Robustness of χ CUSUM and CP CUSUM Using Fast Initial Response in Detecting of Process Dispersion
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Abstract
Statistical quality control relates with monitoring of process disturbances which they may be caused by changing either mean or dispersion process. The aim of this research is to study the robustness of chi-cumulative sum (χ CUSUM) and CP CUSUM charts by giving an initial value of CUSUM statistics in order to quick detect a change in process dispersion. The Fast Initial Response (FIR) or Head Start (HS) are given to 25%, 50% and 75% of control limit of control chart. The performance of control chart is usually measured by an out of control Average Run Length (ARL1) where the best performance of control chart will give the minimum ARL1. The performance of χ CUSUM and CP CUSUM control charts are compared when the processes are distributed Laplace(0,2), Logistic(2,2) and Gamma(9,1). The numerical results are carried out by Monte Carlo simulation with replication 10,000 times. We found that the performance of χ CUSUM is superior to CP CUSUM for small shifts in dispersion parameter, otherwise the CP CUSUM performs better than χ CUSUM for moderate to large shifts with using 75% HS. In addition, those control charts are robust to symmetric and asymmetric distributions of process for all level of ARL0.
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