This paper compares the economic performance of CUSUM and Shewhart schemes for monitoring the process mean. We develop new simple models for the economic design of Shewhart schemes and more accurate ways to evaluate the economic performance of CUSUM schemes. The results of the comparative analysis show that the economic advantage of using a CUSUM scheme rather than the simpler Shewhart chart is substantial only when a single measurement is available at each sampling instance, i.e., only when the sample size is always n = 1, or when the sample size is constrained to low values.
1. Introduction
For many years the research community has allocated a considerable part of its effort to the design of effective quality control charts. The effectiveness of the charts is usually evaluated from a statistical point of view, but it is increasingly recognized that since it is the bottom line that matters, the control chart design must be primarily evaluated using economic criteria. The objective of this paper is to provide a thorough economic comparison between the most frequently used control charts, i.e., the standard Shewhart chart and the CUSUM chart for monitoring the mean of a quality characteristic.
4. Summary and conclusions
We have presented simple and accurate Markov chain models for the economic optimization of Shewhart and CUSUM charts for monitoring the mean of a normally distributed quality characteristic. Our numerical investigation has led to the following conclusions. 1. CUSUM charts are economically far superior to Shewhart charts only if process monitoring must be performed on the basis of individual measurements (sample size n = 1). If there are no restrictions on the size of each sample, the economic performance of the optimal CUSUM chart is almost identical to the performance of the optimal Shewhart chart even when the magnitude of the anticipated shift is small. In between these two extreme cases, namely if the sample size is restricted to low values for reasons such as the need for rational subgrouping, the CUSUM chart may significantly outperform the Shewhart chart when the shifts in the mean are small.
