A phase I nonparametric shewhart-type chart based on sequential normal scores

Abstract

Nonparametric statistical methods are gaining importance in industrial process monitoring due to their robustness to the underlying distribution of the data, a common situation when dealing with real industrial processes. Control charts are regularly used to monitor the behavior of a system over time, often assuming a normal distribution, thus, the exactness of results obtained relies on the truthfulness of given assumptions. Nonparametric solutions based on permutations are limited to deal with small samples due to the computational complexity. Approaches based on rank transformations have shown relatively great power, however, their use in the analysis of series, such as control chart monitoring, involves re-ranking calculations that might become too complex when facing large data flows. This can be avoided by restricting the incorporation of new data into the analysis at the expense of losing power. Sequential rank transformations have shown attractive properties in terms of power and computational complexity, and the normal scores variant has reduced the analytical complexity extending its applicability by adapting parametric approaches that assume normality. This thesis proposes the use of sequential normal scores (SNS) for industrial process monitoring and compares its performance over a wide variety of practical situations and other nonparametric alternatives. The performance showed robustness over different distributions, in terms of the Empirical Alarm Probability (EAP), and an increase in power as new observations were incorporated in the analysis.