The over-adjustment means that the process is adjusted unnecessarily when a false alarm occurs. It may result in shifts in process mean and variance affecting the quality of products and have the effect of an increase in variability and cost. In this paper, the economic variable sample interval (VSI) standard and control charts are proposed to monitor effectively the mean and variance of the over-adjusted process. We use a Markov chain approach to derive the design parameters of the standard and charts by the minimum of the cost function. An example of shampoo making process is used to illustrate the application and performance of the proposed VSI standard and charts in detecting shifts in process mean and variance. Furthermore, we compare the cost and performances for the economic FSI (fixed sampling interval) and VSI control charts. Support for this research was provided in part by the National Science Council of the Republic of China, grant No. NSC 94-2118-M-004-003. / The over-adjustment means that the process is adjusted unnecessarily when a false alarm occurs. It may result in shifts in process mean and variance affecting the quality of products and have the effect of an increase in variability and cost. In this paper, the economic variable sample interval (VSI) standard and control charts are proposed to monitor effectively the mean and variance of the over-adjusted process. We use a Markov chain approach to derive the design parameters of the standard and charts by the minimum of the cost function. An example of shampoo making process is used to illustrate the application and performance of the proposed VSI standard and charts in detecting shifts in process mean and variance. Furthermore, we compare the cost and performances for the economic FSI (fixed sampling interval) and VSI control charts. Support for this research was provided in part by the National Science Council of the Republic of China, grant No. NSC 94-2118-M-004-003.

This article proposes the algorithm of a new control chart (loss function control chart) based on the Taguchi loss function with an adaptive scheme for binomial data. The loss function control chart is able to monitor cost variation from the process by applying loss function in the design. This new angle economically explores production cost. This research provides designs of the loss function control chart with specified VSI, optimal VSI, VSS and VP, respectively. Numerical analyses show that the specified VSI loss function chart, the optimal VSI loss function chart, the optimal VSS loss function chart and the optimal VP loss function chart outperform the Fp loss function chart significantly and show costs can be controlled systematically.