Design of exponential control charts using a sequential sampling scheme

Abstract

Control charts for monitoring the time between events can be applied in various areas. In this study, we focus on the exponential control chart and consider the phase II problem (when process parameters are known) as well as the phase I problem (when process parameters are unknown). An exponential chart designed with the conventional approach has the disadvantage that the Average Run Length (ARL) value may increase when the process deviates from the nominal state. An ARL-unbiased design approach is therefore proposed for both phase II and phase I exponential charts. A sequential sampling scheme is adopted for the phase I exponential chart. The proposed ARL-unbiased design approach has several advantages over the conventional one, as it provides a self-starting feature and can significantly improve the ARL performance. Specific guidelines are suggested regarding the time to stop updating the estimates of parameters and control limits based on the actual false alarm rate. The phase I exponential chart can be calibrated to a constant in-control ARL value for each successive event accumulated to date. Simulated and real data examples are given to demonstrate the use and efficiency of the proposed design approach.

A control chart for the Gamma distribution as a model of time between events

“…exponential random variables (Gan 1998). These control charts include the exponential chart (see Chan et al 2000, Jones and Champ 2002, Xie et al 2002, Zhang et al 2005, 2006, the exponential CUSUM chart (Lucas 1985, Gan 1994, Borror et al 2003) and the exponential EWMA chart (Gan 1998). In general, these control charts could be applied to monitoring the occurrence rate of any discrete event following the homogeneous Poisson process.…”

Design of exponential control charts based on average time to signal using a sequential sampling scheme

“…For this reason, TBE control charts are often called exponential control charts. Since Lucas (1985) and Vardeman and Ray (1985) first proposed the TBE control chart, many recent studies have focused on the TBE control chart, including the exponential chart (Chan, Xie, and Goh 2000;Chan et al 2002;Jones and Champ 2002;Xie, Goh, and Ranjan 2002;Zhang, Xie, and Goh 2005;Zhang, Xie, and Goh 2006;Zhang et al 2011;Dovoedo and Chakraborti 2012), the exponential CUSUM chart (Lucas 1985;Gan 1994;Borror, Kates, and Montgomery 2003;Cheng and Chen 2011;Qu et al 2013;Zhang, Megahed, and Woodall 2014) and the exponential EWMA chart (Gan 1998;Ozsan, Testik, and Wei 2010;Chen 2012).…”

Optimal design of a synthetic chart for monitoring process dispersion with unknown in-control variance

“…Time-between-event (TBE) control chart has been proved to be effective and efficient in monitoring high-yield process. For variable TBE charts, researchers developed exponential CUSUM chart (Lucas, 1985;Vardeman & Ray, 1985), exponential EWMA chart (Gan, 1998) and exponential chart (Xie, Goh, & Ranjan, 2002;Zhang, Xie, & Goh, 2006). And for attribute TBE charts, cumulative count of conforming (CCC) chart has been widely studied (Kuralmani, Xie, Goh, & Gan, 2002;Ranjan, Xie, & Goh, 2003;Xie, Goh, & Kuralmani, 2000).…”