Economic-statistical design of an adaptive X̄ chart

An X̄ chart with adaptive design parameters outperforms a traditional fixed sample-size, fixed sampling-interval X̄ chart. However, an adaptive chart employs more resources by using a rapid mean sampling rate and a large average sample size to improve its performance. In this paper, an economic model for an adaptive chart with dual sample sizes and dual sampling intervals is developed. Using this model, the design parameters of an adaptive chart are optimized by minimizing the cost function. Constraints on the average time to signal are applied to the economic model to satisfy the required statistical properties. The adaptive chart is compared to the nonadaptive chart in terms of cost of operation and average time to signal. Sensitivity of the design parameters of the adaptive chart with respect to the operating cost and adaptive design parameters is also analyzed. An example is presented illustrating the application of the economic model. With some minor changes, the model can also be used to design a pure adaptive sample size chart or a pure adaptive sampling interval chart.