Economic design of X‐ control charts: insights on design variables

Abstract

Statistical process control charts have long been used as tools to ensure high quality of process output. A substantial amount of literature has been reported on the economic design of control charts by considering the trade‐offs between inspection cost, penalty for operating in out‐of‐control state, and the cost of restoring the process. However, the focus of this work has been on the development of solution procedures ‐ exact and approximate, to determine the design parameters and qualitative insights into their behaviour which are obtained by sensitivity analysis. In contrast, analyses an approximate cost function of the widely used X‐ control chart and develops results which characterize the behaviour of design parameters. Provides, through simplifying approximations, several interesting properties characterizing the design parameters. In addition to qualitative observations about the behaviours of design parameters, develops an efficient algorithm to compute optimal values of design parameters. Also discusses alternative quick heuristics to determine near optimal values of design parameters for practical use.