An Economic-Statistical Design of x Control Charts with Multiple Assignable Causes

Duncan first proposed the economic design of x control charts in 1956 to control normal process means and ensure that an economic design control chart actually lowers the cost, compared with a Shewhart control chart. Many authors have studied the control charts from economic viewpoint from then on. An economic design does not consider the statistical properties, such as type I or type II error and average time to signal (ATS). To improve these issues, an economicstatistical design of control charts has been developed under the consideration of one assignable cause. However, there are multiple assignable causes in the real practice such as machine problem, material deviation, human errors, etc. In order to have a real application, this research will extend the original research from single to multiple assignable causes to establish an economic-statistical model of x control chart. A numerical example is used to illustrate the performance of the proposed model and to compare the lost cost between the pure economic and economic-statistical control chart design. A sensitivity analysis is also conducted in this numerical example.