Application of Cost Matrices and Cost Curves to Enhance Diagnostic Health Management Metrics for Gas Turbine Engines

Abstract

Statistically based metrics, incorporating operating costs, for gas turbine engine diagnostic systems are required to evaluate competing products fairly and to establish a convincing business case. Diagnostic algorithm validation often includes engine testing with implanted faults. The implantation rate is rarely, if ever, representative of the true fault occurrence rate and the sample size is very small. Costs related to diagnostic outcomes have a significant effect on the utility of a given algorithm and need to be incorporated into the assessment. Techniques for assessing diagnostics are drawn from the literature and modified for application to gas turbine applications. The techniques are modified with computational experiments and the application demonstrated through examples. New techniques are compared to the traditional methods and the advantages presented. A technique is presented to convert a confusion matrix with a non-representative fault distribution to one representative of the expected distribution. The small sample size associated with fault implantation studies requires a confidence interval on the results to provide valid comparisons and a method for calculating confidence intervals, including on zero entries, is presented. Receiver operating characteristic (ROC) curves evaluate diagnostic system performance across a range of threshold settings. This allows an algorithm’s ability to be assessed over a range of possible usage. Cost curves are analogous to ROC curves but offer several advantages. The techniques for applying cost curves to diagnostic algorithms are presented and their advantages over ROC curves are outlined. This paper provides techniques for more informed comparison of diagnostic algorithms, possibly preventing incorrect assessment due to small sample sizes.