Fuzzy multi-objective economic-statistical design of X-bar control chart

Nowadays manufacturing organisations are aiming towards producing higher quality outputs at lower cost of production to keep stride with the competition. The control charts are the most popular and widely used statistical process control tools that can be used for monitoring the unevenness in quality characteristics of a production process. The economic-statistical design of control chart selects three parameters, namely sample size n, sampling interval h and control limit width k to achieve the lowest cost with desirable statistical properties. However, the cost function and statistical properties are interrelated. Hence, minimising the cost as the only objective is not an efficient method of designing control charts. In this paper, a multi-objective model for the economic-statistical design of X-bar control chart has been proposed with three objectives, i.e., to minimise mean hourly cost, maximise in-control average run length and maximise the power of detecting process shift. A multi-objective evolutionary genetic algorithm is used to obtain the Pareto-optimal solution for this design which is then ranked by fuzzy performance importance index. The performance of the proposed method is compared through a numerical example and observed to be superior to that reported in the literature.