Improved method of estimating the product quality after multiple inspections

Abstract

A complex product is often inspected more than once in a sequential manner to ensure the product’s quality. Based on the number of defects discovered during each round of inspection process, we can estimate the number of defects still remaining in the product. For each defect, the probability that the defect will be detected during each inspection cycle is usually assumed to be a known ‘constant’. However, in many practical situations, some defects are easily detected, while others are much more difficult to identify. In this paper, we propose a ‘beta-geometric’ inspection model in which the heterogeneity in detection probability is described by a beta distribution. In a numerical study, we show that our more realistic inspection model clearly outperforms traditional estimation methods that are based on the assumption of a constant detection probability.

Keywords:

• inspection
• product quality
• reliability
• maximum likelihood estimation

Acknowledgements

I’d like to express my gratitude for the financial support from Cherie H. Flores Endowed Chair of MBA Studies at Louisiana State University. I’d also like to express my sincere thanks to two anonymous referees and Associate Editor for their thorough and knowledgeable reviews that helped me improve the original manuscript significantly.

Disclosure statement

No potential conflict of interest was reported by the author.