Economic Statistical Design of the Variable Sampling Interval CV Chart with Known Shift Size

Abstract

Control charts are essential in Statistical Process Control (SPC) to enhance the product quality by identifying assignable causes within the process. Extensive study on coefficient of variation (CV) charts has been conducted in recent years, indicating their growing significance in a variety of scientific applications. In order to monitor the quality characteristic, it should be noted that the statistical properties and economic perspectives are both indispensable factors. For the economic design, the optimal design parameters that minimise the expected cost function are obtained. However, this design has a major weakness, where it overlooks the statistical performance of the control chart. Therefore, it is of greater importance to examine the economic statistical design, which includes statistical constraints on the cost model. Although the existing variable sampling interval (VSI) CV chart has excellent statistical qualities, it is deficient in taking into account the economic aspects that are necessary for cost-effective process monitoring. In response, this research proposes the economic statistical design of the variable sampling interval (VSI) CV chart with known shift size. Moreover, the study includes sensitivity analyses of the optimal cost and the optimal design parameters for various input parameters. The effects of misspecification of the shift size on the performance of the VSI CV chart are investigated. Additionally, the comparisons in terms of the economic statistical performance between the VSI CV, Shewhart CV and EWMA CV charts are conducted. In comparison with Shewhart CV and EWMA CV charts, the findings clearly demonstrate that the VSI CV chart performs better in all numerical examples. As a result, this research advocates the use of the economic statistical design of the VSI CV chart in process monitoring and provides insightful information for quality practitioners seeking cost-effectiveness and optimal performance in their processes.