The restrictions in economic design model for an x-bar control chart under non-normally distributed data with Weibull shock model

This paper proposed an approach which simultaneously considers the properties of cost and quality based on the Burr distribution to determine three parameters (including sample size, sampling interval between successive samples, and the control limits) when an x bar chart monitors a manufacturing process with Weibull failure characteristic and non-normal data. Most control chart economic statistical designs assumed the failure mechanism, which belongs to the Poisson distribution. However, this is not usually pragmatic. Because the assumption of Poisson failure mechanism was not always appropriate in practice, especially for processes in which machine wear occurs over time. Processes with increasing hazard functions are common in the mechanical and electrical industries. 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. Furthermore, the objective function is to minimize expected cost per hour, and type I error (¿) and power (1- ß) are restricted by maximum value of type I error (¿_U) and minimum value of power (p_L) respectively in non-normally distributed data.