The application of Bayesian estimator’s the shape parameter of The Inverse Gaussian Distribution for The Adjusted Average Control Chart

Abstract

This research aims (1) to develop the average control chart (x-chart) using the shape parameter of the Inverse Gaussian distribution by Bayesian Estimation for estimating mean and variance, and (2) to compare the process potential capability (Cp) and the actual process capability index (Cpk) for Monte Carlo simulation with 10,000 replications assuming that the specification is +- 0.001. The result shows that the process potential capability (Cp) and actual process capability index (Cpk) of the Adjusted x-chart using Bayesian Estimation of the shape parameter of the Inverse Gaussian distribution for estimating mean and variance have more capability than the x-chart under the normal distribution when the sample size is less than 30. For the sample size of 30, the two control charts have the indifferent capability process. And, the capability of process in Gravure printing used the Adjusted x-chart have capability of process of customer requirement.