Applied Modeling Techniques and Data Analysis 1

13 Phase I Non-parametric Control Charts for Individual Observations: A Selective Review and Some Results

Parametric control charts are based on assumptions of a specific form for the underlying process distribution. One challenge, commonly encountered in non-manufacturing processes, is that the underlying process distribution of the quality characteristic(s) significantly deviates from normality and is usually not known. Therefore, statistical properties of the most commonly used parametric control charts are highly affected and their performance generally deteriorates. There are many applications in non-manufacturing operations, where there is insufficient information to justify such assumptions and a normal transformation of the observations is feasible; however, this is at the expense of the interpretability of the analysis. To this end, non-parametric control charts with a minimal set of distributional assumption requirements are in high demand, and such distribution-free charts have been proposed in recent years. However, most of the existing non-parametric control charts are designed for Phase II monitoring. Moreover, little has been done in developing non-parametric Phase I control charts, especially for individual observations that are prevalent in non-manufacturing applications. In this contribution, we bring a selective review forward to 2020, discuss the main ideas that shaped the field of univariate Phase I non-parametric process monitoring (focusing on individual ...