A Reliability and Comparative Analysis of Two Standby System Configurations

Equations are derived which enable one to calculate the system reliability for parallel or triple modular redundant systems with standby spares. Software error detection is introduced into the TMR/Spares system configuration in order to utilize fully all of the units. An indication of the sensitivity of the system reliability to an increase in the number of spares, partitioning, switching, variations in the powered and unpowered failures rates, and time is presented. A comparison of the parallel and the TMR/Spares system configurations, under similar conditions, is given.     

Reliability of Special Redundant Systems Considering Exchange Time and Repair Time

The reliability of a 2-out-of-3 parallel redundant system having a limited number of standby spare units is derived when the exchange of the failed unit for a spare unit is not instantaneous. The reliability can be represented in the form of a failure state diagram. When the number of standby spares and the repair rate are both small, the influence of the exchange rate is small. When the number of standby spares and the repair rate are both large, the influence of the exchange rate is large. The number of standby spares and the repair rate influence the probability that system failure occurs after all spare units have failed. The exchange rate strongly influences the probability of system failure during the exchange time.     

Confidence Limits for Redundant-System Availability

s-Confidence limits are established for the Availability of a standby redundant system (1-out-of-N:G system) for both hot and cold spares consisting of several identical units and repair facilities. The failure and repair rates of the units are s-independent, constant, and estimated from test data.     

Reliability of Some Redundant Systems with Repair

A mathematical model is established for the reliability of modularly redundant systems with repair. The model allows different hazard rates for active units and for standby units. The hazard rates are assumed to be constant. The cases of constant repair rate and constant repair time for a two unit system are evaluated using the reliability and mean time between failure. The approach is then extended to systems with more than two units. A system parameter, relating to certain types of sensing, switching, and/or recovery has a very significant impact on system reliability for modularly redundant systems with repair.     

A rapid smart approach for reliability and failure mode analysis of memories and large systems

This paper presents a novel system simulation methodology based on the known Monte Carlo technique, used for reliability and failure mode analysis of complex and large systems. The presented approach, called “state-merging and assorted random-testing” (SMART), is particularly applicable to systems involving different types of clusters of identical components, and is ideally suited for simulation of huge memories and similar systems. Simulators based on this approach are insensitive to the number of system components, system reliability or the number of associated spares or standby units, and thus they afford an extremely small simulation time compared to the accelerated Monte Carlo simulation time.     

Stochastic programming models for general redundancy-optimization problems

This paper provides a unified modeling idea for both parallel and standby redundancy optimization problems. A spectrum of redundancy stochastic programming models is constructed to maximize the mean system-lifetime, /spl alpha/-system lifetime, or system reliability. To solve these models, a hybrid intelligent algorithm is presented. Some numerical examples illustrate the effectiveness of the proposed algorithm. This paper considers both parallel redundant systems and standby redundant systems whose components are connected with each other in a logical configuration with a known system structure function. Three types of system performance-expected system lifetime, /spl alpha/-system lifetime and system reliability-are introduced. A stochastic simulation is designed to estimate these system performances. In order to model general redundant systems, a spectrum of redundancy stochastic programming models is established. Stochastic simulation, NN and GA are integrated to produce a hybrid intelligent algorithm for solving the proposed models. Finally, the effectiveness of the hybrid intelligent algorithm is illustrated by some numerical examples.     

Evaluation of reliability and safety of long-term unmaintained computer systems

In many applications such as critical life-saving systems, safety is an important design issue as well as reliability. Among various commonly-used approaches in the implementation of on-line unrepairable fault-tolerant systems, standby systems achieve the most satisfactory reliability figure, followed by duplex systems, hybrid systems and triple modular redundancy. Nevertheless, the safety figure of duplex systems is superior to that of the standby approach. In this paper, the failure rate of system modules and hard core is predicted by the M1L-HDBK-217E model, and we show that the reliability and safety figure of cold standby systems can be further dramatically improved by increasing the number of spare units. Furthermore, comparative measures such as the reliability improvement factor, the safety improvement factor and the mission time improvement factor are proposed for showing that long-term unmaintained systems have reliability and safety as high as other systems that must be repaired.     

Techniques for Optimum Spares Allocation: A Tutorial Review

In many modern complex systems the problem of achieving high reliability leads to the use of interchangeable modular components accompanied by a stock of spare parts. This paper examines, compares, and assesses several of the techniques presented in the literature for allocating the numbers of spares of each part type to be stocked in order to maximize the system reliability subject to constraints on resources (i.e., weight, volume, cost, etc.). The problem of optimum spares allocation is complicated since resources are consumed in a discrete fashion and the expression for the system reliability is a nonlinear transcendental function. The classical dynamic programming algorithm produces all optimal spares allocations; however, the solution can become computationally intractable even with the aid of a modern high-speed digital computer. In the case of multiple constraints the time problem is vastly exacerbated. In such a case one must turn to a procedure that yields a near-optimal solution in a reasonable amount of computer time. Two approximate methods discussed in this paper are the incremental reliability per pound algorithm and the Lagrange multiplier algorithm. These algorithms are readily adaptable to handle multiple constraints. Computer programs are developed for each of the three optimization algorithms and are utilized to obtain the spares allocation for a few systems. The optimization theory presented is directly applicable to series or parallel systems. A concluding example illustrates how this can be extended to certain series-parallel systems.     

