I. T. Castro

A periodic inspection and replacement policy for systems subject to competing failure modes due to degradation and traumatic events

Abstract This paper deals with the condition-based maintenance of single-unit systems which are subject to the competing and dependent failures due deterioration and traumatic shock events. The main aim is to provide a model to assess the value of condition monitoring information for the maintenance decision-making. A condition-based periodic inspection/replacement policy is developed and compared with a benchmark time-based block replacement policy. Numerical results show that it is indeed useful to follow closely the actual evolution of the system to adapt the maintenance decisions to the true system state to improve the performance of maintenance policies. The analysis of the maintenance costs savings can be used to justify or not the choice to implement a policy based on condition monitoring information and to invest in condition monitoring devices.

Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks

This paper deals with maintenance strategies with minimal repairs for single-unit repairable systems which are subject to competing and dependent failures due to degradation and traumatic shocks. The main aims are to study different approaches for making a minimal repair decision (i.e. time-based or condition-based) which is a possible corrective maintenance action under the occurrence of shocks, and to show under a given situation which approach can lead to a greater saving in maintenance cost. Two age-based maintenance policies with age-based minimal repairs and degradation-based minimal repairs are modeled, and their performance is compared with a classical pure age-based replacement policy without minimal repairs. Numerical results show the cost saving of the maintenance policies and allow us to make some conclusions about their performance under different situations of system characteristic and maintenance costs. It is shown that carrying out minimal repairs is useful in many situations to improve the performance of maintenance operations. Moreover, the comparison of optimal maintenance costs incurred by both maintenance policies with minimal repairs allows us to justify the appropriate conditions of time-based minimal repair approach and condition-based minimal approach.

A condition-based maintenance of a dependent degradation-threshold-shock model in a system with multiple degradation processes

This paper proposes a condition-based maintenance strategy for a system subject to two dependent causes of failure: degradation and sudden shocks. The internal degradation is reflected by the presence of multiple degradation processes in the system. Degradation processes start at random times following a Non-homogeneous Poisson process and their growths are modelled by using a gamma process. When the deterioration level of a degradation process exceeds a predetermined value, we assume that a degradation failure occurs. Furthermore, the system is subject to sudden shocks that arrive at the system following a Doubly Stochastic Poisson Process. A sudden shock provokes the total breakdown of the system. Thus, the state of the system is evaluated at inspection times and different maintenance tasks can be carried out. If the system is still working at an inspection time, a preventive maintenance task is performed if the deterioration level of a degradation process exceeds a certain threshold. A corrective maintenance task is performed if the system is down at an inspection time. A preventive (corrective) maintenance task implies the replacement of the system by a new one. Under this maintenance strategy, the expected cost rate function is obtained. A numerical example illustrates the analytical results.

A model of imperfect preventive maintenance with dependent failure modes

Consider a system subject to two modes of failures: maintainable and non-maintainable. A failure rate function is related to each failure mode. Whenever the system fails, a minimal repair is performed. Preventive maintenances are performed at integer multiples of a fixed period. The system is replaced when a fixed number of preventive maintenances have been completed. The preventive maintenance is imperfect because it reduces the failure rate of the maintainable failures but does not affect the failure rate of the non-maintainable failures. The two failure modes are dependent in the following way: after each preventive maintenance, the failure rate of the maintainable failures depends on the total of non-maintainable failures since the installation of the system. The problem is to determine an optimal length between successive preventive maintenances and the optimal number of preventive maintenances before the system replacement that minimize the expected cost rate. Optimal preventive maintenance schedules are obtained for non-decreasing failure rates and numerical examples for power law models are given.

A condition-based maintenance for a system subject to multiple degradation processes and external shocks

This paper analyses a condition-based maintenance for a system subject to different competing failure modes: internal degradation and external shocks. Internal degradation is the result of the arrival to the system of multiple cracks that grow according to stochastic deterioration processes. External shocks arrive to the system at random times and provoke the system failure. A condition-based maintenance model with periodic inspection times is developed for this competing failure model. Under this maintenance strategy, a preventive replacement is performed when the degradation level of a given crack in an inspection time exceeds a predetermined threshold. A corrective replacement is performed when the system is failed in an inspection time. Under this maintenance scheme, the expression of the expected cost rate is obtained. A numerical example illustrates the maintenance model.

A delay-time model with safety constraint

Abstract We consider the basic delay-time model in which a system has three states, the perfect functioning state, a defective state and the failure state. The system is deteriorating and to reduce the number of failures, preventive replacements are carried out when the system is in the defective state. The time in the defective state is referred to as the delay time. Inspections are required to check whether the system is in the defective state. System failures are safety critical and to control the risk, management considers two types of safety constraints: (i) the probability of at least one failure in the interval [ 0 , A ] should not exceed a fixed probability ω 1 and (ii) the fraction of time the system is in the defective state should not exceed a fixed limit ω 2 . The problem is to determine optimal inspection intervals T, minimizing the expected discounted costs under the safety constraints. Conditions are established for when the safety constraints affect the optimal inspection time and causes increased costs.

Reward optimization of a repairable system

This paper analyzes a system subject to repairable and non-repairable failures. Non-repairable failures lead to replacement of the system. Repairable failures, first lead to repair but they lead to replacement after a fixed number of repairs. Operating and repair times follow phase type distributions (PH-distributions) and the pattern of the operating times is modelled by a geometric process. In this context, the problem is to find the optimal number of repairs, which maximizes the long-run average reward per unit time. To this end, the optimal number is determined and it is obtained by efficient numerical procedures.

Age-based preventive maintenance for passive components submitted to stress corrosion cracking

This paper deals with an age-based preventive maintenance for critical systems or structures subject to a gradual degradation phenomenon such as stress corrosion cracking. We analyze a system subjected to different cracks. A crack can be only detected when its length exceeds a detection threshold. When the length of the crack reaches a given threshold, the system fails. The length of the crack is modeled using a gamma process. Furthermore, when the number of cracks detected in the system attains a fixed value, the system fails. Corrective maintenance actions are performed after a system failure. A preventive maintenance is performed when the age of the system is T. Maintenance actions replace the system by a new one with an associated cost. The problem is to determine an optimal planned replacement time T, minimizing the expected cost rate of the system. The analytical solution to the problem is obtained under some general assumptions. A numerical example is shown to illustrate the problem.

On the Use of Mean Residual Life as a Condition Index for Condition-Based Maintenance Decision-Making

This paper provides a methodology to analyze the efficiency of mean residual life in condition-based maintenance decision-making. A degradation-threshold-dependent-shock model is used to describe the evolution of a system subject to the dependent and competing failure modes due to degradation and shock. Based on this model, we compute the mean residual life of system and analyze its monotonicity. This property of mean residual life function allows introducing a new condition-based maintenance strategy whose preventive maintenance decision is based on the mean residual life. The proposed strategy is then compared to a maintenance strategy based on the degradation level only. Analyzing the equivalence, the performance and the flexibility of both strategies allow us to give some conclusions on the interest of the mean residual life as a condition index for maintenance decision-making.

Bias of the Maximum Likelihood Doa Estimation from Inaccurate Knowledge of the Antenna Array Response

The estimators of directions of arrival of narrow-band signals using array antennas could be erroneous if we do not model adequately the behaviour of the global antenna system (for example, incorrect modeling of the mutual coupling or coupling of the antennas with the platform). In this paper we obtain an expression for evaluating the bias of the Maximum Likelihood estimators if we model incorrectly the behaviour of the antenna. The results indicate that if we consider an onboard array antenna as an ideal system (without electromagnetic effects) the performance of a direction of arrivals (DOA) estimation system may be degradated.