Approximate Confidence Intervals for Reliability of a Series System

Two solutions are proposed for estimating s-confidence intervals for reliability of a repairable series system comprised of non-constant failure rate components: 1) the system is treated as a sum of renewal processes with the mean and variance of total number of system failures being computed from the moments of failure times of the components; and 2) a pseudo-Bayesian solution is derived for the mean and variance of the log-reliability of a system of Weibull components. In both solution approaches, the central limit theorem is invoked for a sum of component random variables determined from test data such as number of failures or log-reliabilities. s-Confidence limits are then approximated using Gaussian probability tables. The intervals derived yield close-to-exact frequency limits, depending on such variables as number of test failures, number of components, and component parameters.     

Quantitative Reliability Evaluation of Repairable Phased-Mission Systems Using Markov Approach

A quantitative reliability model for a phased mission system is developed using a Markov process. Two cases for the mission-phase change times are assumed: 1) to be known in advance and 2) to be random variables. A method of solution is presented and illustrated by examples. The solution of phased-mission systems is equivalent to solving a sequence of uni-phase systems with appropriate initial conditions.     

大型相控阵雷达天线阵面的任务可靠性设计

大型相控阵雷达的天线阵面系统复杂,故障模式多样,各模式对雷达工作的影响程度也不同。针对这些特点,文中采用了基于任务可靠性的可靠性预计。同时,通过表决冗余及开展定期检修的方式,来确保天线阵面设备及系统的高任务可靠性。推导了各种典型任务剖面的可靠性数学模型,建立了任务可靠性模型,并对雷达天线阵面进行了可靠性预计,从而为大型相控阵雷达天线阵面的高任务可靠性设计提供了理论依据和技术方法。     

Reliability and optimization of systems with periodic modifications in the probability and possibility contexts

In this paper we consider unrepairable systems with periodic modifications in the probability and possibility contexts. Also we assume that durations of intervals between modification instants can be random or fuzzy variables. In the particular case when durations are the determined numbers we solve an optimization problem to maximize the system reliability.     

相关竞争失效场合雷达功率放大系统可靠性评估

针对相关竞争失效场合难以获取高可靠部件的性能分布信息,无法对系统可靠性进行准确估计的问题.提出了相关竞争失效场合下考虑认知不确定性的多态系统可靠性评估方法.该方法首先通过假定部件突发失效阈值为递减型随机过程来表征累积退化与突发失效的相关性,同时为降低对部件认知不确定性的影响,假定冲击引起的部件性能损伤分布参数和突发失效参数均为区间变量,建立基于区间变量的部件性能分布模型;而后对传统的通用生成函数方法进行改进,给出了区间通用生成函数的定义及其运算法则;最后对某型雷达功率放大系统的可靠性进行分析.该方法不仅克服了部件的失效模式复杂、状态信息少的不足,且方法简单、思路清晰,具有很强的通用性和工程应用价值.     

Reliability analysis of time-dependent cascade system with random cycle times

Reliability analysis of time-dependent 2-cascade and 3-cascade systems is carried out using stress/strength models. Each of the stress and strength variables is assumed to be deterministic or random fixed or random independent. The number of cycles in any period of time t is assumed to be random. The particular case when the number of cycles in any period of time t follows a Poisson distribution is also considered. The components are assumed to be identical and the attenuation factors k_i's are assumed to be constants. Also, expressions for the system reliability are obtained, and a few numerical results are computed when the stress and the strength distributions are exponential.     

Stochastic models for mission effectiveness

A stochastic model of mission effectiveness for a system which is required to perform a random number of tasks during its mission is developed. Mission effectiveness is defined as a combined measure of availability and reliability at each task-arrival time. An analytic model is derived under a general set of assumptions. Other models are outlined to show the wide applicability of this model for mission effectiveness     

Probability of Component or Subsystem Failure Before System Failure

A method of determining the probability of having a given set of components failed and another set of components working at the time of system failure is based on the notion of boundary probability. The method is simple and easily applied to any s-coherent system for which the reliability structure is known. The application of this method is limited to the case of continuous probability distributions of time to failure because no simple method of computing boundary probabilities in the discrete case could be found. This is not, however, a major limitation of the method since in the majority of practical applications continuous random variables representing times to failure are used. The method can be extended to the case of non-s-independent random variables. Several examples illustrate the procedure.     

