# Modeling failures times with dependent renewal type models via exchangeability

## TL;DR

This paper introduces a generalized renewal process model with exchangeable inter-arrival times to better capture dependence in failure times, especially after repairs, maintaining tractability and extending classical renewal results.

## Contribution

It proposes a novel renewal process model with exchangeable inter-arrival times, extending classical renewal theory and applying it to machinery failure data.

## Key findings

- Model captures dependence among failure times.
- Extension of renewal functions for exchangeable sequences.
- Successful application to hydraulic machinery reliability data.

## Abstract

Failure times of a machinery cannot always be assumed independent and identically distributed, e.g. if after reparations the machinery is not restored to a same-as-new condition. Framed within the renewal processes approach, a generalization that considers exchangeable inter-arrival times is presented. The resulting model provides a more realistic approach to capture the dependence among events occurring at random times, while retaining much of the tractability of the classical renewal process. Extensions of some classical results and special cases of renewal functions are analyzed, in particular the one corresponding to an exchangeable sequence driven by a Dirichlet process. The proposal is tested through an estimation procedure using simulated data sets and with an application to the reliability of hydraulic subsystems in load-haul-dump machines.