Journal of Quality Engineering and Management

Abstract Statistical quality control methods are the basis for measuring process performance and productivity. Control charts are one of the most widely used statistical control tools and play an important role in improving the quality of processes and products. The main purpose of their implementation is to identify the deviation (s) and take corrective measures to eliminate the root of the deviation. The technical applications of control charts are to determine the sample size, sampling frequency and control limits, which is called control chart design. In most nP chart design research, only one reason deviation is considered as the cause of the chart getting out of control, while several industry deviations can play a role. For this purpose, in this research, the design and statistical-economic development of nP control diagram, in order to reduce costs and average detection time and increase the power of the diagram by using gray values ​​and considering deviations for various reasons. In this regard, in order to achieve the optimal values ​​of these parameters, a multi-objective problem with three constraints has been defined, in which we have considered each possible combination of parameters as a decision unit. Then, using data envelopment analysis and ranking methods, the most efficient design for the decision maker is determined. In the continuation of the research, sensitivity analysis has been performed on some parameters of the model and the effect of these parameters on the optimal values ​​has been analyzed.