Stochastic analysis of standby system with duplex units

This paper investigates a mathematical model of a system composed of two units, one operative and the other cold standby. Each unit of the system is made of two non-identical parallel components and each component is made of n-elements. Henceforth we call each unit of the system a duplex unit. Failure and repair time distributions of each element of a component are negative exponential and vary from element to element, whereas the repair time distribution of a unit is arbitrary. Upon the failure of the operative unit the standby unit does not operate instantaneously. This type of situation may be found in many electronic networks. Several reliability characteristics of interest have been obtained.     

Reliability prediction of imperfect switching systems subject to multiple stresses

Reliability prediction plays a very important role in system design, and the two key factors considered in predicting system reliability are: failure distribution of the component/equipment and system configuration. This paper discusses about the imperfect switching system with one component in active and k spares in the standby state. When the operating component breaks down, the switch will be able to detect the failure using the sensor and replace the defective component with a functionable spare, so the system can keep operating. Therefore, the switch and the sensor have direct impact on normal operations of the switching systems.The reliability of two types of imperfect switching system is thoroughly discussed and compared: (1) a non-repairable system with only one standby component, one switch and one sensor and (2) a non-repairable system with two standby components, one switch and one sensor. Since gamma distribution is fairly adequate to describe the failure mechanism of a system under k-times of shock multiple stresses. This paper then assumes in system (1) and (2), the operating components follow gamma failures, sensor and switch failures follow exponential distribution. In addition, three modes are assumed in regards to the switch failure: under energized, under failing-open and under failing-closed condition.This paper uses MAPLE computer language to perform reliability estimation and comparison on the above-mentioned systems with components, switch and sensor under different failure rate and various intended period of use. Its results can provide guidelines on decision making for improving system design in industries.     

Estimation of Reliability from Multiple Independent Grouped Censored Samples with Failure Times Known

Failure times of one type aircraft-engine component were recorded. In addition, life times are periodically recorded for unfailed engine components. The data are considered as multiple s-independent grouped censored samples with failure times known. The assumed failure model is the 2-parameter Weibull distribution. Maximum likelihood estimates are derived. The exponential model is used for comparison. Monte Carlo simulation is used to derive s-bias and mean square error of the estimates. The asymptotic covariance matrix was computed for the sampling conditions studied. The maximum likelihood estimates of the reliability were obtained as a function of component operating time since overhaul.     

Fault tolerant real time control system for steer-by-wire electro-hydraulic systems

A steer-by-wire (SBW) control system is presented with emphasis on safety issues. The applications are in articulated vehicles such as the wheel type loaders, articulated trucks, and others. The electro-hydraulic (EH) power circuit is controlled by two embedded electronic control modules (ECM), the primary ECM and backup ECM. The two ECMs monitor each others condition. If one detects fault in the other, it takes over the control functions. There are two main control algorithms that run in the ECMs in real-time: the steering valve control algorithm and the failure detection algorithm. The valve control algorithm basically generates command signal to the steering valve based on operator steering column signal as well as other machine condition sensors.The failure detection algorithm implements a fault detection logic for both input sensors and output drivers, and flags the corresponding warning for to the operator, and take a predefined action depending on the type of the failure detected. A unique fault strategy organization is implemented by inspecting the failure behavior on both the component and the system levels. The failure detection algorithm also determines the most likely “good” sensor signal from a set of redundant sensors for each critical measurement. Based on these good sensors data, the steering control algorithm sends two output signals: the control signal to the steering EH circuit valve and the control signal to the steering wheel force feedback device (i.e. a brake or a motor) to give operator feedback about the steering conditions.Finite state machine (FSM) concept is used to design the fault handling algorithms for both the component level and the system level failure. The probability of the system being at normal steering state or at any other steering failure state is determined. Failure mode probabilities of steering system components are also determined.     

Approximated reliability of r-out-of-n(F) system with common cause failure and maintenance

In modern industries very high reliability system are needed. To improve the reliability of system, the component redundancy and maintenance of component or system play an impotant role and must be studied. This paper presents a reliability model of a r-out-of-n(F) redundant system with maintenance and Common Cause Failure. Failed component repair times are arbitrarily distributed. The system is in a failed state when r units failed because of the combination of single element failure or CCF(Common Cause Failure). Laplace transformation of reliability is derived by using analysis of Markov state transition graph. By using the analyzed MTBF, we compute MTBF of r-out-of-n(F) system. The MTBF with CCF is saturable even if repair rate is large.Approximated reliability of the r-out-of-n(F) system with maintenance and Common Cause Failure O.SummaryThe paper presents a reliability model of a r-out-of-n(F) redundant system with maintenance and Common Cause Failure. Failed component repair times are arbitrarily distributed. The system is in a failed state when r units failed because of the combination of single element failure or Common Cause Failure. Laplace transformation of reliability is derived by using analysis of Markov state transition graph. By analyzing this mean visiting time equations, we compute MTBF and shows computational example. The MTBF with CCF is saturable even if repair rate is large. In general the maintenance overcomes MTBF bounds, But the repair method not overcome the MTBF saturation when the system has Common Cause Failure.     