Reliability analysis of time-dependent cascade system with deterministic cycle times

Reliability analysis of time-dependent 2-cascade and 3-cascade systems is carried out using stress/strength models by considering each of the stress and strength variables as deterministic or random fixed or random independent. The number of cycles in any period of time t is assumed to be deterministic. The components are identical in the sense that the components have exactly the same strength if the strength variable is deterministic and have independent and identical distributions if the strength variable is random. Attenuation factors, K_i's, are constants. Expressions for system reliability are obtained and reliability values are computed for specific values of N, the number of cycles, when stress and strength distributions are exponential.     

Analysis of Mission-Oriented Systems

Several measures of system reliability that are applicable to a mission-oriented or time-dependent system are defined: 1) the probability that the system is in a given state at the end of a given mission phase; 2) the probability density function of the random variable time spent in a state, given that the system has just transited into that state; 3) the probability of mission success. Equations for 1)-3) are derived, and an application of the formulas performed for the Naval Air Development Center, Johnsville, Pa., is discussed.     

Reliability and Maintainability Parameters Evaluated with Simulation

In order to achieve a high probability of mission success (reliability), prolonged manned space missions require low failure rates for critical subsystems or components whose failure can be corrected before a mission abort or mission degradation, i.e., in-flight maintenance is one method of increasing mission success probability. In-flight repair or replacement of subsystems, subject to random times to failure, must be made before the maximum subsystem downtime is exceeded. Also, in-flight maintenance must take into account such factors as crew availability, time to repair, redundancy, failure rates, maximum allowable downtimes, and distributions of the preceding factors. The deterministic approach to obtain mission success probability is often too difficult to be applied within budget constraints. Therefore, a computer program was developed to estimate the reliability through simulation. Failures and repairs within a space vehicle were simulated, assuming a specific number of crewmen initially available for repair, constant failure rate, and lognormal repair times. Various parametric and sensitivity analyses of the important parameters were performed to determine their effects on mission success. For example, the effect of a subsystem's mean time between failures on mission success for selected crew sizes (keeping other variables constant) can be shown. An important realistic feature of the program is the associating of a repair priority with each subsystem. A higher priority subsystem can displace a lower priority subsystem already under repair and can be placed ahead of a lower priority subsystem in a waiting queue.     

A non-homogeneous Markov model for phased-mission reliabilityanalysis

Three assumptions of Markov modeling for reliability of phased-mission systems that limit flexibility of representation are identified. The proposed generalization has the ability to represent state-dependent behavior, handle phases of random duration using globally time-dependent distributions of phase change time, and model globally time-dependent failure and repair rates. The approach is based on a single nonhomogeneous Markov model in which the concept of state transition is extended to include globally time-dependent phase changes. Phase change times are specified using nonoverlapping distributions with probability distribution functions that are zero outside assigned time intervals; the time intervals are ordered according to the phases. A comparison between a numerical solution of the model and simulation demonstrates that the numerical solution can be several times faster than simulation     

Dynamic Reliability Model of Components Under Random Load

The dynamic reliability model of components is developed using order statistics, and probability differential equations. The relationship between reliability and time, and that between the hazard rate and time, are discussed in this paper. First, according to the statistical meaning of random load application, the cumulative distribution function, and probability density function of equivalent load, when random load is applied at multiple times, are derived. Further, the reliability model of components under repeated random load, is developed. Then, the loading process described under a Poisson process, the dynamic reliability model of components without strength degeneration, and that with strength degeneration are developed respectively. Finally, the reliability, and the hazard rate of components are discussed. The result shows that, when strength doesn't degenerate, the reliability of components decreases over time, and the hazard rate of components decreases over time, too. When strength degenerates, the reliability of components decreases over time more obviously, and the hazard rate curve is bathtub-shaped.      

Mission Reliability for a 1-Unit System with Allowed Down-Time

This paper considers a 1-unit system; the unit is repaired upon failure. The failure and repair rates need not be constant. The system fails if the unit is not repaired within a fixed time, or if the number of failures during the mission exceeds a fixed number. As a special case, that number is allowed to be ``infinite.' The Laplace transforms of the reliability and mean time to system failure are derived; they are not easily solved. The special case of constant failure and repair rates is treated. The results are compared with those of Calabro.     

