Condition-based maintenance policies and some properties of geometric-like processes

This thesis proposes maintenance polices from different conditions in real life and investigates some properties of geometric-like processes so that the economic impact due to the failures of a technical system can be reduced. Therefore, this thesis consists of two parts. Part A involves Chapter 3 and Chapter 4, which optimises maintenance policies for two scenarios. Scenario 1 aims at deriving maintenance policies for k-out-of-n technical systems, where the degradation process of each component is modelled by the gamma process and the uncertainties of models and their parameters, along with the expected maintenance cost of the maintenance policy, are regarded as model choice criteria in maintenance policy optimisation. Scenario 2 aims at optimising maintenance policies for multi-component systems and compares the maintenance policies under four cases, where the degradation process of each component is modelled by the Wiener process and the system fails when a linear combination of the degradation levels of the components exceeds a pre-specified value. Part B involves Chapter 5 and Chapter 6, which investigates the impact of the uncertainty of the parameter estimation of an extension of the geometric process (GP) on the expected maintenance cost, derives the least square estimation method for another extension of the GeP, and then compares the goodness-of-fit of seven GP-like models on twenty-five real datasets. As such, the main contributions of this thesis include the following:

• A multi-criteria model-selecting method of k-out-of-n system for maintenance policy optimisation is proposed, where the degradation process of each component in the system is modelled by the gamma process.

• It proposes a maintenance policy for a multi-component system in which the degradation level of each component is modelled with a Wiener process and the system is said "failed" once a weighted linear combination of the degradation level of the components exceeds a pre-specified value. The proposed maintenance policy is compared with four other maintenance policies.

• Sensitivity analysis due to the uncertainty of the parameter estimation of an extension of the geometric process is carried out. The impact of the uncertainty on the expected cost ratio and the optimal PM (preventive maintenance) intervals is analysed.

• The least square method for estimating the parameters in an extension of the geometric process is derived and the performance of the goodness-of-fit of the geometric process and six of its extensions on twenty-five real-world datasets are compared.