Optimal inspection policy for three-state systems monitored by control charts

Abstract

This paper presents the formulations of the expected long-run cost per time unit for a system monitored by a static control chart and by an adaptive control chart respectively. The static chart has a fixed sampling interval and a fixed sample size. The adaptive chart has a fixed sample size but variable sampling intervals. The system is supposed to have three states, normal working state, failure delay time state, and failed state. Two levels of repair are used to maintain the system. A minor repair is used to restore the system if a detectable defect is confirmed by an inspection. A major repair will be performed if the system fails. The expected cost per time unit for maintaining such a system is obtained. The objective of such analysis is to find an optimal sampling policy for the inspection process. An artificially generated data example and a real data example are used to compare the expected cost per time unit for both the static and adaptive control charts.

Preventive replacement for systems with condition monitoring and additional manual inspections

“…However, in practice we have observed that there are mostly just one or two thresholds. A two-threshold policy defines a three-state process that was popularly accepted and used in CM practice and in most CM related literature (Christer & Wang 1995;Wu & Wang, 2011). This problem can be observed in reality, e.g., in induction furnaces, battery systems, motors, industrial pumps and bearings.…”

“…However, the inspection defined in Jiang's paper is the action used to obtain the accurate CM measurement rather than the manual inspection defined in our paper. Moreover, Wang (2011b) and Wu and Wang (2011) used a similar idea to ours when modeling two types of errors in statistical quality control.…”

An integrated model of statistical process control and maintenance based on the delayed monitoring

“…In their model, the time of shift to an out-of-control condition and the time of equipment failure are assumed to be two different random variables. Panagiotidou and Nenes [20] and Wu and Wang [21] improved the integrated model in terms of the monitoring method and they replaced the traditional static fixedparameter (Fp) Shewhart control chart by employing an adaptive variable-parameter (Vp) Shewhart control chart with PM to monitor process mean. Kuo [22] and Xiang [23] formulated the deterioration process as a discrete-time Markov chain and jointly optimized the integrated model of SPC and maintenance.…”

An integrated preventive maintenance and production planning model with sequence‐dependent setup costs and times

“…Delay‐time–based PM models differ from other PM models in that they directly model the relationship between PM and the number of system failures. Many case studies have shown the validity of such models …”