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A dependent complex degrading system with non-periodic inspection times

Inma T. Castro, L. Landesa

TL;DR

This work addresses reliability for a system subject to multiple interdependent degradation processes that initiate randomly in time and propagate with gamma increments. It introduces a dynamic non-periodic inspection policy, where the next inspection time depends on the current degradation state and the number of active processes, and analyzes maintenance via a semi-regenerative framework. Key contributions include analytic survival and reliability bounds for a dependent NHPP-GP model, the characterization of a stationary distribution for post-inspection states, and a renewal-based long-run cost minimization over inspection timing and preventive thresholds (with extensions to joint optimization over an additional shaping parameter). Numerical examples illustrate policy performance under realistic parameter settings and demonstrate practical guidance for inspection scheduling and maintenance decisions. The methodology provides a tractable approach to aging systems with interacting degradation sources and offers directions for incorporating coalescence and heterogeneous degradation mechanisms in future work.

Abstract

This paper analyses a system subject to multiple dependent degradation processes. Degradation processes start at random times following a non homogeneous Poisson process and next dependently propagate. The growth of these degradation processes is modeled using gamma increments. We assume that the arrival of a new process to the system triggers the degradation rate of the processes present in the system. Under this framework, the analytic expression of the system reliability is obtained and bounds of the system reliability are also analyzed. Furthermore, the system is inspected at certain times. Information on the system health is recorded at these inspection times and the decision on performing maintenance actions on the system is taken at these times. We consider in this paper a dynamic inspection policy since the information that becomes available in an inspection time is taken into account to schedule the next inspection time. The maintenance cost for this system is dealt with the use of semi-regenerative process. Numerical examples are performed to illustrate the analytic expressions.

A dependent complex degrading system with non-periodic inspection times

TL;DR

This work addresses reliability for a system subject to multiple interdependent degradation processes that initiate randomly in time and propagate with gamma increments. It introduces a dynamic non-periodic inspection policy, where the next inspection time depends on the current degradation state and the number of active processes, and analyzes maintenance via a semi-regenerative framework. Key contributions include analytic survival and reliability bounds for a dependent NHPP-GP model, the characterization of a stationary distribution for post-inspection states, and a renewal-based long-run cost minimization over inspection timing and preventive thresholds (with extensions to joint optimization over an additional shaping parameter). Numerical examples illustrate policy performance under realistic parameter settings and demonstrate practical guidance for inspection scheduling and maintenance decisions. The methodology provides a tractable approach to aging systems with interacting degradation sources and offers directions for incorporating coalescence and heterogeneous degradation mechanisms in future work.

Abstract

This paper analyses a system subject to multiple dependent degradation processes. Degradation processes start at random times following a non homogeneous Poisson process and next dependently propagate. The growth of these degradation processes is modeled using gamma increments. We assume that the arrival of a new process to the system triggers the degradation rate of the processes present in the system. Under this framework, the analytic expression of the system reliability is obtained and bounds of the system reliability are also analyzed. Furthermore, the system is inspected at certain times. Information on the system health is recorded at these inspection times and the decision on performing maintenance actions on the system is taken at these times. We consider in this paper a dynamic inspection policy since the information that becomes available in an inspection time is taken into account to schedule the next inspection time. The maintenance cost for this system is dealt with the use of semi-regenerative process. Numerical examples are performed to illustrate the analytic expressions.
Paper Structure (9 sections, 7 theorems, 83 equations, 8 figures)

This paper contains 9 sections, 7 theorems, 83 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Probabilistic modeling
  3. System reliability
  4. System reliability in a degraded system
  5. Non-periodic inspection times
  6. Stationary distribution
  7. Optimal maintenance policy
  8. Numerical examples
  9. Conclusions and further works

Key Result

Lemma 1

The expectation of the process $\left\{W_j(t), t \geq 0\right\}$ given by Equations (Wj) and (WN) is equal to for $j=1, 2, \ldots$.

Figures (8)

  • Figure 1: Simulation of a dependent NHPP-GP
  • Figure 2: Average degradation for different processes versus $t$
  • Figure 3: Survival function of crack detection
  • Figure 4: Mean time between inspections for different values of $k$
  • Figure 5: Histograms for a sample of $\pi$
  • ...and 3 more figures

Theorems & Definitions (18)

  • Example 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Example 2
  • Lemma 4
  • proof
  • ...and 8 more