An economic-statistical design of synthetic Tukey’s control chart with Taguchi’s asymmetric loss functions under log-normal distribution

Abstract

The synthetic Tukey’s control chart (denoted by Syn-TCC) applies a single observation in the process monitoring and is relatively robust to outliers. For a complex process, the probability distribution of quality characteristic must be carefully identified and the loss of quality characteristic, which is defined as the deviation from the target value, must be accurately estimated so that the quality state of the process may be more comprehensively described. However, the literature rarely studied the economic design of the Syn-TCC with Taguchi’s loss function under non normality. In the present study, it is assumed that the quality characteristic follows a log-normal distribution and Taguchi’s asymmetric linear and quadratic loss functions are involved to develop the economic-statistical design of the Syn-TCC for multiple assignable causes. A case study is presented to illustrate the application of this economic-statistical design of the Syn-TCC to an IC package industry. The sensitivity analysis of this case study reveals that a larger production lot size and larger two coefficients of loss functions generally lead to a higher total expected cost.