Asymptotic Failure Rate Research Articles

The exact and asymptotically value of the failure rate of a parallel system

The problem of determining the failure rate of a series system according to the failure rates of the component elements is solved in the literature, a reference in the field being the work [4]. There is no direct relationship between the failure rate of a parallel system and the failure rates of the component elements. In this paper we will deduce an exact relation between the failure rate of a parallel system and the failure rates of the component elements, their reliability and the reliability of the system. Starting from the exact relationship we will deduce a simpler relation of the failure rate of a parallel system by studying the asymptotic failure rate behavior.

Asymptotic failure rates for a general class of frailty models

Abstract We elucidate the long-term behavior of failure rates for a broad class of frailty models in survival analysis. The class properly includes the proportional hazard frailty model, the additive frailty model, and the accelerated failure time frailty model. A complete asymptotic expansion is derived and compared with the corresponding result for the limiting behavior obtained by Finkelstein and Esaulova (2006a). Several examples are provided to facilitate the comparison and to illustrate both the applicability and the limitations of our approach.

The asymptotic hazard rate of sums of discrete random variables

We show that the asymptotic hazard rate of the sum of discrete random variables is dominated by the smallest asymptotic failure rate of the summands.

Risk acceptance and maintenance optimization of aging civil engineering infrastructures

The renewal model for cost-benefit optimization including maintenance is presented. Three types of maintenance strategies are proposed, i.e. age-dependent maintenance, block maintenance and maintenance by inspection and (perfect) repair. Then, new concepts for risk acceptability based on the life quality index philosophy are introduced. It is demonstrated that in limiting the failure rate three concepts can be used, the first addressing the maximum failure rate, a second using a time-average and the third an asymptotic value which may be proposed for practical use. All concepts, however, require computation of the exact failure rate (renewal intensity) or, at least, the asymptotic failure rate. A suitable asymptotic failure rate related to all corrective renewals after failure is given. A numerical example is given showing that the inspection/repair maintenance strategy is more cost-effective than the age-dependent strategy.

On asymptotic failure rates in bivariate frailty competing risks models

A bivariate competing risks problem is considered for a rather general class of survival models. The lifetime distribution of each component is indexed by a frailty parameter. Under the assumption of conditional independence of components the correlated frailty model is considered. The explicit asymptotic formula for the mixture failure rate of a system is derived. It is proved that asymptotically, as t → ∞ , the remaining lifetimes of components tend to be independent in the defined sense. Some simple examples are discussed.

Asymptotic failure rate of a continuously monitored system

This paper deals with a perfectly continuously monitored system which gradually and stochastically deteriorates. The system is renewed by a delayed maintenance operation, which is triggered when the measured deterioration level exceeds an alarm threshold. A mathematical model is developed to study the asymptotic behavior of the reliability function. A procedure is proposed which allows us to identify the asymptotic failure rate of the maintained system. Numerical experiments illustrate the efficiency of the proposed procedure and emphasize the relevance of the asymptotic failure rate as an interesting indicator for the evaluation of the control-limit preventive replacement policy.

Shock model in Markovian environment

AbstractA Markov modulated shock models is studied in this paper. In this model, both the interarrival time and the magnitude of the shock are determined by a Markov process. The system fails whenever a shock magnitude exceeds a pre‐specified level η. Nonexponential bounds of the reliability are given when the interarrival time has heavy‐tailed distribution. The exponential decay of the reliability function and the asymptotic failure rate are also considered for the light‐tailed case. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005

Markov Decision Processes with Asymptotic Average Failure Rate Constraint

In this paper, we introduce a constrained Markov Decision Process with absorbing states and periodic classes. The objective is to find a policy which maximises the infinite horizon expected average reward before the failure of the system, with a constraint on the asymptotic average failure rate. We propose an algorithm to find a stationary policy, ξ-optimal in the history dependent class. Finally, we apply the method to optimize the maintenance strategy of an aeronautical system.

Asymptotic failure rate of a Markov deteriorating system with preventive maintenance

We consider a system with a finite state space subject to continuous-time Markovian deterioration while running that leads to failure. Failures are instantaneously detected. This system is submitted to sequential checking and preventive maintenance: up states are divided into ‘good’ and ‘degraded’ ones and the system is sequentially checked through perfect and instantaneous inspections until it is found in a degraded up state and stopped to allow maintenance (or until it fails). Time between inspections is random and is chosen at each inspection according to the current degradation degree of the system. Markov renewal equations fulfilled by the reliability of the maintained system are given and an exponential equivalent is derived for the reliability. We prove the existence of an asymptotic failure rate for the maintained system, which we are able to compute. Sufficient conditions are given for the preventive maintenance policy to improve the reliability and the asymptotic failure rate of the system. A numerical example illustrates our study.

