Robust design of a VP-NCS chart for joint monitoring mean and variability in series systems under maintenance policy

Statistical process monitoring and maintenance policy are two important tools to improve system reliability and products quality. To simplify mathematical modeling, most existing papers in the literature suffer from four major drawbacks: (1) designing the control charts under maintenance action for the single-unit systems, in spite of the fact that most real manufacturing processes include multiple units; (2) using control charts with fixed parameters that are slow in detecting small and moderate shifts; (3) this assumption that the occurrence of assignable cause only changes the process mean, which means it doesn't have any effect on variance of quality characteristic, and (4) emplying the point estimates of input parameters while the precise estimation of them are unavailable in the real industrial situations due to the existence of uncertainty. To overcome the mentioned disadvantages, this study integrates the economic-statistical design of an adaptive non-central chi-square chart with maintenance policy for joint monitoring mean and variability of two-unit series systems. In addition, a robust optimization method is presented to minimize model costs under uncertain parameters. Finally, a case study is applied to indicate the model efficiency. The results confirm that the suggested control chart has better performance in cost-saving in comparison with the other control charts. Furthermore, the results demonstrate that when the number of uncertain parameters increases, the model cost increases obviously.