Distribution-Free Phase I Control Charts for Subgroup Location

Abstract

Much of the work in statistical quality control is dependent on the proper completion of a Phase I study. Many Phase I control charts are based on an implicit assumption of normally distributed process observations. In the beginning stages of process control, little information is available about the process and the normality assumption may not be reasonable. Existing robust and distribution-free control charts are concerned with the establishment of Phase II control limits that are robust to nonnormality or outliers from the Phase I sample. Our literature review revealed no purely distribution-free Phase I control-chart methods. We propose a distribution-free method for defining the in-control state of a process and identifying an in-control reference sample. The resultant reference sample can be used to estimate the process parameters for the Phase II procedure of choice. The proposed rank-based method is compared with the traditional X chart using Monte Carlo simulation. The rank-based method compares favorably to the X chart when the process is normally distributed and performs better than the X chart in many situations when the process distribution is skewed or heavy tailed.

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