The Optimum Combination of Full System and Subsystem Tests for Estimating the Reliability of a System

• Activity Number: 565
• Type: Contributed
• Date/Time: Thursday, August 6, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Coire J. Maranzano*+ and James C. Spall
• Companies: Johns Hopkins University Applied Physics Laboratory and Johns Hopkins University Applied Physics Laboratory
• Keywords: Reliability ; Test Sizing ; Model Bias ; Mean-Squared Error ; Maximum Likelihood Estimation

Abstract

This paper develops a method for finding an optimum test plan, which consists of a mixture of full system and subsystem tests, to estimate the reliability of a system. An optimum test plan is developed by trading off the number of full system and subsystem tests to minimize the mean-squared error (MSE) of the maximum likelihood estimate (MLE) of system reliability and testing costs. The MSE is decomposed into a the variance of the MLE and a bias from incorrectly specifying the function that relates the subsystem reliabilities to the full system reliability (series, parallel, other). The variance of the MLE comes from Fisher theory. The bias is due to the modeling error. Optimum test plans involve tradeoffs between the MSE (estimation accuracy), the degree of modeling error, and the cost of doing system and subsystem tests. A Pareto frontier can be identified, as illustrated in the paper.