The effect of model misspecification of the bounded transformed gamma process on maintenance optimization

Although the degradation growth of several technological units is naturally bounded, stochastic models used to describe them are typically unbounded. In general, this manifest contradiction does not significantly affect the effectiveness of unbounded degradation models, because degrading units are conventionally considered failed when their degradation level exceeds a threshold that is far below the physical bound. Yet, this is not always the case. Motivated by these arguments, the main aim and novel contribution of this paper is investigating the impact on a condition based maintenance policy and related costs of using a degradation model that neglects the presence of the bound when it exists. In particular, the paper focuses on situations where bound and failure threshold have comparable values. The study is conducted considering as competing models a bounded and an unbounded transformed gamma. The competing models are used to formulate a condition-based maintenance policy for the liners of a marine engine. An example of application based on real data is firstly developed. Hence, the results of a Monte Carlo simulation study are presented and discussed. Obtained results highlight that, neglecting the presence of the upper bound when it really exists, can cause substantial (unnecessary) additional maintenance costs.