Control Charts for Monitoring the Zero-Inflated Generalized Poisson Processes

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 c(G) - Chart. We first develop the control limits of the c(G) - Chart by using the expected and variance of ZIGP distribution; namely c(zG) - 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 cog - 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 c(Gg) - Chart, we developed c(G) - Chart by using the expected and variance of the geometric distribution. For c(Gk) 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 (mu), proportion zero(omega), mean shift(rho) and over dispersion (phi). For an out-of-control process, the c(Gg) - Chart is the best for mu = 1 at low w for all p and y. The C-Gk - Chart is the best for mu = 2 at all parameters and for mu = 3, 4 at high w for all p and y. The c(zG) - Chart is the best for j = 3 at low omega and mu = 4 at high w for all p and y.