Premium
Bias‐Corrected Estimation in Continuous Sampling Plans
Author(s) -
Decrouez Geoffrey,
Robinson Andrew
Publication year - 2018
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/risa.12811
Subject(s) - estimator , sampling (signal processing) , computer science , process (computing) , sampling bias , work (physics) , statistics , sample size determination , engineering , mathematics , mechanical engineering , filter (signal processing) , computer vision , operating system
Abstract Continuous sampling plans (CSPs) are algorithms used for monitoring and maintaining the quality of a production line. Although considerable work has been done on the development of CSPs, to our knowledge, there has been no corresponding effort in developing estimators with good statistical properties for data arising from a CSP inspection process. For example, information about the failure rate of the process will affect the management of the process, both in terms of selecting appropriate CSP parameters to keep the failure rate after inspection at a suitable level, and in terms of policy, for example, whether the process should be completely inspected, or shut down. The motivation for this exercise was developing sampling protocols for Australia's Department of Agriculture and Water Resources for monitoring the biosecurity compliance of incoming goods at international borders. In this study, we show that maximum likelihood estimation of the failure rate under a sampling scheme can be biased depending on when estimation is performed, and we provide explicit expressions for the main contribution of the bias under various CSPs. We then construct bias‐corrected estimators and confidence intervals, and evaluate their performance in a numerical study.