OPTIMAL DESIGNS OF THE VARIABLE PARAMETERS X ̄ CHART WITH ESTIMATED PROCESS PARAMETERS - Yahaya, Masthura; Lim, Sok Li; Ibrahim, Adriana Irawati; Yeong, Wai Chung; Khaw, Khai Wah (International Journal of Industrial Engineering: Theory, Applications and Practice, 2021)
Among adaptive charts, the variable parameters chart shows the best performance as it varies all charting parameters. The existing variable parameters chart is designed by assuming that process parameters are known. However, process parameters are rarely known but are usually estimated based on Phase-I data. Hence, the variable parameters chart with estimated parameters is proposed. Formulae to evaluate various performance measures are derived through Markov chains. This paper shows that adopting the optimal charting parameters by incorrectly assuming that process parameters are known results in a large deterioration on the actual performance, especially for small shifts, a small number of subgroups, and small sample sizes. Subsequently, this paper proposes algorithms to obtain the optimal charting parameters for estimated parameters that show better performance, especially for small shift sizes, number of subgroups, and sample sizes. Finally, from an illustrative example, the proposed variable parameters chart is able to detect more out-of-control samples.