A variable parameter Shewhart control scheme for joint monitoring of process mean and variance

This paper presents a new Statistical Process Control model for the economic optimization of a variable-parameter control chart monitoring a process operation where two assignable causes may occur, one affecting the mean and the other the variance of the process. Therefore, it is possible for the process to operate in statistical control, when none of the two assignable causes has occurred, or under the effect of one or both the assignable causes. By making the assumption that the occurrence rate of each assignable cause is exponential, a Markov chain approach is utilized to determine the probabilities that the process operates at any of the above possible states. The model uses an economic (or an economic/statistical) optimization criterion for the time to the next sampling instance, the size of the next sample, as well as the control limits of the inspection. That is, all design parameters of the control scheme are selected so as to minimize the total expected quality-related costs. The superiority of the proposed model is estimated by comparing its expected quality control cost vs. the outcome of the Fp (Fixed-parameter) Shewhart control chart, the Variable Sample Size (VSS) control chart, the Variable Sampling Interval (VSI) and the Variable Sample Size and Sampling Interval (VSSI) control chart, for a benchmark of examples. The numerical investigation indicates that the economic improvement of the proposed model may be significant.