Reliability Measures Of System Research Articles

Analysis of a computer system with arbitrary distributions for h/w and s/w replacement time and priority to repair activities of h/w over replacement of s/w

The present paper deals with reliability and economic measures of a computer system introducing the concepts of inspection and priority to repair activities of the h/w over replacement of the s/w. The computer system has two identical units- one is operative and the other is kept as spare in cold standby. Each unit has h/w and s/w components which may fail completely directly from normal mode. The h/w and s/w components fail independently. There is a single server who visits the system immediately when needed to do inspection, repair and replacement of the h/w and s/w components. Sever inspects the unit at its h/w failure to see the feasibility of repair. If repair of the failed h/w components is not feasible, these are replaced by new one with some replacement time. However, only replacement of the s/w components in the unit is made by new one. Also, priority is given to replacement and repair of the h/w over replacement of the s/w components. The failure time of the unit follow negative exponential while the distributions of inspection, repair and replacement times of the h/w and s/w components are taken as arbitrary with different probability density functions (pdf). The expressions for some measures of system effectiveness are derived by using semi-Markov process and regenerative point technique. The numerical results for a particular case are also obtained to depict the graphical behaviour of MTSF, availability and profit with respect to h/w failure rate.

Reliability and covariance estimation of weighted k-out-of-n multi-state systems

In the literature of reliability engineering, reliability of the weighted k-out-of-n system can be calculated using component reliability based on the structure function. The calculation usually assumes that the true component reliability is completely known. However, this is not the case in practical applications. Instead, component reliability has to be estimated using empirical sample data. Uncertainty arises during this estimation process and propagates to the system level. This paper studies the propagation mechanism of estimation uncertainty through the universal generating function method. Equations of the complete solution including the unbiased system reliability estimator and the corresponding unbiased covariance estimator are derived. This is a unified approach. It can be applied to weighted k-out-of-n systems with multi-state components, to weighted k-out-of-n systems with binary components, and to simple series and parallel systems. It may also serve as building blocks to derive estimators of system reliability and uncertainty measures for more complicated systems.

Reliability of Various 2-Out-of-4:G Redundant Systems With Minimal Repair

In safety critical applications, it is becoming quite common to improve reliability through the use of quadruplexed, redundant subsystems organized with 2-out-of-4:G (2oo4:G) logic. As the subsystems involved will generally be complex, comprising many individual components, they are likely to fail at a time-dependent rate λ(t). The maintenance schedule here is assumed to require failed subsystems to be repaired and workable within a given time τ of failure; and repairs are assumed to be minimal so that all functioning subsystems possess the same rate λ(t). Within this context, we consider the dependence of the system reliability measures on the allowed repair time τ by providing solutions to two integro-differential-delay equations (IDDEs) which bound the exact solution above and below; these bounds may be tightened by iterating the IDDEs to higher order. Results for the stationary system are used to investigate the order required to provide sufficiently tight bounds for the general case. In addition, we consider examples in support of the conjecture of Solov'yev and Zaytsev (Engineering Cybernetics, 1975) that if λ(t)τ is small, then the (asymptotic) instantaneous hazard function of the system hs(t), with a time-varying λ(t), will approach (λ(t)τ → 0) the limit hso(λ(t),τ), where hso(λ, τ) is the asymptotical hazard rate for the same system with constant failure rates. This method then allows for a simple analysis of the case of arbitrary time-varying λ(t) in terms of the much simpler stationary case.

NABS: Novel Approaches for Biometric Systems

Research on biometrics has noticeably increased. However, no single bodily or behavioral feature is able to satisfy acceptability, speed, and reliability constraints of authentication in real applications. The present trend is therefore toward multimodal systems. In this paper, we deal with some core issues related to the design of these systems and propose a novel modular framework, namely, novel approaches for biometric systems (NABS) that we have implemented to address them. NABS proposal encompasses two possible architectures based on the comparative speeds of the involved biometries. It also provides a novel solution for the data normalization problem, with the new quasi-linear sigmoid (QLS) normalization function. This function can overcome a number of common limitations, according to the presented experimental comparisons. A further contribution is the system response reliability (SRR) index to measure response confidence. Its theoretical definition allows to take into account the gallery composition at hand in assigning a system reliability measure on a single-response basis. The unified experimental setting aims at evaluating such aspects both separately and together, using face, ear, and fingerprint as test biometries. The results provide a positive feedback for the overall theoretical framework developed herein. Since NABS is designed to allow both a flexible choice of the adopted architecture, and a variable compositions and/or substitution of its optional modules, i.e., QLS and SRR, it can support different operational settings.

