Economic Design of A Modified Variable Sample Size and Sampling Interval X ̄ Chart

Abstract: A comprehensive economic cost function is derived for a modified variable sample size and sampling interval X (MVSSI) chart. As a variable sample size and sampling interval, a variable sample size, a variable sampling interval, and a static X charts are particular cases of an MVSSI X chart, the model is directly applicable to these charts, too. The cost function can be used to obtain optimal design parameters of these charts that minimize the process control related cost per hour for given process and cost parameters. It can also be used to compare the economic performances of these charts. A numerical study shows that the optimal adaptive X charts differ in their performance only marginally from each other. However, both the statistical and economic performances of an optimal MVSSI X chart are superior to that of the other adaptive X charts. A sensitivity analysis for a particular example reveals that the optimal design obtained using the cost function is relatively insensitive to errors in specifying various process and cost parameters