Distribution-Free Exceedance CUSUM Control Charts for Location

作者：Mukherjee A^*; Graham M A; Chakraborti S

来源：Communications in Statistics - Simulation and Computation, 2013, 42(5): 1153-1187.

DOI：10.1080/03610918.2012.661638

• Binomial
• CUSUM chart
• Exceedance statistic
• Markov chain
• Nonparametric
• Precedence statistic
• Quality control
• Robust
• Simulation

Distribution-free (nonparametric) control charts can be useful to the quality practitioner when the underlying distribution is not known. A Phase II nonparametric cumulative sum (CUSUM) chart based on the exceedance statistics, called the exceedance CUSUM chart, is proposed here for detecting a shift in the unknown location parameter of a continuous distribution. The exceedance statistics can be more efficient than rank-based methods when the underlying distribution is heavy-tailed and/or right-skewed, which may be the case in some applications, particularly with certain lifetime data. Moreover, exceedance statistics can save testing time and resources as they can be applied as soon as a certain order statistic of the reference sample is available. Guidelines and recommendations are provided for the chart%26apos;s design parameters along with an illustrative example. The in- and out-of-control performances of the chart are studied through extensive simulations on the basis of the average run-length (ARL), the standard deviation of run-length (SDRL), the median run-length (MDRL), and some percentiles of run-length. Further, a comparison with a number of existing control charts, including the parametric CUSUM chart and a recent nonparametric CUSUM chart based on the Wilcoxon rank-sum statistic, called the rank-sum CUSUM chart, is made. It is seen that the exceedance CUSUM chart performs well in many cases and thus can be a useful alternative chart in practice. A summary and some concluding remarks are given.

• 出版日期2013-5-1