An X-Bar Control Chart Economic Design Sampling Strategy for Non-normally Distributed Data under Gamma (λ, 2) Failure Models

This study compares an x-bar control chart economic design with a variable sampling interval (VSI) and a fixed-length sampling (FSI) for non-normal data under Gamma (lambda, 2) shock models. In earlier investigations, constant sampling intervals were widely employed by the control chart's designers and users because of their administrative simplicity. Most control chart economic designs assumed the failure mechanism, which belongs to the Poisson distribution. However, this is not usually pragmatic. Banerjee and Rahim (1993) presented a cost model using VSI under a process-failure mechanism that followed a Gamma (lambda, 2) model with an increased hazard rate. These subgroup measurements were assumed to be normally distributed when designing control charts. However, that assumption may not be tenable in this research. Hence, this study employs a numerical example to indicate the solution procedure and to implement the sensitivity analysis while comparing the results of using various sampling interval approaches in non-normally distributed data.