Advances and Applications in Statistics
Volume 56, Issue 2, Pages 95 - 112
(June 2019) http://dx.doi.org/10.17654/AS056020095 |
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ARL OF CUSUM CONTROL SCHEMES FOR ZIB MODEL WHEN THE UNDERLYING DISTRIBUTION IS THE RATIO OF TWO POISSON MEANS
Direk Bualuang, Yupaporn Areepong and Saowanit Sukparungsee
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Abstract: The aim of this paper is to present average run length of cumulative sum (CUSUM) control chart for zero-inflated binomial model when the underlying distribution is the ratio of two Poisson means (CUSUMZIB_poi). The CUSUMZIB_poi control chart using the Markov chain approach (MCA) was effective in detecting small shifts as same as the Monte Carlo method (MC). However, the computational time for MCA method is preferable to the MC method. The sensitivity of θ can more detect all shifts when the value of θ increases. In addition, the MCA method for evaluating ARL0 and ARL1 can produce a set of optimal parameters, which depend on the reference value (g) and the width of the control limit (h) for designing the CUSUM chart with a minimum ARL1. |
Keywords and phrases: cumulative sum, zero-inflated binomial, average run length, Markov chain.
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