Multi-Objective Genetic Algorithm for Economic Statistical Design of the T~2 Control Chart with Variable Sample Size: The Updated Markov Chain Approach

摘要

T~2 control charts are used to primarily monitor the mean vector of quality characteristics of a process. Recent studies have shown that using variable sample size (VSS) schemes results in charts with more statistical power for detecting small to moderate shifts in the process mean vector. In this study, we have presented a multiple-objective economic statistical design of VSS T~2 control chart with the adjusted average time to signal (AATS) as the statistical objective and the expected cost per hour as the economic objective. Then a multi-objective genetic algorithm for economic statistical design is proposed for identifying the Pareto optimal solutions of control chart design. Through an illustrative example, the advantages of the proposed approach are shown by providing a list of viable optimal solutions and graphical representations, which indicate the advantage of flexibility and adaptability of our approach.