Acceptance X-bar chart considering the sample distribution of capability indices, C ˆ p and C ˆ p k

Abstract

Purpose The traditional Shewhart control chart, the X-bar and R/S chart, cannot give support to decide when it is not economically feasible to stop the process in order to remove special causes. Therefore, the purpose of this paper is to propose a new control chart design – a modified acceptance control chart, which provides a supportive method for decision making in economic terms, especially when the process has high capability indices. Design/methodology/approach The authors made a modeling expectation average run length (ARL), which incorporates the probability density function of the sampling distribution of Cpk, to compare and analyze the efficiency of the proposed design. Findings This study suggested a new procedure to calculate the control limits (CL) of the X-bar chart, which allows economic decisions about the process to be made. By introducing a permissible average variation and defining three regions for statistical CL in the traditional X-bar control chart, a new design is proposed. Originality/value A framework is presented to help practitioners in the use of the proposed control chart. Two new parameters (Cp and Cpk) in addition to m and n were introduced in the expected ARL equation. The Cpk is a random variable and its probability function is known. Therefore, by using a preliminary sample of a process under control, the authors can test whether the process is capable or not.