Economic design of a variable sample size -chart

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Abstract
An economic design model for an -chart which uses a variable sample size feature is developed in this paper. In a variable sample size control chart the sample size at each sampling time depends on the value of the previous sample statistic, whereas the sample size is set to be fixed constant in traditional control charts. In order to detect shifts quickly, the variable sample size chart takes a larger sample if there is any indication that the process is running in an out-of-control state and a smaller sample otherwise. for practical purposes only two possible sample sizes are considered. The objective of the econo,ic design is to find the optimal sampling interval, control limit and sample sizes to minimize the expected cost per unit operating time. The determination of the optimal design requires the computation of the averge number of samples and the average number of observations taken when the process is in control and out of control. The characteristics can be computed using the Markov chain property of the control procedure. Application of the variable sample size fezture of the -chart for the case in which there are multiple assignable causes shows improved efficiency and statistical performance compared to the fixed sample size chart