Multi-objective economic-statistical design of fraction defective control chart for high quality processes using a heuristic algorithm

In statistical quality control, the p control chart is used to monitor the fraction of nonconforming units in a sample. In practice, high quality processes with very low rate of nonconformities are often observed. The traditional control chart suffers a serious inaccuracy in control limits specification in this way. This paper presents a new chart based on simple adjustments derived from Cornish-Fisher (C-F) expansions to improve the inaccuracy. Generally, the design of a control chart requires determination of some parameters that optimally selecting them depends on several process parameters, which have been considered from statistical and/or economic aspects in the literature. This study presents a multi-objective economic-statistical design (MOESD) of the improved np-chart. Due to the structure of the model, we apply a recently used heuristic algorithm to solve nonlinear multi-objective problems by nonlinear lexicography goal programming (NLGP). A numerical example is used to illustrate the algorithm procedure.