Reliability Measures of a Repairable System with Standby Switching Failures and Reboot Delay

In this paper, we study the reliability measures of a repairable system with M operating units, W warm standby units, and R repairmen in which switching failures and reboot delay are considered. It is assumed that there is a significant failure probability q in the switching process. Failure times of an operating unit and of a standby unit are assumed to be exponentially distributed with parameters 1 and a, respectively. The delay times of reboot are also assumed to be exponentially distributed with parameter p. The explicit expressions of the reliability characteristics such as the system reliability, R Y (t), and the mean time to system failure (MTTF) are derived. Several cases are analyzed graphically to investigate the effects of various system parameters on the R Y (t) and the MTTF. We also perform a sensitivity analysis for the reliability characteristics along with changes in specific values of the system parameters.

Reliability Prediction During Development Phase of a System

Reliability Growth analysis is a process of collecting, modeling, analyzing and interpreting data from the reliability development test program to achieve reliability goal. Many mathematical models have been developed for reliability growth in the literature. In general, it is not possible to fix a priori the model to be used in a given situation. A physical motivation of the problem, based on failure or defect causes/mechanisms, can help in such a choice. The Power Law Process (PLP) is vastly used for monitoring reliability growth during the development test phase. However, in the reliability growth context, the intensity function of the PLP model has two unrealistic situations, viz., it tends to infinity as t tends to zero and tends to zero as t tends to infinity. In this paper, we have proposed Modified PLP model to overcome the second drawback and Doubly Bounded PLP model to overcome both the drawbacks. For the proposed models, the estimates of the model parameters and other quantities of interest have been obtained using Maximum Likelihood approach, for both failure truncated and time truncated data. Reliability Prediction is done using system reliability measures of intensity function and mean time between failures (MTBF). Further confidence intervals of the relevant parameters have been obtained. The procedures developed have been illustrated using numerical examples.

Efficient exceedance probability computation for randomly uncertain nonlinear structures with periodic loading

A method is developed to compute low-level response amplitude exceedance probabilities associated with uncertain nonlinear structures with random parameters and deterministic periodic forcing. Emphasis is focused on accurate and efficient computation in the tails of the exceedance probability distribution function associated with the largest possible response of one displacement variable for unspecified forcing frequency and normally distributed parameters. This gives a measure of system reliability when a large amplitude response exceedance of a specified threshold is designated as the mode of failure. The method exploits the First-Order Reliability Method (FORM) in which the failure surface is constructed via the Harmonic Balance Method (HBM). This combined approach is tested on a Duffing oscillator with harmonic forcing and up to three uncertain parameters, for which the frequency of multiple-solution-maximum-amplitude is found directly, and the probability computed via the Hasofer-Lind reliability index. The accuracy of the proposed HBM-FORM, in the tails of the amplitude exceedance probability, is shown for the Duffing example to be acceptably accurate, whereas the efficiency is shown to be around 1000 times faster than Direct Integration and around 200 times faster than Monte Carlo simulation.

Warranty Cost Analyses Using Quasi-Renewal Processes for Multicomponent Systems

In this paper, warranty cost models are presented based on the quasi-renewal processes and exponential distribution. Cost analyses are conducted for various systems under the basic assumption that a repair service is imperfect. We develop warranty cost models, reliability, and other measures for several systems, including multicomponent systems. This paper focuses on warranty cost analysis, including repairable products with a given warranty period considering conditional probabilities and renewal theory. The exponential distribution is used to analyze and obtain the warranty cost. Numerical examples are discussed to demonstrate the applicability of the methodology derived in this paper.

Structural optimization of uncertain dynamical systems considering mixed-design variables

In this paper attention is directed to the reliability-based optimization of uncertain structural systems under stochastic excitation involving discrete–continuous sizing type of design variables. The reliability-based optimization problem is formulated as the minimization of an objective function subject to multiple reliability constraints. The probability that design conditions are satisfied within a given time interval is used as a measure of system reliability. The problem is solved by a sequential approximate optimization strategy cast into the framework of conservative convex and separable approximations. To this end, the objective function and the reliability constraints are approximated by using a hybrid form of linear, reciprocal and quadratic approximations. The approximations are combined with an effective sensitivity analysis of the reliability constraints in order to generate explicit expressions of the constraints in terms of the design variables. The explicit approximate sub-optimization problems are solved by an appropriate discrete optimization technique. The optimization scheme exhibits monotonic convergence properties. Two numerical examples showing the effectiveness of the approach reported herein are presented.

