Visualizing uncertainty in reliability functions with application to aero engine overhaul

• Published in: Applied statistics Vol. 59; no. 1; pp. 163 - 173
• Main Authors: Ebden, Mark, Stranjak, Armin, Roberts, Stephen
• Format: Journal Article
• Language: English
• Published: Oxford, UK Oxford, UK : Blackwell Publishing Ltd 2010; Blackwell Publishing Ltd; Wiley-Blackwell; Royal Statistical Society; Oxford University Press
• Series: Journal of the Royal Statistical Society Series C
• Subjects: Aerospace industry; Air transport; Applications; Audiovisual material; Censored data; Censorship; Confidence interval; Datasets; Density estimation; Engineering; Engines; Estimate reliability; Exact sciences and technology; Global analysis, analysis on manifolds; Jet engines; Mathematics; Mixed Weibull distribution; Model uncertainty; Nonparametric inference; Parametric models; Probability and statistics; Probability theory and stochastic processes; Reliability functions; Reliability, life testing, quality control; Sciences and techniques of general use; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Statistical methods; Statistics; Studies; Survival analysis; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Weibull mixture model; Censored data; Mixed distribution; Hazard function; Censored sample; Reliability theory; Statistical estimation; Life test; Statistics; Industry; Statistical method; Survival analysis; Engineering; Database; Mixed Weibull distribution; Reliability; Weibull distribution; Model uncertainty; Application; Weibull mixture model
• ISSN: 0035-9254; 1467-9876
• DOI: 10.1111/j.1467-9876.2009.00692.x

We propose an approach for estimating the date of lost confidence of jet engines, which are devices with multiple components subject to disruption. A mixed Weibull distribution is estimated from a large data set subject to censoring at various times. Parametric uncertainty is derived analytically and mapped visually onto the functions of use in reliability theory, including the hazard function. We demonstrate the use of the method on a database of disruption times for components in 325 jet engines.