Phase I Distribution-Free Control Charts for Individual Observations Using Runs and Patterns

Abstract

Phase I distribution-free runs- and patterns-type control charts are proposed for monitoring the unknown target value (or location parameter) for both continuous and discrete individual observations. Our approach maintains the nominal in-control signal probability at a prescribed level by employing the finite Markov chain imbedding technique combined with random permutation and conditioning arguments. To elucidate the methodology, we examine two popular runs- and patterns-type statistics: the number of success runs and the scan statistic. Numerical results indicate that the performance of our proposed control charts is comparable to that of existing Phase I nonparametric control charts for individual observations.