Control Charts for Skewed Distributions: Johnson’s Distributions

Abstract

In this study, some important issues regarding process capability and performance have been highlighted, particularly in case when the distribution of a process characteristic is non-normal. The process capability and performance analysis has become an inevitable step in quality management of modern industrial processes. Determination of the performance capability of a stable process using the standard process capability indices (Cp, Cpk) requires that the quality characteristics of the underlying process data should follow a normal distribution. Statistical Process Control charts widely used in industry and services by quality professionals require that the quality characteristic being monitored is normally distributed. If, in contrast, the distribution of this characteristic is not normal, any conclusion drawn from control charts on the stability of the process may be misleading and erroneous. In this paper, an alternative approach has been suggested that is based on the identification of the best distribution that would fit the data. Specifically, the Johnson distribution was used as a model to normalize real field data that showed departure from normality. Real field data from the construction industry was used as a case study to illustrate the proposed analysis.