Design and implementation of distribution-free Phase-II charting schemes based on unconditional run-length percentiles

Abstract

Traditionally, the mean of the run-length distribution (ARL) of an in-control (IC) process is used to design and implement statistical process charting schemes. When standards are unknown (Case U), the unconditional ARL is considered during Phase-II monitoring—surprisingly, by suppressing the term “unconditional.” The literature has recently highlighted the difference between the unconditional and the conditional ARL in studying the properties of Phase-II charting schemes under the Case U. The effects of bias in the Phase-I sample may lead to remarkably high rates of early false alarms. We explore the idea of restricting the probability of unconditional early false alarms by using lower percentile points of the unconditional run-length distribution to design nonparametric charting schemes. This new approach is named “the lower percentile-based (LPL) design.” We consider the design and implementation of six distribution-free schemes: five precedence-type schemes and the rank-sum scheme. We carry out simulations to compare the six schemes with a prefixed value of some lower percentile point of the IC run-length distribution. The best scheme is the one with the lowest value for a specific higher percentile point of the out-of-control run-length distribution. We illustrate the new design and implementation strategies with real data, and offer a summary and concluding remarks.