A head-to-head comparative study of the conditional performance of control charts based on estimated parameters

Abstract

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A head-to-head comparison of the out-of-control performance of control charts adjusted for parameter estimation

“…We denote the Phase II mean as l ¼ l 0 þ dr 0 : Note that d ¼ 0 corresponds to the in-control situation. This setup is similar to that of the one used in the comparison papers of Hawkins and Wu (2014) and Zwetsloot and Woodall (2017).…”

“…We refer to Jensen et al (2006) and Psarakis, Vyniou, and Castagliola (2014) for literature reviews on this topic. Zwetsloot and Woodall (2017) perform a comparative study on the conditional performance of the Shewhart, CUSUM, and EWMA control charts, where they compare the effect of estimation error across these charts. They conclude that the Shewhart chart is most affected by estimation error, and that the EWMA and CUSUM charts behave quite differently when evaluated on conditional performance.…”

Control charts for paired differences: and Sd charts

“…We used the pairwise chart comparison procedure for in‐control ARLs when the parameters are estimated from small samples given by Zwetsloot & Woodall, p 10. This comparison allows evaluation of chart performance as equal, better, and eventually worse as compared to the in‐control ARL.…”

“…This comparison allows evaluation of chart performance as equal, better, and eventually worse as compared to the in‐control ARL. We restate the definition from Zwetsloot & Woodall using our notation. Let us consider the set of unknown parameters for difference charts and their alternatives as , be the in‐control ARLs of control chart C 1 and be the in‐control ARLs of control chart C 2 .…”

Phase II monitoring of multivariate simple linear profiles with estimated parameters

“…There are many studies in which the effect of parameter estimation on the performance of control charts is estimated for quality characteristics except profiles, including Burroughs et al (1993), Chen (1997), Chakraborti (2000), Zeinal Hamadani (2009), Shishebori et al (2015), Jones et al (2001Jones et al ( , 2004, Shu et al (2004), Jones (2002), Zhang and Chen (2002), Zwetsloot and Woodall (2017), Khoo (2005), Castagliola et al (2016), Saleh et al (2015). For information on more research on this area, see the following review papers: Jensen et al (2006) and Psarakis et al (2014).…”