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https://prod.org.br/article/doi/10.1590/0103-6513.113112
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Article

Steady-state behavior of nonparametric control charts using sign statistic

Khilare, Shashikant Kuber; Shirke, Digambar Tukaram

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Abstract

If process is running for a long period in an in-control condition, it will reach in a steady-state condition. In order to study the long term properties of a control chart, it is appropriate to investigate the steady-state average time to signal. In this article, we discussed runs rules representation of a nonparametric synthetic control chart using sign statistic for detecting shifts in location parameter. We compared zero-state average time to signal with steady-state average time to signal of the synthetic control chart for symmetric and asymmetric distributions. We also present the m-of-m control chart using sign statistic. For comparison study, we computed average time to signal of the m-of-m control chart, the sign chart (1-of-1 chart) and the synthetic control chart for normal, Cauchy, double exponential and gamma distributions. Steady-state and zero-state performance of the m-of-m control chart with m = 2, 3 compared with the sign chart (1-of-1 chart) and synthetic control chart. The zero-state and steady-state average time to signal of the synthetic and the m-of-m control charts computed using Markov chain approach.

Keywords

Steady-state. Markov chain. Synthetic. Nonparametric. Average time to signal.

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