Abstract
Statistical approaches have recently been used to solve industrial process control problems. In particular, the control chart technique, developed using a statistical theory by Dr. Shewhart in 1924, is a well-known statistical method and is widely applied to monitor the variance of a manufacturing process, such that it can ensure that the quality of products is consistent with the expectations of customers. Traditionally, when an economic model is applied to determine the parameters of control charts, it is assumed that the occurrence of an assignable cause follows Poisson distribution when the status of a process changes from in-control into out-of-control condition. Furthermore, it is also assumed that the within-group sampled data and the sampling statistics are also normally distributed. However, the exponential distribution is not an appropriate failure mechanism for some components, mechanical equipment, or machines of electronic products, because their hazard functions will gradually increase with an increase in the time of use. In addition, considering the savings on sampling cost and time, soothe industries usually try to reduce sample size when applying control charts for process monitoring. In these situations, the distribution of subgroup data sets violates the assumption of normal distribution since the central limit theorem cannot be applied. This may reduce the capability of a control chart when applying it for the detection of process variations. This research intends to study the economic and economic-statistical design of x-bar control charts based on the assumption of Burr distribution instead of normal distribution. Meanwhile, fixed sampling interval (FSI) and variable sampling interval (VSI) approaches will be employed under the cost model of Weibull and Gamma distributions. Moreover, the non-linear search approach is applied to determine the parameters of the control chart. To evaluate the performance of different control chart designs, three performance indexes, namely, ECT, Type I error, and power, are employed. It is expected that the research results can provide industries a process monitoring tool with reduced cost at same quality level.