A Computer Algorithm for Optimal Maintenance of Standby Redundant Systems

A class of standby redundant systems with exponential failure-time and repair-time distributions is considered. There are several alternatives available in each state (up or down) to maintain the system. A computer algorithm is developed to obtain the maintenance policy that maximises s-expected profit of a standby redundant system.     

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.     

A cold standby system with multiple switch-over devices attended by a monitor

We introduce a cold standby redundant system with multiple switch-over devices attended by a monitor. All distributions involved are arbitrary. We also consider the case of a single switch-over device and we compare the performance of both systems.A numerical example shows the impact of standby redundancy and imperfect switching on a system's overall reliability.Particular results obtained in previous literature are generalized.     

General Expressions for Reliability of Redundant Systems

General expressions for reliability and mean time-to-failure of parallel and standby redundant systems are shown. Each unit in the system has a constant failure rate and need not be good at the beginning.     

Reliability of a 3-unit cold redundant system with Weibull failure

Redundancy technique is applied to increase the reliability of a system where maintenance or repair is either not possible or is too costly. Reliability of a cold redundant system is always higher than a hot one. Moreover the increase in reliability due to adding of a unit in sequence can always be exactly determined.Literature is full of derivation of reliability expressions of a cold redundant system whose units obey exponential failure density. Due to extreme difficulty in evaluation of integrals involving Weibull density function, few attempts on derivation of reliability of redundant systems have been made. We have here derived reliability of a simple case of a 3-unit cold standby system whose units obey Weibull failure density.     

LD Redundancy System Using Polarization Components for a Submarine Optical Transmission System

An LD redundancy system having one cold standby laser diode is proposed to improve reliability in submarine optical transmission systems. This system makes use of the intrinsic laser polarization and consists of two LD modules and a polarization coupler connected by polarization maintaining (PANDA) fibers. The optical power insertion loss of this LD redundant system is 5.5 dB, including coupling loss between the laser diode and PANDA fiber. This LD redundant system will be applied in submarine optical repeaters.     

LD redundancy system using polarization components for a submarine optical transmission system

An LD redundancy system having one cold standby laser diode is proposed to improve reliability in submarine optical transmission systems. This system makes use of the intrinsic laser polarization and consists of two LD modules and a polarization coupler connected by polarization maintaining (PANDA) fibers. The optical power insertion loss of this LD redundant system is 5.5 dB, including coupling loss between the laser diode and PANDA fiber. This LD redundant system will be applied in submarine optical repeaters.     

Reliability of Some Modularly Redundant Systems

A mathematical model is established for the reliability of modularly redundant systems with unequal failure rates for the operating and standby units. The failure modes include failures of the active and standby units, three types of switch failures, and failures on system recovery. System reliability is considered for cases of both similar and dissimilar units, and for various restrictions on the failure parameters. It is shown that the most important failure parameters are those related to catastrophic failures, and that putting more reliable units as basic units, which operate initially, is important when switches and recovery are imperfect.     

Reliability of a Special Class of Redundant Systems

This paper develops equations for predicting the reliability of a special class of redundant systems. Applicable systems include those which operate in a standby mode for a long period of time in anticipation of participation in a single mission. Manual repair is allowed in the standby mode but not in the mission mode. The analysis is also applicable to the single-mission case alone (no standby), where the reliability in this case is evaluated as a function of the reliability state at the start of the mission. The development employs the traditional approach using the concept of failure states and the attendant birth-and-death equations.     

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     

Some Problems of Tradeoff When the Standby Units and Operating Units of a Redundant System Have Different Probabilities of Success

This note considers a redundant system in which the standby units may have a different probability of success than the operating units for a given mission profile. A model is developed so that one can calculate the system reliability for the mission. Furthermore, for the case where reliabilities (probabilities of mission success) of the standby units can be related to the cost of these units, a tradeoff study is made in a few special cases to determine the optimum number of standby components (in the sense of maximizing system reliability) to be installed when there is a fixed sum of money available for the installation of standby units.     

Reliability analysis of a biogas plant having two dissimilar units

A biogas system with two dissimilar production units is considered. Mathematical modelling is carried out for the system to calculate the reliability and mean time to system failure of the system. Two models (parallel redundant and standby redundant) are given. Formulation is done using a simple probabilistic approach and the supplementary variable technique. The problem is solved using simple methods for solving differential equations. Expressions for profit function are given.