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

摘要

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