Optimizing joint location-scale monitoring – An adaptive distribution-free approach with minimal loss of information

Nonparametric statistical process monitoring (NSPM) schemes are very effective in monitoring various non-normal and complex processes. Nevertheless, there is one disadvantage of the traditional NSPM schemes. We often lose some information during scoring or ranking. For example, we sometimes ignore the information related to the shape or tail-weights of the underlying process distribution. In this paper, we introduce distribution-free adaptive Shewhart-Lepage (SL) type schemes for simultaneous monitoring of location and scale parameters using information about symmetry and tail-weights of the process distribution. We consider an adaptive SL type scheme, referred to as the LPA scheme, based on the three modified Lepage-type statistics. Using numerical results obtained via Monte-Carlo, and considering operational simplicity, we also propose a new adaptive SL type scheme, referred to as the MLPA scheme, with finite sample correction. These adaptive approaches use the Phase-I data to assess the tail-weights of the process distribution, and then select an appropriate SL type statistic for process monitoring. Consequently, these schemes correct the disadvantage of the traditional distribution-free schemes to a great extent. We compare the two adaptive schemes with the three individual SL type schemes, and also with the classical SL and Shewhart-Cucconi (SC) schemes in terms of the average, the standard deviation and some percentiles of the run length distribution. Numerical results establish that the MLPA scheme is superior for jointly monitoring the parameters of a broad class of process distributions belong to the location-scale family.