Economic-Statistical Design of X-bar Control Charts Using Taguchi Loss Functions

Abstract

Abstract Duncan is the pioneer to provide a control chart design from economic-view point in 1956 and ensure that the economic design of control charts is really lower the cost compared with a conventional Shewhart charts. An economic design does not consider the statistics properties, such as type I or type II error and average time to signal (ATS). In order to improve these issues, an economic-statistical design of control charts was proposed under the statistical consideration. Usually, a product is accepted if the product measurements meet specification requirements and there are no quality losses in the most of economic or economic-statistics design of control charts. Taguchi's Quadratic loss function was employed in this research to construct the quality losses for economic-statistical design of control charts with multiple assignable causes. A numerical example is also used to illustrate its working of the proposed model and to compare the lost cost among the pure economic, economic-statistical control charts design and economic-statistical control charts design using Taguchi's loss function. The example shows that the social loss from the Taguchi's Quadratic loss function is the most important cost compared with the original cost items.