A nonparametric control chart for a symmetric process: A Markovian approach

Document Type

Article

Publication Date

1-1-2000

Abstract

We propose a rank-based process control chart that is distribution-free and does not require any parameter estimations. The nonparametric control chart is based on the rank distribution of the cumulative sum of individual observations. When the process is in control, the changes of ranks in successive cumulative sums follow a specific transition probability matrix in the Markov chain. Using the chi-square goodness-of-fit test for the Markov chain, we can determine whether or not the observations come from the process with the given transition probability matrix. In a Monte Carlo simulation, we show that our rank-based control chart is consistently better than the traditional Shewhart control chart in detecting a small shift of the process mean and that its coefficient of variation of the run length is even better than those of the EWMA and the CUSUM control charts.

Publication Source (Journal or Book title)

Quality Engineering

First Page

447

Last Page

461

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