A reliability physics model for parallel system

Reliability analysis of a nonrepairable 2-unit parallel system is carried out using the stress-strength model of failure physics. The analysis is carried out for correlated strengths and altered stress distribution depending upon the number of components surviving. The analysis includes both the cases of deterministic and random cycle times. In the case of random cycle times, Poisson distributed stress cycle occurrences have been considered. Various system characteristics, such as failure time distribution, reliability and moments of time to failure of the system, have been evaluated for both deterministic and random cycle times. Two particular cases, namely (i) bivariate exponential distribution for strength variables and univariate exponential distributions for stress variables and (ii) bivariate normal distribution for strength variables and univariate normal distributions for stress variables, have also been considered.     

Optimal Design of a Series-Parallel System with Time-Dependent Reliability

The paper formulates an optimal reliability design problem for a series system made of parallel redundant subsystems. The variables for optimization are the number of redundant units in each subsystem and the reliability of each unit. There is a cost-constraint. The time for which the system reliability exceeds a specified value is to be maximized. Similarly the cost could be minimized for a constraint on the mission time and reliability. A solution method for the formulated problems is presented along with an example.     

A unified performance reliability analysis of a system with a cumulative down time constraint

We discuss unified performance and reliability analysis of a system which operates in a critical environment, in the sense that a catastrophic condition is reached when the accumulated down time exceeds a given threshold. Assuming that the system must process a task with a specified work requirement, we evaluate the probability that the task will be completed at a given time before the system reaches the catastrophic state.We show that several other important measures (like the distribution of the lifetime, the distribution of the interval availability, and the instantaneous availability) can be derived from the knowledge of the distribution of the completion time. A numerical example, based on the use of Phase (PH) type distributed random variables, concludes the paper.     

Proper complex random processes with applications to informationtheory

The covariance of complex random variables and processes, when defined consistently with the corresponding notion for real random variables, is shown to be determined by the usual complex covariance together with a quantity called the pseudo-covariance. A characterization of uncorrelatedness and wide-sense stationarity in terms of covariance and pseudo-covariance is given. Complex random variables and processes with a vanishing pseudo-covariance are called proper. It is shown that properness is preserved under affine transformations and that the complex-multivariate Gaussian density assumes a natural form only for proper random variables. The maximum-entropy theorem is generalized to the complex-multivariate case. The differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper, Gaussian, and zero-mean. The notion of circular stationarity is introduced. For the class of proper complex random processes, a discrete Fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain. An application of the theory is presented     

Reliability prediction models to support conceptual design

During the early stages of conceptual design, the ability to predict reliability is very limited. Without a prototype to test in a lab environment or without field data, component failure rates and system reliability performance are usually unknown. A popular method for early reliability prediction is to develop a computer model for the system. However, most of these models are extremely specific to an individual system or industry. This paper presents three general procedures (using both simulation and analytic solution techniques) for predicting system reliability and average mission cost. The procedures consider both known and unknown failure rates and component-level and subsystem-level analyzes. The estimates are based on the number of series subsystems and redundant (active or stand-by) components for each subsystem. The result is a set of approaches that engineers can use to predict system reliability early in the system-design process. Software was developed (and is discussed in this paper) that facilitates the application of the simulation-based techniques. For the specific type of system and mission addressed in this paper, the analytic approach is superior to the simulation-based prediction models. However, all three approaches are presented for two reasons: (1) to convey the development process involved with building these prediction tools; and (2) the simulation-based approaches are of greater value as the research is extended to consider more complex systems and scenarios     

Stochastic Bayes measures to compare forecast accuracy ofsoftware-reliability models

ARE (absolute relative error) and SqRE (squared relative error), are random variables that are suggested as measurements of forecast accuracy of the total number of estimated software failures at the end of a mission time. The purpose is to compare the predictive merit of competing software reliability models, an important concern to software reliability analysts. This technique calculates the Bayes probability of how much better the prediction accuracy is for one method relative to a competitor. This novel approach is more realistic, in the assessment of predictive merit, than (a) comparing merely the average values of ARE and SqRE as conventionally done; and (b) conducting statistical hypothesis tests of pair-wise means of ARE and SqRE, an approach somewhat more sensible than (a), because (b) incorporates variability of predicted values, which (a) does not. To implement this technique, first noninformative (across the border) are used and then informative (specified) priors. For the informative case, half-normal priors are placed on the mean of the ARE or SqRE random variables, because these means are hypothesized to remain peaked around zero relative-error (ideal error percentage). This problem is related to the general problem of ranking usual means discussed in the literature by Berger and Deely (1988), and is a follow-up to an invited research paper presented at ISI-97 by Sahinoglu and Capar (1997)