Non parametric PROS quality control chart for monitoring the process mean

A non parametric Shewhart-type control chart based on a partially rank-ordered set (PROS) sampling design is considered in this study to monitor the process mean. Four non parametric estimators are proposed for the variance of PROS sample mean; also, the performances of these estimators are discussed theoretically and numerically. Then, three non parametric PROS control charts are proposed including the classic 3-sigma control chart, a non parametric bootstrap approach-based control chart, and a hybrid control chart based on a combination of classic 3-sigma and bootstrap control charts. The performance of the proposed PROS control charts is compared with the available chart in terms of controlling the false alarm rate. Results show the merits of both non parametric bootstrap and hybrid PROS control charts. Finally, control charts are illustrated with a real example.