Optimal control limits for CCC charts in the presence of inspection errors

Abstract

The control chart based on cumulative count of conforming (CCC) items between the occurrence of two non-conforming ones, or the CCC chart, has been shown to be very useful for monitoring high-quality processes. However, as in the implementation of other Shewhart-type control charts, it is usually assumed that the inspection is free of error. This assumption may not be valid and this may have a significant impact on the interpretation of the control chart and the setting of control limits. This paper first investigates the effect of inspection errors and discusses the setting of control limits in such cases. Even if inspection errors are considered, the average time to alarm increases in the beginning when the process deteriorates. Since this is undesirable, the control limits in the presence of inspection errors should be set so as to maximize the average run length when the process is at the normal level. A procedure is presented for solving this problem.

Optimal assignment of resources to strengthen the weakest link in an uncertain environment

“…, X n } in order statistics when X i 's follow, respectively, the Bernoulli and standard power distributions (Balakrishnan and Nevzorov 2003). Similarly, E(R) * = 1 1−(1−p) n , E(R) * = nβ nβ−1 , and E(R) * = √ πα 2 √ n in Theorems 3, 4, and 5, Pin et al (2002) Nuclear power plant maintenance Tidström (2004) Analysis of voting behavior Degan (2004) (Standard) Power Supply chain coordination Cachon (2002) Financial engineering van Dorp and Kotz (2002) Labor economics Barlevy (2003) Geometric Healthcare industry Carnahan et al (2006) Housing market Huang and Palmquist (2001) Quality control charts Ranjan et al (2003) (Standard) Pareto Automobile insurance Cohen (2003) Marketing Research Miller and Liu (2006) Satellite communications Jiang and Leung (2003) Rayleigh Budget forecasting Lee et al (1997) Image Processing Kuruoglu and Zerubia (2004) Solar energy engineering Moriarty et al (2002) respectively, if the probability distributions of the same family share a common parameter. These, too, coincide with the respective expected values of X (1) = Min{X 1 , X 2 , .…”

A study of time‐between‐events control chart for the monitoring of regularly maintained systems

“…An inspection error may occur when either a system failure is classified as a non-failure or a nonfailure is classified as a system failure. Ranjan et al 26 show that even if inspection errors are present, the average time to signal an alarm, in terms of the ARL of a geometric chart increases in the beginning when the process deteriorates. They discuss an approach to set the control limits in order to maximize the ARL when the process is at the nominal level and inspection errors are present.…”

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

“…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). In fact, some researchers utilize the name of conforming run length (CRL) instead of the name of CCC, but they have the same statistical meaning.…”