Multi-aspect NPC control charts: A new class of Shewhart-type control charts

Abstract

In the last decades, control charts have proven to be an effective tool to improve the quality of production processes. In recent years, as the Industry 4.0 revolution is progressing, also the interest in Statistical Process Control (SPC) and control charts is growing.

Distribution-free control charts are an interesting family of control charts that has recently been receiving increasing attention from both industry and science. The defining characteristic of distribution-free control charts is that their in-control performances are not affected by the underlying process distribution, so no knowledge regarding the process distribution is required for their practical implementation. This feature makes distribution-free control particularly useful in the early stages of the SPC monitoring phase.

Several Shewhart-type distribution-free control charts for different kinds of monitoring problems have been proposed in the last two decades. The majority of these charts are based on linear rank statistics. In this thesis, we explore a new scheme for devising distribution-free control charts which is based on the Nonparametric Combination of Dependent Tests framework (NPC), borrowed from hypothesis testing and permutation testing theory. The NPC combination idea is very flexible and has already been used for designing multivariate control charts. In this work, we analyze the application of NPC to combine several tests in order to address different aspects of the problem or viewpoints of the data. Studying these multi-aspect NPC charts, we have discovered that combining only linear rank tests leads to a distribution-free NPC chart, whereas combining at least one non linear rank test may lead to a non distribution-free NPC chart.

From a practical perspective, we also propose and evaluate several distribution-free multi-aspect NPC charts for the univariate location and joint location-scale monitoring problems in the standards unknown case. To provide calibration and evaluation routines for multi-aspect NPC charts, a high-performance R package has been developed. Using the implemented algorithms a simulation study has been conducted to compare the proposed charts with the competitors. One of the most interesting results has been obtained with the NPC Wilcoxon-Klotz chart for the location-scale problem. This chart takes full advantage of the flexibility of the NPC framework and has really good performance under a wide variety of interesting distributions.