Acceptance X-bar chart considering the sample distribution of capability indices, ${\hat{C}}_p$ and ${\hat{C}}_{pk}$ : A practical and economical approach

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 C_pk, 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 (C_p and C_pk) in addition to m and n were introduced in the expected ARL equation. The C_pk 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.

Citation

Oprime, P.C., Lizarelli, F.L., Pimenta, M.L. and Achcar, J.A. (2019), "Acceptance X-bar chart considering the sample distribution of capability indices, ${\hat{C}}_p$ and ${\hat{C}}_{pk}$ : A practical and economical approach", International Journal of Quality & Reliability Management, Vol. 36 No. 6, pp. 875-894. https://doi.org/10.1108/IJQRM-11-2017-0239