Estimators for Reliability Measures in Geometric Distribution Model Using Dependent Masked System Life Test Data

Masked system life test data arises when the exact component which causes the system failure is unknown. Instead, it is assumed that there are two observable quantities for each system on the life test. These quantities are the system life time, and the set of components that contains the component leading to the system failure. The component leading to the system failure may be either completely unknown (general masking), isolated to a subset of system components (partial masking), or exactly known (no masking). In the dependent masked system life test data, it is assumed that the probability of masking may depend on the true cause of system failure. Masking is usually due to limited resources for diagnosing the cause of system failures, as well as the modular nature of the system. In this paper, we present point, and interval maximum likelihood, and Bayes estimators for the reliability measures of the individual components in a multi-component system in the presence of dependent masked system life test data. The life time distributions of the system components are assumed to be geometric with different parameters. Simulation study will be given in order to 1) compare the two procedures used to derive the estimators for the reliability measures of system components, 2) study the influence of the masking level on the accuracy of the estimators obtained, and 3) study the influence of the masking probability ratio on the accuracy of the estimators obtained     

A multivariant exponential shared-load model

A shared-load model of the exponential distribution is used to describe the characteristics of dependent redundancies. In the shared-load model, the redundant components equally share the workload. Upon failure of one or more components, the remaining components must carry an increased load. This study extends the Freund bivariate model to a three-component model and a special N-component model. A general form for system reliability is developed. Failure rates are estimated using maximum likelihood. Systems such as a multiprocessor computer, a multiple-engine system, and a paired system can be described by this model     

Dependability analysis of systems with on-demand and active failuremodes, using dynamic fault trees

Safety systems and protection systems can experience two phases of operation (standby and active); an accurate dependability analysis must combine an analysis of both phases. The standby mode can last for a long time, during which the safety system is periodically tested and maintained. Once a demand occurs, the safety system must operate successfully for the length of demand. The failure characteristics of the system are different in the two phases, and the system can fail in two ways: (1) it can fail to start (fail on-demand), or (2) it can fail while in active mode. Failure on demand requires an availability analysis of components (typically electromechanical components) which are required to start or support the safety system. These support components are usually maintained periodically while not in active use. Active failure refers to the failure while running (once started) of the active components of the safety system. These active components can be fault tolerant and use spares or other forms of redundancy, but are not maintainable while in use. The approach, in this paper, automatically combines the "availability analysis of the system in standby mode" with the "reliability analysis of the system in its active mode." The general approach uses an availability analysis of the standby phase to determine the initial state probabilities for a Markov model of the demand phase. A detailed method is presented in terms of a dynamic fault-tree model. A new "dynamic fault-tree construct" captures the dependency of the demand-components on the support systems, which are required to detect the demand or to start the demand system. The method is discussed using a single example sprinkler system and then applied to a more complete system taken from the off-shore industry     

A k-out-of-N:G redundant system with dependent failure rates and common-cause failures

This paper presents a k-out-of-N: G redundant system with dependent failure rates, common-cause failures and r repair facilities. The failure rates of the components increase as the number of components failed increases, while the repair rates are constant. Common-cause failure is not considered in Model I. In Model II the common-cause failures are involved. Steady-state probabilities and steady-state availability are derived.     

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.     

Optimal Consecutive-k-out-of-n:F Component Sequencing

A consecutive-k-out-of-n:F system is an ordered linear arrangement of n components that fails if and only if at least k consecutive components fail. Suppose that all components are interchangeable, that component failures are s-independent, and that component failure probabilities need not be equal. When k = 2, a certain ordering of the components minimizes the probability of system failure regardless of the particular component failure probabilities. This paper characterizes all other values of k and n for which such an optimal configuration can be determined without knowledge of the component failure probabilities.     

A method to test whether a system is near failure

A method is presented for the identification of system states near system failure before its occurrence, from observations of component states. State vectors of components are classified into finite system states, based on two measures of the distance from system failure; the logical distance and the probabilistic distance. The method first obtains the Boolean function representing the structural relation between component states and system states classified by the logical distance and then computes the probabilistic distance of the current state vector from system failure.     

