Evaluation of MTTF and reliability of a power plant by BF technique

In this paper, investigations have been carried out for the evaluation of reliability and MTTF (mean time to failure) of a parallel redundant complex system; viz. a power plant. The object of the system is to supply power generated by generators from a power house to a very important consumer, connected by cables and switches. The reliability and MTTF have been evaluated by using Boolean Function (BF) technique. Failure times for the various components of the complex system follow arbitrary distribution. A numerical example has also been appended to highlight the important results. Two graphs on reliability and MTTF have also been given in the end to forecast the operable behaviour of the system at any time.     

Reliability and availability analysis of on surface transit systems

This paper presents four Markov models pertaining to repairable and non-repairable on surface transit systems. The expressions for state probabilities, system reliability, mean time to failure (MTTF) and steady state availability are developed. System reliability, MTTF and steady state availability plots for various assumed values of system parameters are shown.     

Moments of N-unit redundant systems with time dependent failure rates

This paper presents expressions for system reliability, mean time to failure and variance for three types of redundant systems whose components follow Gompertz (extreme value), linearly increasing and stange hazard rates. Seven mathematical models are presented. Mean-Time-to-Failure (MTTF) plots are shown for three models for n=2.     

Two formulas for computing the reliability of incompletek-out-of-n:G systems

Reliability computation of highly redundant systems most commonly uses approximate methods. Except for k-out-of-n:G systems or consecutive k-out-of-n:G systems, exact reliability formulas offering a broader range of applicability are rare. This paper gives two new formulas for this purpose: the first handles k-out-of-n:G systems of which some paths are not present; the second allows for the reliability calculation of a coherent binary system in general. Both formulas express system reliability in terms of the reliabilities of k-out-of-n:G systems. In practice, these new formulas cope with highly redundant systems with certain similarities to k-out-of-n:G systems. For example, a reliability of the control-rod system of a nuclear reactor is computed. Although the paper is directed to system reliability, the results can be used for computing the failure probability of a system which in practical applications is sometimes more convenient. In which case, the formulas are to be changed such that a system is given by its minimal cut-sets instead of minimal path-sets, and p should be a component unreliability instead of its reliability. The first proof of formula uses domination theory and, in thus contributes to the state of the art in this field     

Comment on: Reliability of k-out-of-n:G systems with imperfectfault-coverage

This note comments on the paper “Reliability of k-out-of-n:G systems with imperfect fault-coverage” by S. Akhtar (1994). An alternative probability argument can be used to obtain the MTBF (mean time between failures) and MTTF (mean time to failure) for such systems. This has the advantage that higher moments of such failure times can also be determined     

Generalized multi-state k-out-of-n:G systems

In a binary k-out-of-n:G system, k is the minimum number of components that must work for the system to work. Let 1 represent the working state and 0 the failure state, k then indicates the minimum number of components that must be in state 1 for the system to be in state 1. This paper defines the multi-state k-out-of-n:G system: each component and the system can be in 1 of M+1 possible states: 0, 1, ..., M. In Case I, the system is in state ⩾j iff at least k_j components are in state ⩾j. The value of k_j I 1 can be different for different required minimum system-state level j. Examples illustrate applications of this definition. Algorithms for reliability evaluation of such systems are presented     

The mean residual life function of a k-out-of-n structure at the system level

In the study of the reliability of technical systems, k-out-of-n systems play an important role. In the present paper, we consider a k-out-of-n system consisting of n identical components with independent lifetimes having a common distribution function F. Under the condition that, at time t, all the components of the system are working, we propose a new definition for the mean residual life (MRL) function of the system, and obtain several properties of that system.     

Optimal design of k-out-of-n:G subsystems subjected to imperfect fault-coverage

Systems subjected to imperfect fault-coverage may fail even prior to the exhaustion of spares due to uncovered component failures. This paper presents optimal cost-effective design policies for k-out-of-n:G subsystems subjected to imperfect fault-coverage. It is assumed that there exists a k-out-of-n:G subsystem in a nonseries-parallel system and, except for this subsystem, the redundancy configurations of all other subsystems are fixed. This paper also presents optimal design polices which maximize overall system reliability. As a special case, results are presented for k-out-of-n:G systems subjected to imperfect fault-coverage. Examples then demonstrate how to apply the main results of this paper to find the optimal configurations of all subsystems simultaneously. In this paper, we show that the optimal n which maximizes system reliability is always less than or equal to the n which maximizes the reliability of the subsystem itself. Similarly, if the failure cost is the same, then the optimal n which minimizes the average system cost is always less than or equal to the n which minimizes the average cost of the subsystem. It is also shown that if the subsystem being analyzed is in series with the rest of the system, then the optimal n which maximizes subsystem reliability can also maximize the system reliability. The computational procedure of the proposed algorithms is illustrated through the examples.     

