In this article, we provide a nonparametric Shewhart-type synthetic control chart based on the signed-rank statistic to monitor shifts in the known in-control process median. The synthetic control chart is a combination of a signed-rank chart due to Bakir (2004) and a conforming run length chart due to Bourke (1991). The operation and design of the chart are discussed and the performance of the chart has been studied. The chart has an attractive average run length behavior as compared to the parametric control chart for a class of symmetric continuous process distributions. The proposed chart performs better than the nonparametric signed-rank chart given by Bakir (2004) and Chakraborti and Eryilmaz (2007).
The article studied the steady-state behaviour of the synthetic control chart using signed-rank statistic for shifts in the process median. The steady-state ATS (Average Time to Signal) values are computed using Markov chain approach. To compute steady-state ATS, the performance of the synthetic control chart and two-of-L+1 control chart can be made identical over all samples with head start features. When subgroup sample size n=10, the steady-state performance of the synthetic control chart is worth for small to moderate shifts under all considered symmetric distributions. When subgroup sample size n=5, steady-state ATS values are larger under normal and double exponential distributions only for small shifts. However, under the Cauchy distribution zero-state ATS values are larger but not significantly larger as compared to steadystate ATS values. Usefulness of proposed control chart explored using numerical example. Proposed control chart is simple and easy to use for practitioners.
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