Variance-based importance analysis measure for mission reliability of phased mission system

Importance measures are used to estimate the relative importance of components to system reliability. Phased mission systems (PMS) have many components working in several phases with different success criteria, and their component structural importance is distinct in different phases. Additionally, reliability parameters of components in PMS always have uncertainty in practice. Therefore, existing component importance measures based on either the partial derivative of system structure function or component structural importance may have difficulties in PMS importance analysis. This paper presents a simulation method to evaluate the component global importance for PMS based on the variance-based method and the Monte-Carlo method. To facilitate the practical use, we further discuss the correlation relationship between the component global importance and its possible influence factors, and present here a fitting model for evaluating component global importance. Finally, two examples are given to show that the fitting model displays quite reasonable component importance.     

Assessing component reliability using lifetime data from systems

ABSTRACT

In this paper, we introduce a competing risks model for the lifetimes of components that differs from the classical competing risks models by the fact that it is not directly observable which component has failed. We propose two statistical methods for estimating the reliability of components from failure data on a system. Our methods are applied to simulated failure data, in order to illustrate the performance of the methods.     

Confidence interval procedures for system reliability and applications to competing risks models

System reliability depends on the reliability of the system’s components and the structure of the system. For example, in a competing risks model, the system fails when the weakest component fails. The reliability function and the quantile function of a complicated system are two important metrics for characterizing the system’s reliability. When there are data available at the component level, the system reliability can be estimated by using the component level information. Confidence intervals (CIs) are needed to quantify the statistical uncertainty in the estimation. Obtaining system reliability CI procedures with good properties is not straightforward, especially when the system structure is complicated. In this paper, we develop a general procedure for constructing a CI for the system failure-time quantile function by using the implicit delta method. We also develop general procedures for constructing a CI for the cumulative distribution function (cdf) of the system. We show that the recommended procedures are asymptotically valid and have good statistical properties. We conduct simulations to study the finite-sample coverage properties of the proposed procedures and compare them with existing procedures. We apply the proposed procedures to three applications; two applications in competing risks models and an application with a $k\text{-out-of-}s$ system. The paper concludes with some discussion and an outline of areas for future research.     

System reliability estimation for the Exponential load-strength model

A system comprising k identical components is considered. The system load that is common to all components is treated as a random variable, modeled by a one-parameter Exponential distribution. Each component's resistance to load is also taken as a random variable, modeled by another one-parameter Exponential distribution that applies to each component. The system is considered redundant, meaning that the system remains operative so long as any m out of k components function, where 1≤m≤k. An expression for system reliability of this load-strength model is derived. The maximum likelihood estimator is compared with the structural expectation of system reliability.     

Simulated and unbiased reliability sampling plans

Statistical estimation and hypothesis testing are two ways in which the data of a sample can be made to yield information concerning the parameters of the population from which the sample is drawn. The most important applications of these two ways is the acceptance sampling methods used in industrial quality control, systems reliability and failure detection. The use of these sampling methods is connected with the risk of unnecessary rejection of satisfactory lots and the risk of acceptance of lots with defective units, these decisions can occur when selecting biased samples containing most defective units or no defective units despite the fact that the lot has the contrary. The aim of this research is to make this kind of decision an improbable or impossible event. The parameters and techniques determining the sampling methods must be correctly chosen. The formulation of an optimised statistical model of these problems is the basic condition of obtaining objective results. By the essence of statistical simulation the process of functioning of the complex system was used to represent a mathematically formulated model which was isomorphic in all essential aspects of the research objectives. This model was repeatedly tested to determine the required statistical characteristics, based on the complex stochastic process.     

Reliability evaluation subject to assured accuracy rate and time for stochastic unreliable-node computer networks

In many real-life networks such as computer networks, branches and nodes have multi-state capacity, lead time, and accuracy rate. The network with unreliable nodes is more complex to evaluate the reliability because node failure results in the disabled of adjacent branches. Such a network is named a stochastic unreliable-node computer network (SUNCN). Under the strict assumption that each component (branch and node) has a deterministic capacity, the quickest path (QP) problem is to find a path sending a specific amount of data with minimum transmission time. The accuracy rate is a critical index to measure the performance of a computer network because some packets are damaged or lost due to voltage instability, magnetic field effects, lightning, etc. Subject to both assured accuracy rate and time constraints, this paper extends the QP problem to discuss the system reliability of an SUNCN. An efficient algorithm based on a graphic technique is proposed to find the minimal capacity vector meeting such constraints. System reliability, the probability to send a specific amount of data through multiple minimal paths subject to both assured accuracy rate and time constraints, can subsequently be computed.     

