Optimal statistical, economic and economic statistical designs of attribute np control charts using a full adaptive approach
Abstract The chart is commonly used for monitoring processes where the quality of products is characterized by classifying the product characteristic as either conforming or nonconforming. Recent studies have approved the advantages of using adaptive schemes rather than static one in monitoring such processes. In this paper, we develop a full adaptive model for control charts in which all design parameters (sample size, sampling interval, control limit and warning line) could take any value between two predetermined values based on the most recent process information. The proposed scheme is investigated from statistical, economic and economic statistical viewpoints. Thus, a cost model is developed by using the Markov chain approach. Using numerical examples, we illustrate the performance of the proposed models and compare their efficiency with the other schemes. A sensitivity analysis is also carried out to investigate the effects of model parameters on the solution of the economic and economic statistical designs by using the design of experiments. AbbreviationsSPC: statistical process control;FRS: fixed ratio sampling;VSI: variable sampling interval;VSS: variable sample sizes;VSSI: variable sample sizes and sampling interval;FA: full adaptive;WL: warning limit;LCL: lower control limit;UCL: upper control limit;ED: economic design;ESD: economic statistical design;ANF: average number of false alarms;AATS: adjusted average time to signal;GA: genetic algorithm