Economic design of variable-parameter X-Shewhart control chart used to monitor continuous production

Abstract

Control charts are a quantitative management tool used in statistical process control to monitor product quality in production processes. This study proposes a new economic design of the variable-parameter (Vp) -Shewhart control chart for monitoring a continuous production process. In this design, the mean monitoring quality may exhibit an upward or downward shift due to two types of assignable causes. In certain continuous production settings, product quality directly affects production profit; the mean shift in monitoring quality influences lost cost, unit income and product yield. Thus, for modelling continuous production, using a maximum profit objective function for the optimization algorithm of this economic model is more appropriate than using minimum cost. Therefore, the Vp -Shewhart control chart uses an economic criterion for optimum parameter design to maximize the anticipated quality-related profit. The assignable cause occurrence is assumed to be an exponentially distributed random variable; Markov chain theory with a 9 × 9 transition probability matrix is used to subdivide the process operation into three actual states and three necessary actions. A numerical investigation is used to demonstrate the superiority of the proposed profit model compared to existing models. The proposed Vp -Shewhart control chart is applied to an example case to show its feasibility and practical application.

Keywords:

• Shewhart scheme
• variable parameter control chart
• Markov chain
• profit maximization

Acknowledgements

The authors would like to thank the anonymous reviewers and the editor whose comments and suggestions improved greatly the presentation of the paper.