Asymptotic failure rate of a Markov deteriorating system with preventive maintenance

We consider a system with a finite state space subject to continuous-time Markovian deterioration while running that leads to failure. Failures are instantaneously detected. This system is submitted to sequential checking and preventive maintenance: up states are divided into ‘good’ and ‘degraded’ ones and the system is sequentially checked through perfect and instantaneous inspections until it is found in a degraded up state and stopped to allow maintenance (or until it fails). Time between inspections is random and is chosen at each inspection according to the current degradation degree of the system. Markov renewal equations fulfilled by the reliability of the maintained system are given and an exponential equivalent is derived for the reliability. We prove the existence of an asymptotic failure rate for the maintained system, which we are able to compute. Sufficient conditions are given for the preventive maintenance policy to improve the reliability and the asymptotic failure rate of the system. A numerical example illustrates our study.

Reliability of several component sets with inspections at random times

We consider a random process which represents a system of components with constant failure rates and subjected to inspections at times defining a renewal process. We give an analytic method for calculating the reliability function, its Laplace transform and the mean time to failure (MTTF). These formulas are computable if the Laplace transform of the inter-arrival law of the renewal process is explicit. We also study the asymptotic behavior of the reliability and determine the asymptotic failure rate of the system.

Non-ergodic Markov decision processes with a constraint on the asymptotic failure rate: general class of policies

In this paper, we introduce a Markov decision model with absorbing states and a constraint on the asymptotic failure rate. The objective is to find a policy which maximizes the infinite horizon expected average reward, given that the system never fails. First, we show that it is sufficient to consider markovian policies. Second, for solving the problem, we restrict ourselves to find a stationary policy. Finally, we give sufficient conditions for optimality in the Markovian policies class.

Markov Decision Processes with a Constraint on the Asymptotic Failure Rate

In this paper, we introduce a Markov decision model with absorbing states and a constraint on the asymptotic failure rate. The objective is to find a stationary policy which minimizes the infinite horizon expected average cost, given that the system never fails. Using Perron-Frobenius theory of non-negative matrices and spectral analysis, we show that the problem can be reduced to a linear programming problem. Finally, we apply this method to a real problem for an aeronautical system.

Reliability of a system with Poisson inspection times

For systems subject to inspections at Poisson random times, we present an analytic method which gives upper and lower bounds for the reliability. We also study its asymptotic behaviour and derive the asymptotic failure rate.

Reliability of a system with Poisson inspection times

For systems subject to inspections at Poisson random times, we present an analytic method which gives upper and lower bounds for the reliability. We also study its asymptotic behaviour and derive the asymptotic failure rate.

Reliability of a system with Poisson inspection times

For systems subject to inspections at Poisson random times, we present an analytic method which gives upper and lower bounds for the reliability. We also study its asymptotic behaviour and derive the asymptotic failure rate.

Fiabilité de plusieurs groupes de composants avec maintenance à des instants aléatoires

We consider a random process which represents the behaviour of a system of components with constant failure rates and subject to inspections at times which define a renewal process. We give an analytic method for calculating the Laplace transform of the reliability and the MTTF. We propose a frame of the same quantities for the other cases. We also study the asymptotic behaviour of the reliability and we determine the asymptotic failure rate of the system.

Asymptotic Poisson distribution for the number of system failures of a monotone system

It is well known that for highly available monotone systems, the time to the first system failure is approximately exponentially distributed. Various normalising factors can be used as the parameter of the exponential distribution to ensure the asymptotic exponentiality. More generally, it can be shown that the number of system failures is asymptotic Poisson distributed. In this paper we study the performance of some of the normalising factors by using Monte Carlo simulation. The results show that the exponential/Poisson distribution gives in general very good approximations for highly available components. The asymptotic failure rate of the system gives best results when the process is in steady state, whereas other normalising factors seem preferable when the process is not in steady state. From a computational point of view the asymptotic system failure rate is most attractive.

Semi-Markov processes for reliability studies

We study the evolution of a multi-component system which is modeled by a semi-Markov process. We give formulas for the avaibility and the reliability of the system. In the r-positive case, we prove that the quasi-stationary probability on the working states is the normalised left eigenvector of some computable matrix and that the asymptotic failure rate is equal to the absolute value of the convergence parameter r.

Some general characteristics of two-state reliability models for maintained systems

Formulas for the asymptotic failure rate, long-term average availability, and the limiting distribution of the number of long ‘outages' are obtained for a general class of two-state reliability models for maintained systems. The results extend known formulas for alternating renewal processes to a wider class of point processes that includes sequences of dependent or non-identically distributed operating and repair times.