Another approach to reliability measures for systems with correlated observations

An approach to internal reliability analysis is presented which, compared to existing approaches, offers further insight into the system responses to observation gross errors. The proposed reliability measures are defined on the diagonal and non-diagonal elements of the modified reliability matrix being an oblique projector. It maps the observations into the least squares residuals, both expressed as multiples of the a priori standard deviations of the observations. The system responses to a single gross error, such as the local, the quasi-global or the global response, are discussed and their consistency with non-correlation case is proved. Also, the reliability criteria interpretable in terms of those responses are proposed. They enable one to evaluate the observation systems with correlated and uncorrelated observations with respect to internal reliability. An attempt is also made to relate the global responses to reliability numbers that are the basis for determining the magnitude of the minimal detectable bias. Some differences of the new reliability measures in relation to existing measures are indicated. A numerical example is provided, showing the reliability analysis for a simulated horizontal network (distances, angles and GPS vectors), with given covariance matrix for GPS-vector components. In addition, a reliability analysis is presented for a simple leveling network being a study case for other authors referred to in this paper.

Discrete–continuous variable structural optimization of systems under stochastic loading

The paper deals with the optimization of structural systems involving discrete and continuous sizing type of design variables. In particular, the reliability-based optimization of non-linear systems subject to stochastic excitation where some or all of the design variables are discrete is considered. The reliability-based optimization problem is formulated as the minimization of an objective function subject to multiple reliability constraints. The probability that design conditions are satisfied within a given time interval is used as measure of system reliability. The basic mathematical programming statement of the structural optimization problem is converted into a sequence of explicit approximate primal problems of separable form. The explicit approximate primal problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple non-negativity constraints on the dual variables. A gradient projection type of algorithm is used to find the solution of each dual problem. The effectiveness of the method is demonstrated by presenting a numerical example of a non-linear system subject to stochastic ground acceleration.

Performance assessment of multi-state systems with critical failure modes: Application to the flotation metallic arsenic circuit

This paper considers a number of alternative measures of multi-state systems with two failure modes. Almost all of them are based on a probabilistic model and the extent to which the multi-state system performance analysis may typically lead. The conventional multi-state theory is used to assess the fundamental problems of the performance of complex systems. In real life, it may be difficult to obtain sufficient data to estimate the precise values of the performance levels of modern engineering systems. This paper suggests reliability measures for multi-state systems with two failure modes, and presents a procedure for evaluating these measures. Generalized assumptions of multiple factors that may affect the reliability of such systems are introduced by developing multi-state operators that obey the commutative and the associative laws. The concepts of relevancy, coherency, and equivalence are used to characterize the properties of such systems. Mathematical problems raised by applications of multi-state system model in system failure engineering are addressed. Engineering case study of the flotation circuit of mineral processing plant is modeled as a homogeneous coherent multi-state system composed of homogeneous coherent multi-state subsystems, and its reliability is calculated.

Massive Sensor Array Fault Tolerance: Tolerance Mechanism and Fault Injection for Validation

As today's machines become increasingly complex in order to handle intricate tasks, the number of sensors must increase for intelligent operations. Given the large number of sensors, detecting, isolating, and then tolerating faulty sensors is especially important. In this paper, we propose fault tolerance architecture suitable for a massive sensor array often found in highly advanced systems such as autonomous robots. One example is the sensitive skin, a type of massive sensor array. The objective of the sensitive skin is autonomous guidance of machines in unknown environments, requiring elongated operations in a remote site. The entirety of such a system needs to be able to work remotely without human attendance for an extended period of time. To that end, we propose a fault-tolerant architecture whereby component and analytical redundancies are integrated cohesively for effective failure tolerance of a massive array type sensor or sensor system. In addition, we discuss the evaluation results of the proposed tolerance scheme by means of fault injection and validation analysis as a measure of system reliability and performance.

3.2.4 Study on the Influence of Component Uncertainty on Reliability Estimation of Multi‐State Systems with Continuous States

AbstractExisting reliability evaluation methods rely on the availability of accurate component states data. They will become ineffective when the states themselves are uncertain or unknown, which usually happens during the early stages of the development of new systems. In such cases it is important to understand how uncertainties will affect the system reliability measures. Another drawback of current methods studying reliability of Multi‐State System (MSS) is that they only considered the systems whose components have several discrete states. For those whose components have continuous states, these methods are not effective either. This paper considered the continuous distribution of components states during the approximation of Multi‐State System (MSS) reliability and proposed a method to assess the reliability of this kind of system using Monte‐Carlo simulation. This method will also be useful when we have no enough data to know the exact discrete states and related probability, and can only estimate components states distribution types and related parameters. Two examples were employed to illustrate the method. Comparison of the two examples shows that component state uncertainty has significant influence on the assessment of system reliability. Our effort will make the reliability approximation more realistic compared with existing methods.

