Control Charts for Monitoring the Zero-Inflated Generalized Poisson Processes

Narunchara Katemee, Tidadeaw Mayureesawan

Abstract


This paper developed the c-Chart based on the Zero-Inflated Generalized Poisson (ZIGP) processes. We called the c-Chart based on ZIGP distribution the cG-Chart. We first develop the control limits of cG-Chart by using the expected and variance of ZIGP distribution; namely cZG-Chart. We then develop an approximated ZIGP distribution by a geometric distribution with parameter p. The p estimated the fit for ZIGP distribution used in calculating the expected skewness and variance of geometric distribution for constructing the control limits of cG-Chart; namely cGg-Chart, cGk-Chart and also to study the effects of the cumulative count of conforming items chart (CCC-Chart) which is used for monitoring a ZIGP process we call CCCg-Chart. For cGg-Chart, we developed cG-Chart by using the expected and variance of the geometric distribution. For cGk-Chart, the skewness and variance were used for constructing the control limits. The CCCg-Chart developed control limits of CCC-Chart from the p estimation of geometric distribution. The performance considered the Average Run Length and Average Coverage Probability. We found that for an in-control process, the CCCg-Chart is superior for all levels of the mean , proportion zero , mean shift and over dispersion . For an out-of-control process, the cGg-Chart is the best for mean = 1 at low proportion zero for all mean shift and over dispersion. The cGk-Chart is the best for mean = 2 at all parameters and for mean = 3, 4 at high proportion zero for all mean shift and over dispersion. The cZG-Chart is the best for mean = 3 at low proportion zero and mean = 4 at high proportion zero for all mean shift and over dispersion.


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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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