Economic design of a variable sampling rate (X)over-bar chart

Abstract

An economic model is developed for a variable sampling rate (VSR) Shewhart (X) over bar chart in which the sample size and sampling interval to be used for the next sample can vary depending on the value of the current sample mean. The economic model expresses the long-run cost per hour of operating the VSR chart as a function of the design parameters of the chart, the process parameters which describe the behavior of the process, and the cost parameters associated with the operation of the chart. This model can be used to quantify the reduction in cost that can be achieved by using the VSR chart instead of a traditional chart which uses a fixed sampling rate. It is shown that the cost reduction can range from modest to substantial, depending on the values of the process and cost parameters. The model can also be used to gain insight into the best way to design a VSR chart for applications. It is shown that the same threshold limit can be used for both the sample size and the sampling interval with little increase in cost. It is also shown that in most cases it is best to design the VSR chart with a very low false alarm rate.