The sensitivity analysis of the economic and economic statistical designs of the synthetic X chart

The economic and economic statistical designs allow the practitioner to implement the control chart in an economically optimal manner. For the economic design, the optimal chart parameters are obtained to minimize the cost, while for the economic statistical design, additional constraints in terms of the average run length is imposed. However, these designs involve the estimation of quite a number of input parameters. Some of these input parameters are difficult to estimate accurately. Thus, a sensitivity analysis is required in order to identify which parameters need to be estimated accurately, and which requires just a rough estimation. This study focuses on the significance of 11 input parameters toward the optimal cost and average run lengths of the synthetic X chart. The significant input parameters are identified through a two-level fractional factorial design, which allows interaction effects to be identified. An analysis of variance is performed to obtain the P-values by using the Minitab software. The significant input parameters and interactions on the optimal cost and average run lengths are identified based on a 5% significance level. The results of this study show that the input parameters which are significant towards the economic design may not be significant for the economic statistical design, and vice versa. This study also shows that there are quite a number of significant interaction effects, which may mask the significance of the main effects.