Optimal Scheduling of Inspections: A Delayed Markov Model with False Positives and Negatives

• Published in: Operations research Vol. 39; no. 2; pp. 261 - 273
• Main Authors: Ozekici, Suleyman, Pliska, Stanley R
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.03.1991; Operations Research Society of America; Institute for Operations Research and the Management Sciences
• Subjects: Age distribution; Applications; applications: optimal inspection schedule model; Applied sciences; Approximation; Boundary conditions; Breast cancer; diagnosis: stochastic model for optimal medical screening; Dynamic programming; dynamic programming/optimal control: semi-Markov inspection scheduling model; Exact sciences and technology; False positive errors; Health care; Markov analysis; Markov chains; Markov processes; Mathematical models; Medical screening; Operational research and scientific management; Operational research. Management science; Optimization; Patient assessment; probability; Reliability theory. Replacement problems; Scheduling; stochastic model; Stochastic models; Studies; Semimarkovian process; Inspection; Hospital environment; Scheduling; Maintenance; Dynamic programming; Optimization
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.39.2.261

A system subject to catastrophic failure deteriorates according to a delayed Markov process and is subjected to a series of binary tests that may yield false negative and false positive outcomes. A corrective action is carried out when a true positive is observed, thereby reducing the chance of system failure. Costs of inspections, false positives, the corrective action, and failure are incurred, and dynamic programming is used to compute the optimal inspection schedule. Two tractable computational methods are developed. The model, which is suited for medical screening, is applied to the problems of post-operative periumbilical pruritis and breast cancer.