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<p>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.</p>

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Phase I distribution-free control charts for individual observations using runs and patterns

  • 期刊论文

  • 发表日期：

    2026年1月17日

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  • Tung-Lung Wu

摘要

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.