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Maintenance policy for a system with a weighted linear combination of degradation processes

Shaomin Wu, Inma T. Castro

TL;DR

The main objective of this paper is to optimise the time between preventive maintenance actions and the number of the preventive maintenance.

Abstract

This paper develops maintenance policies for a system under condition monitoring. We assume that a number of defects may develop and the degradation process of each defect follows a gamma process, respectively. The system is inspected periodically and maintenance actions are performed on the defects present in the system. The effectiveness of the maintenance is assumed imperfect and it is modelled using a geometric process. By performing these maintenance actions, different costs are incurred depending on the type and the degradation levels of the defects. Furthermore, once a linear combination of the degradation processes exceeds a pre-specified threshold, the system needs a special maintenance and an extra cost is imposed. The system is renewed after several preventive maintenance activities have been performed. The main concern of this paper is to optimise the time between renewals and the number of renewals. Numerical examples are given to illustrate the results derived in the paper.

Maintenance policy for a system with a weighted linear combination of degradation processes

TL;DR

The main objective of this paper is to optimise the time between preventive maintenance actions and the number of the preventive maintenance.

Abstract

This paper develops maintenance policies for a system under condition monitoring. We assume that a number of defects may develop and the degradation process of each defect follows a gamma process, respectively. The system is inspected periodically and maintenance actions are performed on the defects present in the system. The effectiveness of the maintenance is assumed imperfect and it is modelled using a geometric process. By performing these maintenance actions, different costs are incurred depending on the type and the degradation levels of the defects. Furthermore, once a linear combination of the degradation processes exceeds a pre-specified threshold, the system needs a special maintenance and an extra cost is imposed. The system is renewed after several preventive maintenance activities have been performed. The main concern of this paper is to optimise the time between renewals and the number of renewals. Numerical examples are given to illustrate the results derived in the paper.
Paper Structure (23 sections, 2 theorems, 63 equations, 5 figures)

This paper contains 23 sections, 2 theorems, 63 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Assumptions
  3. Model development
  4. Modelling the occurrences of the defects
  5. Degradation processes
  6. First hitting time
  7. The process of repair cost
  8. Incorporating random effect
  9. First hitting time
  10. Maintenance Policies
  11. Special cases
  12. Special cases of $c_{k,y}$
  13. Special cases of $a_1(T)$, $a_2(T)$, and $\alpha_k(T)$
  14. Economic constraint analysis
  15. Numerical examples
  16. ...and 8 more sections

Key Result

Lemma 1

The conditional probability $f_{U(t)|Y(t)}(y,z)$ is given by

Figures (5)

  • Figure 1: Degradation processes and a linear combination
  • Figure 2: Expected cost $\mathrm{Q}_0(N,T)$ versus $N$ and $T$.
  • Figure 3: Variable cost $\mathrm{CV}(N,T)$ versus $N$ and $T$.
  • Figure 4: Variable cost $\mathrm{CV}(N,T)$ versus $T$.
  • Figure 5: Expected cost rate $\mathrm{Q}_0(N,T)$ versus $T$ in $\Omega$.

Theorems & Definitions (6)

  • Example 1
  • Lemma 1
  • proof
  • Definition 1
  • Lemma 2
  • proof