#### Title

Fitting a Piecewise Exponential Model for the Reliability of Repairable Systems Using Hierarchical Bayesian Approaches

#### Document Type

Presentation

#### Publication Date

10-11-2013

#### Abstract

This research develops methods for Bayesian analysis of a general piecewise exponential model for the reliability of multiple repairable systems. Common approaches to this problem model the expected time between failures using a geometric type sequence. In this research we consider generalizing this model, so that the expected time between failures is a monotone sequence. The model is then fit using hierarchical Bayesian approaches. The ordering of the mean time between failures is implemented into the model by considering prior distributions on the ordered subset of the parameter space. We also consider model selection problems concerning the validity of the monotonicity of the expected time between failures as well as the validity of a common parametric model for the monotone sequence. The methods are demonstrated on a well-known example concerning the reliability of mining equipment.

#### Sponsorship/Conference/Institution

International Conference on Statistical Distributions and Applications (ICSDA)

#### Location

DeKalb, IL

#### Recommended Citation

Chatterjee, Arpita.
2013.
"Fitting a Piecewise Exponential Model for the Reliability of Repairable Systems Using Hierarchical Bayesian Approaches."
*Mathematical Sciences Faculty Presentations*.
Presentation 91.

https://digitalcommons.georgiasouthern.edu/math-sci-facpres/91