Economic statistical design of x-bar control charts for correlated data and Gamma failure mechanism with genetic algorithm

This study proposed an approach which simultaneously considers the properties of cost and quality by minimum value of expected cost per hour which is restricted by maximum value of type I error (α
_U
) and minimum value of power (p
_L
) to determine three parameters (including sample size, sampling interval between successive samples, and the control limits) when an x bar chart supervises a manufacturing process with an increased hazard rate and the measurements within the sample being correlated. Most control chart economic statistical designs assumed the failure mechanism, which belongs to the Poisson distribution. Furthermore, the subgroup measurements within a sample undergo an independent distribution. However, the above-mentioned assumptions are not usually pragmatic. As a result the assumption of Poisson failure mechanism for processes in which machine wear occurs over time is not appropriate. Also, this supposition of independently distributed in the subgroup measurements in which collected from the production process, multiple pins on an integrated circuit chip, may not be tenable. Hence, this study employs combining Rahim and Banerjee's cost model with Yang and Hancock's multivariate normal distribution model to search the optimal parameters of control charts under correlated data. Meanwhile, a genetic algorithm is adopted.