Bias Correction for CSP: Better Border Biosecurity Estimates

• Activity Number: 203
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 11:35 AM to 12:20 PM
• Sponsor: Quality and Productivity Section
• Author(s): Andrew Robinson* and Geoffrey Decrouez
• Companies: The University of Melbourne and
• Keywords: CSP ; Approach Rate ; Contamination

Abstract

The Continuous Sampling Plan (CSP) was designed in the 1940's for monitoring the quality of a production line. CSP is used by the Australian Department of Agriculture for monitoring the biosecurity compliance of incoming goods at international borders. CSP amounts to a sample design: it specifies the probability with which consignments should be inspected, but the probability is a function of the inspection history. The probability of contamination of a unit arriving at the border is valuable information for inspection policy. We develop and then assess the performance of maximum-likelihood estimators of the probability of non-compliance under CSP. We show that ML estimators of the probability of non-compliance at the end of a CSP cycle are biased, and we provide expressions for the main contribution of the bias. We then construct bias-corrected estimators and confidence intervals, and evaluate their performance in a numerical study. Although the methodology is presented in the context of border inspections, it can be applied in many more settings.