Inference Based on Data from Superpositions of Renewal Processes

• Activity Number: 298
• Type: Topic Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): William Meeker* and Ye Tian and Luis Escobar
• Companies: Iowa State University and Facebook and Louisiana State University
• Keywords: Maintenance Data ; Maximum likelihood ; Recurrence data ; Reliability ; Weibull

Abstract

This paper proposes a procedure for estimating the component lifetime distribution using the aggregated event data from a fleet of systems. Typically a fleet contains multiple systems, with each system a set of identical replaceable components. For each component replacement event, we have the system-level information that components were replaced, but do not know which particular components in the system were replaced. Thus the observed data is a collection of superpositions of renewal processes (SRP), one for each system in the fleet. We show how to compute the likelihood function for the SRP and provide suggestions for more efficient computations. We compare performance of this incomplete-data ML estimator with an alternative method that is based on a nonhomogeneous Poisson process approximation and with the complete-data ML estimator.