Tolerance limits for mixture-of-normal distributions with application to COVID-19 data

Tolerance intervals (TIs) are widely used in various applications including manufacturing engineers, clinical research, and pharmaceutical industries. TIs can be used to construct limits of control charts for monitoring quality characteristics. For manufacturing processes where multiple factors may contribute to defects or multiple-stream processes, a mixture distribution of several suitable probabilistic models may be a better choice than a simple distribution for modeling the data. TIs for the normal mixture distribution have been studied in the literature. This article reviews the TIs of the normal mixture distribution, the applications of the mixture distribution, and the control charts of the mixture distribution. A rule for constructing modified two-sided TIs of the normal mixture distribution is summarized, and this rule may be extended to construct modified two-sided TIs for general mixture distributions. The feasibility of using TIs to build control charts for mixture distributions is also discussed. A real data example of coronavirus disease 2019 is used to illustrate the method by linking the TI to control charts. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification.