Distribution-Free Exceedance CUSUM Control Charts for Location |
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| Authors: | A Mukherjee M A Graham S Chakraborti |
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| Institution: | 1. Department of Mathematics and System Analysis , Aalto University , Finland;2. Department of Information Systems, Statistics and Management Science , University of Alabama , Tuscaloosa , Alabama , USA;3. Department of Mathematics , IIT Madras , India |
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| Abstract: | 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'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  | |
| Keywords: | Binomial CUSUM chart Exceedance statistic Markov chain Nonparametric Precedence statistic Quality control Robust Simulation |
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