Economic statistical design of -control charts: Modified version of Rahim and Banerjee (1993) model

Rahim and Banerjee considered a constant integral of the hazard function for all sampling intervals. This led the sampling intervals to depend on the extended first sampling interval (h(1)). Since this limitation might not lead to an optimal situation, we first showed that elimination of the mentioned restriction did not cause any significant change in the average quality cycle cost. So if one is looking for an ideal cost and the simplicity of the process, the approach taken in Rahim and Banerjee's study is the best procedure to adopt. Moreover, in many cases of non-uniform sampling method the first sampling interval becomes so large and this can sometimes lead the production system to the out-of-control state due to unexpected failures that might happen during that time. Therefore, we proposed a new model of uniform and non-uniform sampling intervals combination that allows us to confine the value of h(1) without undergoing high costs. The proposed model showed that the quality cycle cost of the proposed model is lower than Rahim and Banerjee's model in the economic-statistical state. For more illustration, we conducted sensitivity analysis and gave numerical examples.