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1 Management and Production Engineering Review

1 2016

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Economic statistical design of variable sampling interval X̅ control chart based on surrogate variable using genetic algorithms

Lee T.-H., Hong S.-H., Kwon H.-M., Lee M.

Management and Production Engineering Review

2016

Vol. 7, No. 4

54--64

In many cases, a X̅ control chart based on a performance variable is used in industrial fields. Typically, the control chart monitors the measurements of a performance variable itself. However, if the performance variable is too costly or impossible to measure, and a less expensive surrogate variable is available, the process may be more efficiently controlled using surrogate variables. In this paper, we present a model for the economic statistical design of a VSI (Variable Sampling Interval) X̅ control chart using a surrogate variable that is linearly correlated with the performance variable. We derive the total average profit model from an economic viewpoint and apply the model to a Very High Temperature Reactor (VHTR) nuclear fuel measurement system and derive the optimal result using genetic algorithms. Compared with the control chart based on a performance variable, the proposed model gives a larger expected net income per unit of time in the long-run if the correlation between the performance variable and the surrogate variable is relatively high. The proposed model was confined to the sample mean control chart under the assumption that a single assignable cause occurs according to the Poisson process. However, the model may also be extended to other types of control charts using a single or multiple assignable cause assumptions such as VSS (Variable Sample Size) X̅ control chart, EWMA, CUSUM charts and so on.