri, 14 Kazemzadeh et al, 15 Khedmati and Niaki, 16 Chiang et al, 17 and Zhang et al 18 Following those earlier works, we obtained only one UCL value for the classical approach (see Table 1). We then considered different values of m to monitor this effect on the detection performance of the Bayesian control chart.…”

“…The above simulations results, for both control charts (C_MEWMA and B_MEWMA), were obtained under the assumption that the true profile parameters (eg, B and Σ ε ) are known. This has been a common assumption in most of the related studies; see, for example, Abbas et al, Eyvazian et al, Kamranrad and Amiri, Kazemzadeh et al, Khedmati and Niaki, Chiang et al, and Zhang et al…”

“…. In our simulation study, we follow Eyvazian et al 40 and assume the covariance matrix Σ ε to be known from phase I, so that it stays fixed and does not have to be resampled from Equation 18. We propose the following Bayesian MEWMA (B_MEWMA) statistic:…”

“…Most studies that have been published in the literature focus either on phase I or on phase II. Kim et al, Zhang et al, Saghaei et al, Mahmoud et al, Noorossana and Zerehsaz, De Magalhães and Von Doellinger, Kamranrad and Amiri, Kazemzadeh et al, Khedmati and Niaki, Chiang et al, and Zhang et al investigated linear profile monitoring in phase II, whereas Mahmoud and Woodall, Mahmoud et al, Noghondarian and Ghobadi, Amiri and Moein, Yeh and Zerehsaz, Ghobadi et al, Riaz and Touqeer, and Taghipour et al focused on phase I linear profile monitoring. Methods for monitoring nonlinear profiles have been proposed by Vaghefi et al, Ding et al, Jin and Shi, Jensen and Birch, Walker and Wright, and Steiner et al For a more thorough review about profile monitoring approaches in phases I and II, we refer to the review paper by Woodall and the textbook edited by Noorossana et al An overview on recent profile monitoring papers (2008‐2018) based on a conceptual classification scheme has been done by Maleki et al…”

A Kullback‐Leibler information control chart for linear profiles monitoring

“…The assumption is widely used in Phase II process control. Related works include Kim et al, 6 Zou et al, 7 Saghaei et al, 8 Li and Wang, 9 Mahmoud et al, 10 Eyvazian et al, 11 Chen and Nembhard, 12 Mahmoud, 13 Xu et al, 14 Xu et al, 15 Aly et al, 16 and Zhang et al 17 Phase I process control for profiles monitoring was discussed in Ding et al, 18 Kazemzadeh et al, 19 and Paynabar et al 20 Integration of the Phase I estimation of profile parameters with Phase II monitoring is discussed in Zou et al 21 Ren et al 22 proposed an EWMA‐like scheme with principal component analysis to monitor multichannel profiles. The goal of these profile control charts is to detect abrupt changes in profile parameters as fast as possible.…”