Numerical Approach for Assessing System Dynamic Availability Via Continuous Time Homogeneous Semi-Markov Processes

Continuous-time homogeneous semi-Markov processes (CTHSMP) are important stochastic tools to model reliability measures for systems whose future behavior is dependent on the current and next states occupied by the process as well as on sojourn times in these states. A method to solve the interval transition probabilities of CTHSMP consists of directly applying any general quadrature method to the N2 coupled integral equations which describe the future behavior of a CTHSMP, where N is the number of states. However, the major drawback of this approach is its considerable computational effort. In this work, it is proposed a new more efficient numerical approach for CTHSMPs described through either transition probabilities or transition rates. Rather than N2 coupled integral equations, the approach consists of solving only N coupled integral equations and N straightforward integrations. Two examples in the context of availability assessment are presented in order to validate the effectiveness of this method against the comparison with the results provided by the classical and Monte Carlo approaches. From these examples, it is shown that the proposed approach is significantly less time-consuming and has accuracy comparable to the method of N2 computational effort.

Semi-Parametric Estimation of P X,Y (X > Y)

In the context of reliability the stress-strength model describes the life of a component which has a random strength X and is subject to a stress Y. The component fails at the instant the stress applied to it exceeds the strength and the component will work satisfactory in case of the event {(x, y) | x > y}. Thus R = PX,Y ({(x, y) | x > y}) is a measure of system reliability. In this paper, we obtain semi parametric estimators of the reliability under stress-strength model for the exponential distribution under complete and censored samples. We illustrate the performance of the estimators using a simulation study.

Genetic algorithm optimisation of the maintenance scheduling of generating units in a power system

A new method for optimisation of the maintenance scheduling of generating units in a power system is developed. Maintenance is scheduled to minimise the risk through minimisation of the yearly value of the loss of load expectation (LOLE) taken as a measure of the power system reliability. The proposed method uses genetic algorithm to obtain the best solution resulting in a minimal value of the annual LOLE value for the power system in the analysed period. The operational constraints for generating units are included in the method. The proposed algorithm was tested on a Macedonian power system and the obtained results were compared with the results received from the approximate methodology. The results show the improved reliability of a power system with the maintenance schedule obtained by the new method compared to the results from the approximate methodology.

Reliability analysis of linear dynamical systems using approximate representations of performance functions

A method to carry out reliability analysis of linear systems with random structural parameters and random excitation is presented. Probability that design conditions are satisfied within a given time period is used as a measure of system reliability. An efficient importance sampling technique is used to estimate the failure probabilities. This technique is combined with high quality approximations of the performance functions in terms of uncertain structural parameters. The number of dynamic analyses required during the estimation process is minimized since the simulations are carried out by evaluating explicit expressions. The explicit quantities correspond to approximate representations of the performance functions in terms of the uncertain structural parameters. A numerical example corresponding to problem 2, sub-case 2 of the benchmark study is presented to illustrate the accuracy and computational efficiency of the proposed computational procedure.

A system model for reliability assessment of smart structural systems

Smart structural systems are defined as ones that demonstrate the ability to modify their characteristics and/or properties in order to respond favorably to unexpected severe loading conditions. The performance of such a task requires a set of additional components to be integrated within such systems. These components belong to three major categories, sensors, processors and actuators. It is wellknown that all structural systems entail some level of uncertainty, because of their extremely complex nature, lack of complete information, simplifications and modeling. Similarly, sensors, processors and actuators are expected to reflect a similar uncertain behavior. As it is imperative to be able to evaluate the impact of such components on the behavior of the system, it is as important to ensure, or at least evaluate, the reliability of such components. In this paper, a system model for reliability assessment of smart structural systems is outlined. The presented model is considered a necessary first step in the development of a reliability assessment algorithm for smart structural systems. The system model outlines the basic components of the system, in addition to, performance functions and inter-relations among individual components. A fault tree model is developed in order to aggregate the individual underlying component reliabilities into an overall system reliability measure. Identification of appropriate limit states for all underlying components are beyond the scope of this paper. However, it is the objective of this paper to set up the necessary framework for identifying such limit states. A sample model for a three-story single bay smart rigid frame, is developed in order to demonstrate the proposed framework.

Analytical method for reliability and MTTF assessment of coherent systems with dependent components

This paper discusses engineering systems with structural as well as failure dependence among their components. Using the Markov process approach, a coherent system of components with multivariate phase type life distribution is introduced to model the components working in a common random environment. The phase type model is flexible enough to comprise many realistic situations, and also manages to yield the explicit matrix representations of the system reliability measures. Some examples are also presented to illustrate the fact that ignoring the failure dependence among the components often results in over-estimating or under-estimating the system reliability.