ECONOMIC-STATISTICAL DESIGN APPROACH FOR A VSSI X-BAR CHART CONSIDERING TAGUCHI LOSS FUNCTION AND RANDOM PROCESS SHIFTS

Economic design approaches of control charts are commonly based on the assumption that various cost parameters values and the occurrence risk of assignable causes have to be a priori known with precision. However, in real operative contexts, such parameters can be really difficult to accurately estimate, especially considering costs arising from out-of-control conditions of the process. As consequence, pure economic design approaches can involve chart schemes with low statistical performance. To overcome such limitation, it is herein proposed a multi-objective economic-statistical design approach for an adaptive X-bar chart. In particular, such approach aims at the minimization of both the total quality related costs and the out-of-control average run length, in such a way assuring an optimal trade-off between economic and statistical performance of the related control procedure. Moreover, for a robust design approach, the mean shift is considered as a random variable. A mixed integer nonlinear constrained mathematical model is formulated to solve the treated problem, whereas the Pareto optimal frontier is described by the ε-constraint method. In order to show the employment of the proposed approach, an illustrative example is developed and the related considerations are given. Finally, some sensitivity analysis is also performed to investigate the effects of operative and costs parameters on chart parameters.