Dynamic reliability models with conditional proportional hazards

A dynamic approach to the stochastic modelling of reliability systems is further explored. This modelling approach is particularly appropriate for load-sharing, software reliability, and multivariate failure-time models, where component failure characteristics are affected by their degree of use, amount of load, or extent of stresses experienced. This approach incorporates the intuitive notion that when a set of components in a coherent system fail at a certain time, there is a jump from one structure function to another which governs the residual lifetimes of the remaining functioning components, and since the component lifetimes are intrinsically affected by the structure function which they constitute, then at such a failure time there should also be a jump in the stochastic structure of the lifetimes of the remaining components. For such dynamically-modelled systems, the stochastic characteristics of their jump times are studied. These properties of the jump times allow us to obtain the properties of the lifetime of the system. In particular, for a Markov dynamic model, specific expressions for the exact distribution functions of the jump times are obtained for a general coherent system, a parallel system, and a series-parallel system. We derive a new family of distribution functions which describes the distributions of the jump times for a dynamically-modelled system.     

Estimation of parameters and reliability from generalized life models

Simultaneous estimation of parameters with p (≥ 2) components, where each component has a generalized life distribution, is considered under a sum of squared error loss function. Improved estimators are obtained which dominate the maximum likelihood and the niinimum mean square estimators. Robustness of the improved estimators is shown even when the component distributions are dependent. The result is extended to the estimation of the system reliability when the components are connected in series. Several numerical studies are performed to demonstrate the risk improvement and the Pitman closeness of the new estimators.     

Estimation of reliability in freund model for two component system

The simultaneous failure of a pair of components of a system is so rare or to say, impossible and the failure of one of the two components of the system may result in more (less) workload on the other component, Freund(1961) bivariate model is applicable to such cases. The uniformly minimum variance unbiased estimator (UMVUE) of the parallel system reliability for the Freund bivariate exponential distribution (BVED) is obtained.     

A continuous approximation for evaluating reliability of complex systems under stress-strength model.

Evaluation of system reliability for complex systems based on Taylor's approximation becomes increasingly intractable. Taguchi's concept of random experimentation has been exploited by English et al (1996) for discretization of complex systems and determination of reliability values. We indicate a few demerits of discretization method and propose to retain the continuous character of the original problem by evaluating system reliability using a range approximation method. Our proposed method works better than discretization approach in all the three engineering problems considered for the purpose of demonstration.     

Early inference on reliability of upgraded automotive components by using past data and technical information

When a new product is the result of design and/or process improvements introduced in its predecessors, then the past failure data and the expert technical knowledge constitute a valuable source of information that can lead to a more accurate reliability estimate of the upgraded product. This paper proposes a Bayesian procedure to formalize the prior information available about the failure probability of an upgraded automotive component. The elicitation process makes use of the failure data of the past product, the designer information on the effectiveness of planned design/process modifications, information on actual working conditions of the upgraded component and, for outsourced components, technical knowledge on the effect of possible cost reductions. By using the proposed procedure, more accurate estimates of the failure probability can arise. The number of failed items in a future population of vehicles is also predicted to measure the effect of a possible extension of the warranty period. Finally, the proposed procedure was applied to a case study and its feasibility in supporting reliability estimation is illustrated.     

Data gold mining

The Motorway Incident Detection and Automatic Signalling (MIDAS) system data are summaries of traffic volumes, speeds and vehicle types, derived from loop detectors that sense traffic passing over them. These sensors are being rolled out across the UK's strategic highway network (motorways and major A-roads) and data from portions of one of the busiest motorways, the M25, now go back 10 years. Richard Gibbens and Wiebke Werft describe a journey time predictor based on MIDAS and explain how the data can shed light on topical issues such as road pricing.     

A stochastic process approach to multilayer neutron detectors

The sparsity of the isotope Helium‐3, ongoing since 2009, has initiated a new generation of neutron detectors. One particularly promising development line for detectors is the multilayer gaseous detector. In this paper, a stochastic process approach is used to determine the neutron energy from the additional data afforded by the multilayer nature of these novel detectors. The data from a multilayer detector consist of counts of the number of absorbed neutrons along the sequence of the detector's layers, in which the neutron absorption probability is unknown. We study the maximum likelihood estimator for the intensity and absorption probability and show its consistency and asymptotic normality, as the number of incoming neutrons goes to infinity. We combine these results with known results on the relation between the absorption probability and the wavelength to derive an estimator of the wavelength and to show its consistency and asymptotic normality.     

