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Effects of misspecification of the loss function on the economic-statistical design of the synthetic X̄ chart

The optimal choice of design parameters has a huge impact on a control chart's performance. The economic-statistical design balances the economic and statistical performance of a chart, by selecting design parameters which minimize the cost subjected to statistical constraints. To compute the quality loss as a result of deviations from the target value, quality loss functions are often used. However, practitioners may incorrectly choose the wrong type of loss function to describe the quality loss. This paper studies the effects when the type of loss function is misspecified. This study is done on the synthetic X̅ chart. We focus our attention on the linear, quadratic and exponential loss functions.