A Time-Dependent Complex System With Preemptive Priority Repairs

A repair system is analyzed that has three kinds of components, each with a different repair priority. Type 1 is essential to system operation and has the highest priority of repair; there is only one such component. Type 2 is nonessential (its failure degrades the system) and has an intermediate priority of repair. Type 3 is similar to type 2 except that it has the lowest priority of repair. There are many types 2 and 3 components. The differential equations for system state probabilities are solved by Laplace transforms, but only in implicit form.     

Availability analysis of a two-unit cold standby system with two switching failure modes

We consider a 2-unit cold standby redundant system with two switching devices—transfer switch and connect switch. The system is analysed under the assumption that each unit works in three different modes—normal, partial failure and total failure. Failure time distributions of units and connect switch are exponential, whereas repair time distributions are general. At any instant after use the transfer switch fails with probability q = 1?p. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated. A few particular cases are discussed.     

Statistical Model for a Failure Mode and Effects Analysis and its Application to Computer Fault-Tracing

This paper presents a mathematical model of a general statistical approach to a system Failure Mode and Effects Analysis (FMEA). It describes, in particular, the FMEA theory itself, and its application to computer fault-tracing, using a Markov model. The theory yields both a reliability table showing system failure-state probabilities, and a criticality table identifying probable causes of system failure. Computer fault-tracing is implemented by using Markov chains to generate system output-state conditional probabilities. Feedback loop effects are eliminated by using Markov recursive relations for absorption probabilities. This statistical FMEA technique examines individual outputs on every individual component to determine statistically its critical impact on every system output. The fault tracing required is done by computer processing and is exhaustive. The reliability analyst is not required to make any intultive assumptions or simplifications on the complexity of the system block diagram or the effects of feedback loops, and the analyst does not have to decide which components should be examined for criticality. Instead, the analyst's work is shifted to understanding how each component works and relating this understanding to the FMEA technique.     

Availability Allocation Using a Family of Hyperbolic Cost Functions

This paper develops a technique for allocating the parameters, repair time and failure rate, to each component of a system at the lowest possible cost. The allocations are subject to the constraint of a required availability. To make an analytic solution possible, the assumptions of constant failure rates, s-independent components, series system, and no multiple failures were made. Each component is assumed to have a hyperbolic cost function associated with changing its failure rate and its repair time. A Lagrange Multiplier method was used to solve the problem.     

A Method for Predicting System Downtime

A system whose components, upon failure, are repaired or replaced is considered. Only two system states, the ``operating' state and the ``failed' state, are distinguished. The system is by defined a reliability network and by the failure rate and repair rate of each component. The time to failure and the time to repair of the components are assumed to be exponentially distributed. A criterion of system worth is the random variable ``downtime,' denoted by D(t), which is defined as the time the system is down during the time interval (0, t). The following questions are answered: 1) What is the distribution function of D(t)? 2) What are the mean and the variance of D(t)? 3) What is the asymptotic behavior of D(t) for large values of t? 4) How can one make approximate probability statements about D(t)? It is shown that the beta distribution is a suitable approximation for the conditional distribution of D(t)/t, given that at least one failure has occurred, and that for t greater than 20 mean failure times the distribution of D(t) is practically normal.     

Optimal arrangement of components in a consecutive k-out-of-r-from n:F system

A consecutive k-out-of-r-from n:F system is an ordered linear arrangement of n components that fails if and only if at least k in a “window” of r consecutive components fail. Suppose that all components are interchangeable and that component failures are s-independent. Component failure probabilities need not be equal. In this paper the ordering of the components in order to minimize the probability of system failure is examined. All values of k,r,n for which an optimal configuration can be determined, without knowledge of the component failure probabilities, are given.     

ESD tester parasitics and stress conditions and their impact on device failure levels and failure mechanisms

A comparative study of Human Body and Machine Model (HBM/MM) testers is performed using a very large sample size for statistical significance. Failure mechanisms and types of damage are categorized with the use of photoemission spectrum analysis. Tester parasitic values are extracted for each machine, and a correlation is established to failure thresholds, distributions and failure mechanisms.     

Reliability analysis of a fault tolerant computer system

This paper investigates a mathematical model of an information computer network system. In this model, the system has two parts—a controller and a terminal. It is also linked with a satellite by a disk antenna. Each part has two failure modes; one is transient failure and second is latent failure. After latent failure, the terminal is recoverable, but the controller is not recoverable. The system may also fail due to a common-cause failure when it is in the normal state or in a partially normal state. Failure rates are constant and recovery rates are general. Using the regenerative point technique several measures of system effectiveness are obtained.