The Economic Design of the Double Sampling X Chart with Measurement Errors

Abstract

Objective: The purpose of this study is to investigate the effect of measurement errors on the economic design of the double sampling (DS) X chart. Methods/Statistical analysis: The economic design of the DS X chart with measurement errors is investigated by using the linear covariate error model. The optimal design parameters of the DS X chart are determined through the minimization of the cost function. The effect of the measurement errors is evaluated based on the numerical example over a wide range of the parameters of the measurement errors, where the parameters of the measurement errors are the coefficient B and the measurement error ratio. Findings: The numerical results show that an increase in the value of the coefficient B or a decrease in the value of the measurement error ratio in the linear covariate error model leads to the lower false alarm rate and cost with more frequent sampling interval and 260 K. S. Khee Yong Si et al smaller number of multiple measurements per item. It can be noticed that the sample sizes at the first and second stages of the DS scheme as well as the out-of-control statistical performance of the DS X chart are robust to the measurement errors. In addition, the warning and control limits of the DS X chart are also not affected by the measurement errors. Application/Improvements: An example is provided to illustrate the implementation of the economic design of the DS X chart with measurement errors.