Economic statistical design of non-uniform sampling scheme X bar control charts under non-normality and Gamma shock using genetic algorithm

This paper presented an approach which simultaneously considered the properties of cost and quality based on the Burr distribution and the non-unifampling scheme. The objective was to determine three parameters, namely, sample size, sampling interval between successive samples, and control limits, when an X bar chart monitors a manufacturing process with Gamma (λ, 2) failure characteristic and non-normal data. The design parameters of the X bar control charts can be obtained through the genetic algorithm (GA) method. An example was also adopted to indicate the solution procedure and sensitivity analyses. The results show that an increase of skewness coefficient (α₃) results in a slight decrease for sample size (n) while an increase of kurtosis coefficient (α₄) leads to a wider control limit width.