Element Failure Rate Research Articles

Real Time Reliability Study of a Model with Increasing Failure Rates

This paper deals with a system with elements with one element is the main element and the other elements are the spare parts of the main element. If one element fails, one of the spare parts starts working immediately. The failure rate of non working elements are zero and the failure rate of working element is time dependent as and the failed elements are not repairable. The system works until all elements failed. In the second part of this paper the differential equations between the state of the system are established and by solving this equation the reliability function of the system () is calculated. In the third part, a numerical example solved to determine the parameters of the system. Nomenclature The notations used in this paper are as follows: : Number of elements, : Failure rate of each element at time, : Probability that the system is in state with spare element at time, : Probability that system works at time, : Mean time to failure of the system,

Fast Simulation of Service Availability in Mesh Networks With Dynamic Path Restoration

A fast simulation technique based on importance sampling is developed for the analysis of path service availability in mesh networks with dynamic path restoration. The method combines the simulation of the path rerouting algorithm with a “dynamic path failure importance sampling” (DPFS) scheme to estimate path availabilities efficiently. In DPFS, the failure rates of network elements are biased at increased rates until path failures are observed under rerouting. The simulated model uses “failure equivalence groups,” with finite/infinite sources of failure events and finite/infinite pools of repair personnel, to facilitate the modeling of bidirectional link failures, multiple in-series link cuts, optical amplifier failures along links, node failures, and more general geographically distributed failure scenarios. The analysis of a large mesh network example demonstrates the practicality of the technique.

Asymptotic methods in reliability theory: a review

Section 1 of this paper reviews some works related to reliability evaluation of systems without repair. The assumption that element failure rates are low enables one to obtain an expression for the main term in the asymptotic representation of system reliability function. Section 2 is devoted to repairable systems. The main index of interest in reliability is the time to the first system failure. A typical situation in reliability is that the repair time is much smaller than the element lifetime. This ‘fast repair' property leads to an interesting phenomenon, that for many renewable systems the time to system failure converges in distribution, under appropriate norming, to an exponential random variable. Some basic theorems explaining this fact are presented and a series of typical examples is considered. Special attention is paid to reviewing the works describing the exponentiality phenomenon in birth-and-death processes. Some important aspects of computing the normalizing constants are considered, among them the role played by the so-called ‘main event'. Section 2 also reviews various bounds on the deviation from exponentiality. Section 3 gives brief comments on some works and techniques related to asymptotic reliability analysis. In particular, attention is paid to the works presenting upper and lower bounds on the reliability function. A considerable part of this review is based on sources originally published in Russian.

Asymptotic methods in reliability theory: a review

Section 1 of this paper reviews some works related to reliability evaluation of systems without repair. The assumption that element failure rates are low enables one to obtain an expression for the main term in the asymptotic representation of system reliability function. Section 2 is devoted to repairable systems. The main index of interest in reliability is the time to the first system failure. A typical situation in reliability is that the repair time is much smaller than the element lifetime. This ‘fast repair' property leads to an interesting phenomenon, that for many renewable systems the time to system failure converges in distribution, under appropriate norming, to an exponential random variable. Some basic theorems explaining this fact are presented and a series of typical examples is considered. Special attention is paid to reviewing the works describing the exponentiality phenomenon in birth-and-death processes. Some important aspects of computing the normalizing constants are considered, among them the role played by the so-called ‘main event'. Section 2 also reviews various bounds on the deviation from exponentiality. Section 3 gives brief comments on some works and techniques related to asymptotic reliability analysis. In particular, attention is paid to the works presenting upper and lower bounds on the reliability function.A considerable part of this review is based on sources originally published in Russian.

Confidence Limits for Highly Reliable Coherent Systems with Exponentially Distributed Component Life

Abstract A method for constructing upper confidence limits (UCL's) for parametric functions of type g(λ) = Σ j Π i∈Ij λ i is considered. It is based on maximization of g(λ) over a confidence set of type {λ | Σ λiTi ≤ Λα & λ i ≥ 0} obtained by pooling statistical data received from separate testing of system components. An asymptotic representation of the reliability function of an arbitrary coherent system is given assuming that the element failure rates are low. It has the form R(t) ≈ 1 - exp (– trg(λ)) and, therefore, a UCL g* for g(λ) provides a lower confidence limit (LCL) for R(t). Explicit formulas are presented for parallel, series-parallel, and k-out-of-n systems, for two types of statistical test data, namely, testing over a given time period and testing until a prescribed number of failures appear. The performance of the method is discussed in terms of two characteristics: the average value of g*/g(λ) and the true confidence coefficient P{g* ≥ g(λ)}.

