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Estimating a Parametric Component Lifetime Distribution from a Collection of Superimposed Renewal Processes

Summary: [This abstract is based on the authors' abstract.] Maintenance data can be used to make inferences about the lifetime distribution of system components. Typically, a fleet contains multiple systems.Within each system, there is a set of nominally identical replaceable components of particular interest (e.g., 2 automobile headlights, 8 dual in-line memory module (DIMM) modules in a computing server, 16 cylinders in a locomotive engine). For each component replacement event, there is system-level information that a component was replaced, but no information on which particular component was replaced. Thus, the observed data are a collection of superpositions of renewal processes (SRP), one for each system in the fleet. This article proposes a procedure for estimating the component lifetime distribution using the aggregated event data from a fleet of systems. We show how to compute the likelihood function for the collection of SRPs and provide suggestions for efficient computations. We compare performance of this incomplete-data maximum likelihood (ML) estimator with the complete data ML estimator and study the performance of confidence interval methods for estimating quantiles of the lifetime distribution of the component. Supplementary materials for this article are available online.

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  • Topics: Engineering
  • Keywords: Approximation, Renewal process, Simulations, Weibull distribution, Maintenance
  • Author: Ye Tian, Wei Zhang; Escobar, Luis A.; Meeker, William Q.;
  • Journal: Technometrics