Stochastic ordering results for consecutive k-out-of-n:F systems

A linear (circular) consecutive k-out-of-n:F system is a system of n linearly (circularly) ordered components which fails if and only if at least k consecutive components fail. We use recursive relationships on the reliability of such systems with independent identically distributed components to show that for any fixed k, the lifetime of a (linear or circular) consecutive k-out-of-n:F system is stochastically decreasing in n. This result also holds for linear systems when the components are independent and not necessarily identically distributed, but not in general for circular systems.     

Reliability Analysis of the k-out-of-n:F System

A class of repairable systems known as k-out-of-n:F systems, 1 ? k ? n, consists of n units in parallel redundancy which are serviced by a single repairman; system failure occurs when k units are simultaneously inoperable for the first time. In this paper, assuming constant failure rates and general repair distributions, reliability characteristics of the k-out-of-n:F system are treated using two different methods. In Part I, a conditional transform approach is applied to the 2-out-of-n:F system. Transforms of distributions are obtained for T (the time to system failure), the time spent on repairs during (0, T) and the free time of the repairman during (0, T). In Part II, the supplementary variable technique is used to investigate time to failure characteristics of the k-out-of-n:F system for k = 2 and k = 3. A model of an airport limousine service illustrates the use of the results.     

Effects of Weibull hazard rate on common cause failure analysis of reliability networks

This paper presents formulae for system mean life, variance of time to failure, hazard rate and reliability of parallel, k-out-of-n, parallel-series and bridge networks with common cause failures. The components in every configuration are assumed to be identical and characterized by a Weibull time to failure density function. The graphical plots of the system reliability and mean life gain are shown.     

Efficient computation of the sensitivity of k-out-of-n system reliability

The first-order sensitivity of system reliability is useful in evaluating several criticality measures, uncertainty measures, and the instantaneous failure rate of the system. Three new algorithms are described herein for the computation of the sensitivity of k-out-of-n system reliability. Generally, the numerical results of these algorithms check very well versus one another as well as versus those of known special cases. The computational complexities of these algorithms vary from almost double to slightly less than that of the best known algorithm for computing the k-out-of-n system reliability. Some observations are made on the important rankings of system components for different values of k, n and component reliabilities.     

Reliability and availability analysis of transit systems

This paper presents three newly developed Markov models representing on-surface transit systems. Transit system reliability, steady-state availability, mean time to failure (MTTF) and variance of time to failure formulas are developed. Selective plots are shown for each model. These plots clearly exhibit the impact of various parameters on transit system reliability, steady-state availability, and MTTF.     

Ring-network with a constrained number of consecutively-bypassedstations

A new technique combines prior graph theoretic and algebraic techniques for obtaining closed-form terminal-pair reliability expressions of ring topology networks. The applicability of this technique is illustrated by obtaining closed-form terminal-pair reliability expressions for dual counter-rotating ring networks that use both self-heal and station-bypass switches in which all components can fail. These expressions appreciably extend the utility of prior work on ring-network reliability by incorporating network configuration limitations caused by optical power loss constraints. The number of consecutively bypassed station failures in an optical fiber ring topology network such as those exemplified by FDDI rings or synchronous optical network (SONET) rings is limited by the optical power loss constraints. The combined graph theoretic and algebraic technique permits the incorporation of known results on the reliability of consecutive k-out-of-n:F systems so that closed-form terminal-pair reliability expressions can be derived. The results are a new approach to network-reliability analysis and appreciably extend known theory to new situations not previously analyzed. In particular, the combined graphical-algebraic analysis tool developed here allows ring-network designers to analyze the reliability of ring-network structures thought previously to be too difficult to analyze with closed-form expressions and to be amenable only to reliability approximation by simulation. We use this technique in our derivation of closed-form expressions for terminal-pair reliability in dual counter-rotating ring networks     

Consecutive k-out-of-n:F system with sequential failures and a single repair

This paper presents a solution for determining the mean time to system failure of a consecutive k-out-of-n:F system with a single repair. The components of the system are subject to sequential failures. The mean time to system failure is evaluated by making use of the relation between the reliability function and the probability of the first passage time to system failure. The Laplace transform of the first passage time to system failure is obtained as a ratio of two determinants.     

