Load-dependent machine failures in production network models

TL;DR

This paper introduces a stochastic production model with load-dependent machine failures, combining deterministic and Markov process theories, and compares it to load-independent models through numerical analysis.

Contribution

It develops a novel load-dependent failure model based on differential equations and Markov processes, extending existing load-independent models.

Findings

Load-dependent failures exhibit different dynamics than load-independent ones.

The model is well-posed and mathematically rigorous.

Numerical examples demonstrate the impact of load dependence on production reliability.

Abstract

In this paper, a production model based on (hyperbolic) differential equations with stochastic and load-dependent machine failures is introduced. We derive the model on the base of a well-established deterministic model and show its well-posedness. To do so, we make use of the theory of piecewise deterministic Markov processes and fuse it with the theory of the underlying deterministic production model. Finally, we compare the load-dependent model to the already established load-independent model and highlight the new properties in numerical examples.