Estimation of reliability for a multicomponent survival stress-strength model based on exponential distributions

Uniformly minimum variance unbiased estimator (UMVUE) of reliability in stress-strength model (known stress) is obtained for a multicomponent survival model based on exponential distributions for parallel system. The variance of this estimator is compared with Cramer-Rao lower bound (CRB) for the variance of unbiased estimator of reliability, and the mean square error (MSE) of maximum likelihood estimator of reliability in case of two component system.     

Multiresolution anomaly detection method for fractional Gaussian noise

Driven by network intrusion detection, we propose a MultiResolution Anomaly Detection (MRAD) method, which effectively utilizes the multiscale properties of Internet features and network anomalies. In this paper, several theoretical properties of the MRAD method are explored. A major new result is the mathematical formulation of the notion that a two-scaled MRAD method has larger power than the average power of the detection method based on the given two scales. Test threshold is also developed. Comparisons between MRAD method and other classical outlier detectors in time series are reported as well.     

Bayesian reliability when system and subsystem failure data are obtained in the same time period

Previously, Bayesian anomaly was reported for estimating reliability when subsystem failure data and system failure data were obtained from the same time period. As a result, a practical method for mitigating Bayesian anomaly was developed. In the first part of this paper, however, we show that the Bayesian anomaly can be avoided as long as the same failure information is incorporated in the model. In the second part of this paper, we consider a problem of estimating the Bayesian reliability when the failure count data on subsystems and systems are obtained from the same time period. We show that Bayesian anomaly does not exist when using the multinomial distribution with the Dirichlet prior distribution. A numerical example is given to compare the proposed method with the previous methods.     

A Basis Function Approach to Position Estimation Using Microwave Arrays

We consider the problem of estimating the bearing of a remote object given measurements on a particular type of non-scanning radar, namely a focal-plane array. Such a system focuses incoming radiation through a lens onto an array of detectors. The problem is to estimate the angular position of the radiation source given measurements on the array of detectors and knowledge of the properties of the lens. The training data are essentially noiseless, and an estimator is derived for noisy test conditions. An approach based on kernel basis functions is developed. The estimate of the basis function weights is achieved through a regularization or roughness penalty approach. Choosing the regularization parameter to be proportional to the inverse of the input signal-to-noise ratio leads to a minimum prediction error. Experimental results for a 12-element detector array support the theoretical predictions.     

Comparing relative importance of the same component in a series system in two environments

The relative performance of a component of a series system in two different environments is considered. The conditional probability of the failure of the system due to the failure of the specified component given that the system failed before time t is regarded as a measure of relative importance of the component to the system. A U-statistic test for checking the equality of the relative importance of the component to the system in two different environments against the alternative that the relative importance is smaller in one of the environments, is proposed. Some simulation results for estimating the power of the test are reported. The proposed test is applied to one real data set and it is seen that a different aspect of the data is brought out by this comparison than that by the comparisons of the absolute importance functions such as the subsurvival functions, considered in earlier studies.     

Estimation of reliability under ordered restriction on the parameters

This paper deals with the estimation of reliability for a strength-stress model under ordered restriction on the parameters. It is assumed that components have exponential distributions and are arranged in a parallel system and the failure of one component, results in increasing the failure rate of the remaining components. Results are derived when (i) the ordering of the means is taken into account and when (ii) the ordering of the means is ignored. Simulation studies are carried out to compare the results. It is noticed that, in almost all cases, in case (i) the estimates are closer to the true value with smaller mean squared error (MSE) and smaller’ standard deviation than in case (ii). Thus when the ordering of the means is present in the model, such information should be incorporated in the estimation of reliability.     

Note on estimation of reliability under bivariate pareto stress-strength model

In this paper, we discuss the problem of estimating reliability (R) of a component based on maximum likelihood estimators (MLEs). The reliability of a component is given byR=P[Y<X]. Here X is a random strength of a component subjected to a random stress(Y) and (X,Y) follow a bivariate pareto(BVP) distribution. We obtain an asymptotic normal(AN) distribution of MLE of the reliability(R).