Modeling Repairs of Systems with a Bathtub-Shaped Failure Rate Function

TL;DR

This paper introduces a new repair modeling approach for systems with non-monotonic, bathtub-shaped failure rates, extending reliability analysis beyond traditional monotonic failure rate assumptions.

Contribution

It proposes a novel repair model based on modifications to the virtual age function for systems with bathtub-shaped failure rates, maintaining standard repair definitions.

Findings

The model accommodates non-monotonic failure rates.

It distinguishes between repair types and replacements.

Numerical illustration demonstrates the model's application.

Abstract

Most of the reliability literature on modeling the effect of repairs on systems assumes the failure rate functions are monotonically increasing. For systems with non-monotonic failure rate functions, most models deal with minimal repairs (which do not affect the working condition of the system) or replacements (which return the working condition to that of a new and identical system). We explore a new approach to model repairs of a system with a non-monotonic failure rate function; in particular, we consider systems with a bathtub-shaped failure rate function. We propose a repair model specified in terms of modifications to the virtual age function of the system, while preserving the usual definitions of the types of repair (minimal, imperfect and perfect repairs) and distinguishing between perfect repair and replacement. In addition, we provide a numerical illustration of the proposed repair model.