Economic design of VSI GCCC charts for correlated samples

Abstract

Generalised cumulative count of conforming (GCCC) charts have been proposed for monitoring a high-yield process that allows the items to be inspected sample by sample and not according to the production order. Recent study has shown that the GCCC chart with a variable sampling interval (VSI) is superior to the traditional one with a fixed sampling interval (FSI) because of the additional flexibility of sampling interval it offers. However, the VSI chart is still costly when used for the prevention of defective products. This paper presents an economic model for the design problem of the VSI GCCC chart, taking into account the correlation of the production outputs within the same sample. In the economic design, a cost function is developed that includes the cost of sampling and inspection, the cost of false alarms, the cost of detecting and removing the assignable cause, and the cost when the process is out-of-control. An evolutionary search method using the cost function is presented for finding the optimal design parameters of the VSI GCCC chart. Comparisons between VSI and FSI charts for expected cost per unit time are also made for various process and cost parameters.

Keywords

• Economic design
• cumulative conformance count
• variable sampling interval
• Markov chain