Confidence Limits for Highly Reliable Coherent Systems with Exponentially Distributed Component Life

Abstract A method for constructing upper confidence limits (UCL's) for parametric functions of type g(λ) = Σ j Π i∈Ij λ i is considered. It is based on maximization of g(λ) over a confidence set of type {λ | Σ λiTi ≤ Λα & λ i ≥ 0} obtained by pooling statistical data received from separate testing of system components. An asymptotic representation of the reliability function of an arbitrary coherent system is given assuming that the element failure rates are low. It has the form R(t) ≈ 1 - exp (– trg(λ)) and, therefore, a UCL g* for g(λ) provides a lower confidence limit (LCL) for R(t). Explicit formulas are presented for parallel, series-parallel, and k-out-of-n systems, for two types of statistical test data, namely, testing over a given time period and testing until a prescribed number of failures appear. The performance of the method is discussed in terms of two characteristics: the average value of g*/g(λ) and the true confidence coefficient P{g* ≥ g(λ)}.

A general Chebyshev complex function approximation procedure and an application to beamforming

A new computational technique is described for the Chebyshev, or minimax, approximation of a given complex valued function by means of linear combinations of given complex valued basis functions. The domain of definition of all functions can be any finite set whatever. Neither the basis functions nor the function approximated need satisfy any special hypotheses beyond the requirement that they be defined on a common domain. Theoretical upper and lower bounds on the accuracy of the computed Chebyshev error are derived. These bounds permit both a priori and a posteriori error assessments. Efforts to extend the method to functions whose domain of definition is a continuum are discussed. An application is presented involving ’’re-shading’’ a 50- element antenna array to minimize the effects of a 10% element failure rate, while maintaining full steering capability and mainlobe beamwidth.

A Reliability Model of Partially Parallel Systems

A mathematical model is derived to simulate the operation of a system consisting of n identical elements and is needed for its survival operation at least m components to be operable. The analysis is carried out in case that the element failure rate is dependable on time and on the loading stresses. A practical example is given to show the solution.

Upper Bounds on Mean Life of Self-Repairing Systems

Upper bounds on mean life of self-repairing systems are established on the basis of a very general system model. Expressions for system mean-life are obtained by formulating the problem as a two-dimensional difference equation in time and the number of nonfailed spare elements. Results indicate that mean life of an isolated system cannot be expected to exceed roughly three times the mean life of the elements which make it up, regardless of how standby elements are employed. If the element failure rate in standby is substantially less than the failure rate in operation, then system mean life is essentially linearly proportional to the number of available standby elements.

Optimum Search Routines for Automatic Fault Location

This paper comprises an extension of Model I of a recent paper of Gluss, (1959) Opns. Res. 7, 468–477, and its purpose is to dictate strategies that minimize the expected cost (in time) of locating a fault in a complex system of equipment. These strategies are specialized for use with automatic testing equipment The model assumes that the complex system consists of N modules containing n(1), …, n(N) elements respectively, that the cost of examining the modules are t1, …, tN respectively, and that the costs of examining the elements within the rth module are tr1, …, trn(r). It is further assumed that module tests are performed to find which module is faulty before element tests are performed, and that there exist probabilities at each stage that errors of two kinds can be made (1) that the test fails to detect an actual fault in the module or item tested, (2) that the test finds a fault that does not exist. The estimation of the probabilities of faults lying in respective modules or elements is performed in a different way from that in Gluss' paper they are computed from element reliability data by manipulation of their λ parameters, where λ is the element failure rate. Furthermore, consideration is given to fault symptoms that are supplied by weighting the probabilities according to the symptom information. Because of the anticipated difficulty in obtaining the necessary parameter estimates, the analysis may be most useful for its illumination of the influence the several required estimates have on the optimum search routine.