Applying SVSSI sampling scheme to np-chart to decrease the time of detecting shifts using Markov chain approach and Monte Carlo simulation

One of the main criteria for judging about the power of control charts is their ability in fast detection of deviations and shifts in the process. Average time to signal (ATS) or adjusted average time to signal (AATS) are among such criteria calculated under a certain state and assumption. Several studies have shown that using the idea of ​​variable design for control charts, by separating their limits to the safe and the warning regions, can allow quick discovery of shifts and increase sensitivities to small changes. In this paper, a new variable sampling scheme with three sample sizes and two different sampling intervals, called SVSSI, is developed to increase the efficiency of the np control chart. Through various numerical examples, the performance of this scheme is evaluated by calculating ATS and AATS values using Markov chain method. Monte Carlo simulation method is used to validate the results of Markov chain method of SVSSI sampling scheme. In comparison with other schemes, better performance of applying SVSSI is proved in all conditions.