Robust control charts for percentiles based on location‐scale family of distributions

Abstract

AbstractIn this paper, robust control charts for percentiles based on location‐scale family of distributions are proposed. In the construction of control charts for percentiles, when the underlying distribution of the quality measurement is unknown, we study the problem of discriminating different possible candidate distributions in the location‐scale family of distributions and obtain control charts for percentiles which are insensitive to model mis‐specification. Two approaches, namely, the random data‐driven model selection approach and weighted modeling approach, are used to construct the robust control charts for percentiles in order to effectively monitor the manufacturing process. Monte Carlo simulation studies are conducted to evaluate the performance of the proposed robust control charts for various settings with different percentiles, false‐alarm rates, and sample sizes. These proposed procedures are compared in terms of the average run length. The proposed robust control charts are applied to real data sets for the illustration of robustness and usefulness.