Incorporating Uncertainty in Diagnostic Analysis of Mechanical Systems

Abstract

The increase in complexity of modern mechanical systems can often lead to systems that are difficult to diagnose and, therefore, require a great deal of time and money to return to a normal operating condition. Analyzing mechanical systems during the product development stages can lead to systems optimized in the area of diagnosability and, therefore, to a reduction of life cycle costs for both consumers and manufacturers and an increase in the useable life of the system. A methodology for diagnostic evaluation of mechanical systems incorporating indication uncertainty is presented. First, Bayes’ formula is used in conjunction with information extracted from the Failure Modes and Effects Analysis (FMEA), Fault Tree Analysis (FTA), component reliability, and prior system knowledge to construct the Component-Indication Joint Probability Matrix (CIJPM). The CIJPM, which consists of joint probabilities of all mutually exclusive diagnostic events, provides a diagnostic model of the system. The replacement matrix is constructed by applying a predetermined replacement criterion to the CIJPM. Diagnosability metrics are extracted from a replacement probability matrix, computed by multiplying the transpose of the replacement matrix by the CIJPM. These metrics are useful for comparing alternative designs and addressing diagnostic problems of the system, to the component and indication level. Additionally, the metrics can be used to predict cost associated with fault isolation over the life cycle of the system.