A distribution-free Phase I monitoring scheme for subgroup location and scale based on the multi-sample Lepage statistic. (March 2019) - Li, Chenglong; Mukherjee, Amitava; Su, Qin
Highlights: This paper introduces a distribution-free Phase I scheme for location and scale. This is a one-chart scheme based on the multi-sample Lepage statistic. This scheme does not require the restriction of equal sizes for each subgroup. A variety of patterned shifts are considered in simulation study. This scheme is superior to or comparable to several existing two-chart schemes in most cases. Abstract: In this paper, we introduce an exactly distribution-free procedure for Phase I analysis which is capable of assessing stability of both location and scale parameters of the process using a single plotting statistic. A large proportion of literature on Phase I or retrospective analysis assumes normality. The normality assumption is often invalid in practice. In recent years, researchers have proposed some distribution-free (nonparametric) Phase I schemes. Most of these schemes facilitate assessing either the location or the scale, individually but not both simultaneously. Practitioners often consider a two-chart scheme, one for monitoring the location parameter and the other the scale parameter in tandem. Nevertheless, such two-chart schemes have certain practical disadvantages. There is a plethora of literature on distribution-free Phase II schemes for simultaneously monitoring the location and scale parameters of a process distribution using a single statistic. To the best of our knowledge, there is no literature on Phase I or retrospective analysis of both location and scale adopting a single statistic. To fill this research gap, we propose a distribution-free Phase I monitoring scheme for both location and scale parameters based on the multi-sample Lepage statistic. The proposed Phase I scheme can be implemented even if subgroup sizes are unequal. Unlike, most of the existing schemes, it does not require the restriction of equal sizes for each subgroup. The design and implementation of the proposed scheme is simple. We clearly outline and illustrate the implementation steps with an example. Compared to several existing two-chart schemes, the proposed one-chart scheme has performance advantages in a variety of cases, especially for skewed and heavy-tailed data. We also study certain interesting features of the proposed scheme.