一类多状态连续n中取k(G)系统的可靠性计算

为了计算多状态连续厅中取后（G）系统的可靠性,引入4个定理,将满足引理的多状态系统转换为二元状态系统。分别推导了多状态线形连续k／n（G）系统和环形连续k／n（G）系统的可靠性计算公式。证明了固定k值增加一个新部件,若部件可靠性独立同分布,线形和环形系统可靠性均增加;若部件可靠性独立但不同分布,环形系统存在一个极值,新增加部件可靠性大于这个极值时得到的新系统可靠性增加,反之系统可靠性下降。     

Estimation of system reliability for uncooled optical transmittersusing system reliability function

This paper investigates the system reliability for 155 Mb/s optical transmitters by deriving a system reliability function from reliability data of each component for transmitters, laser diode, photodiode, optical assembly, and driver IC. The reliability data for each component reliability function have been obtained from accelerated aging test. The reliability parameters such as failure rate, mean time-to-failure (MTTF), standard deviation are obtained from a probability plotting method. From the system reliability function, the MTTF of the optical transmitter at 65°C was estimated to be 47000 h with 95% confidence. In this estimation, we introduced modified lifetime of laser diodes and reliability function of optical assembly     

A simple Markovian method for MTTF calculation

The MTTF of a system design with constant failure and repair rates and with some forms of stand-by redundancy and switching is an important characteristic of the system. Commonly, calculation of the MTTF requires knowledge of the reliability function R(t), which is integrated to yield the MTTF. In many cases obtaining the reliability function is a non-trivial task and its analytic integration may be quite tedious. In the following we describe a simple method of obtaining the MTTF of such systems which avoids the need of knowledge of R(t). The method is Markovian in nature and is based on summing the probabilities of all the possible routes (in the space of states) by which the system can get from its initial state at t = 0 to an absorbing state (failed state), where each such probability is multiplied by the average time required for the system to follow that route. This weighted sum yields the MTTF for any given initial conditions. The method is demonstrated on some useful systems and analytical formulas for the MTTF are derived. It is further demonstrated how the results of the method may be used in the calculation of the MTBF of the system in steady-state.     

Properties of a multivariate survival distribution generated by aWeibull and inverse-Gaussian mixture

The authors consider the influence of the work environment on a system of nonrenewable components. The failure times for the components are Weibull distributed and the work environment has an inverse Gaussian distribution. A multivariate Weibull and inverse Gaussian mixture distribution is derived. Several pertinent properties for this multivariate distribution are discussed that shed some light on the nature of the distribution. The authors account for the operating environment and its changing nature by averaging over a parameter corresponding to the environment. The distribution is applied to find the mean number of components working at some mission time and the reliability for k-out-of-n components     

Reliability Bounds for Multi-State $k$-out-of- $n$ Systems

Algorithms have been available for exact performance evaluation of multi-state k-out-of-n systems. However, especially for complex systems with a large number of components, and a large number of possible states, obtaining "reliability bounds" would be an interesting, significant issue. Reliability bounds will give us a range of the system reliability in a much shorter computation time, which allow us to make decisions more efficiently. The systems under consideration are multi-state k-out-of-n systems with i.i.d. components. We will focus on the probability of the system in states below a certain state d, denoted by Q_sd. Based on the recursive algorithm proposed by Zuo & Tian [14] for performance evaluation of multi-state k-out-of-n systems with i.i.d. components, a reliability bounding approach is developed in this paper. The upper, and lower bounds of Q_sd are calculated by reducing the length of the k vector when using the recursive algorithm. Using the bounding approach, we can obtain a good estimate of the exact Q_sd value while significantly reducing the computation time. This approach is attractive, especially to complex systems with a large number of components, and a large number of possible states. A numerical example is used to illustrate the significance of the proposed bounding approach.