Modeling and analysis of standby redundant computing systems

In this paper, we have developed performance models to represent the fault-tolerant characteristics of standby redundant computing systems. These models have the advantage of being quite general and are useful to study the performance characteristics under any arbitrary life time distribution for the components of the system. For the proposed models, we have derived expressions for three performance metrics for these systems.     

Availability formulae for standby systems of similar units that arepreventively maintained

Some simple approximation formulae for the availability of standby redundant systems comprising similar units that are preventively maintained are presented. The formulae are established using standard Markov theory. A number of simulations have been performed in order to evaluate the formulae. The simulations show that the formulae give very good approximations for various preventive maintenance regimes. These formulae have been used to model the performance of standby systems on offshore platforms     

Cost analysis of a three-state standby redundant electronic equipment

In this paper, the investigations have been carried out for the cost function analysis of a standby redundant system having three states. The two-unit standby redundant system suffers two types of failures: viz. minor and major, which bring the system to degraded or a complete failure stage. There is only one server and is always available. Failure and repair times for the system follow exponential and general distributions respectively. Laplace transforms of the probabilities of the complex system being in various states have been derived, which have been inverted further so as to obtain time dependent probabilities. To highlight the important results, two graphs have also been given in the end.     

A model for optimal repair-effort decision for standby redundant systems with common-cause failures and its application to pulverizer systems

This paper presents a model to allocate the repair efforts optimally between the individual unit and the subsystem contributing to the common cause failure of the system with a view to improving the overall system availability. It describes a general model to solve repair-effort decision problem for a redundant system with common-cause failures and three types of repair. The application of this model to a pulverizer system is also presented in this paper.     

Multi-state device redundant systems with common-cause failures and one standby unit

This paper presents two mathematical models. Model I represents a two identical unit active redundant system whose units may fail in either of the two mutually exclusive failure modes. Similarly, model II represents a two non-identical unit active parallel system whose units either fail or survive. In addition, models I and II comprise the occurrence of common-cause failures and one standby unit. Systems are only repaired when all the system units fail (including the standby unit). System repair times are arbitrarily distributed. Laplace transforms of the state probability equations are developed.     

G/G/G two-unit standby redundant systems

This paper discusses the availability and reliability characteristics of three models of two-unit standby redundant systems in which all the distributions involved are arbitrary.     

A warm standby redundant system with correlated failures and repairs

This paper presents the analysis of a two-unit warm standby system assuming a bivariate exponential density for the joint distribution of failure and repair times of the units. Investigations regarding the stochastic behaviour and important reliability characteristics of the system have been made and earlier results have been verified as particular cases. A few graphs have also been provided to support the theoretical results.     

A three-unit standby redundant system with repair and preventive maintenance

This paper deals with the reliability of a renewable three-unit system under preventive maintenance activity. The Laplace transform of the reliability function and the mean lifetime of the system have been obtained under the assumption that the failure times, repair times, inspection times and maintenance times are random variables having different distributions. Some special cases also have been obtained.     

Reliability analysis of a three-state multi-component warm standby redundant complex system with waiting for repair

Investigations have been carried out with the help of Laplace transforms and supplementary variable techniques for the evaluation of reliability analysis of a three-state multi-component warm standby redundant complex system suffering three types of failures, namely minor, major, and human due to critical human errors incorporating the concept of waiting for repair.     

Reliability analysis of a two-unit cold standby redundant system with two operating modes

This paper considers a two unit cold standby redundant system subject to a single repair facility with exponential failure and general repair time distribution. Each unit can work in three different modes — normal, partial failure and total failure. There is a perfect switch to operate the standby unit on total failure of the operative unit. The system has been analysed to determine the reliability parameters e.g. mean time to system failure (MTSF), steady state availability, mean recurrence to a state and expected number of visits to a state, first two moments of time in transient state, by using the theory of Semi-Markov Process. Howard's reward structure has been super-imposed on the Semi-Markov Process to obtained expected profit of the system. A number of results obtained earlier are derived as particular cases.     

Human error analysis of a standby redundant system with arbitrarily distributed repair times

This paper presents human error analysis of a (two units working and one on standby) system with arbitrarily distributed repair times. The supplementary vairables method is used to develop the system availability expressions. A general formula for the system steady-state availability is developed when the failed system repair times are gamma distributed. Time-dependent availability, system reliability with repair, mean time to failure and variance of time to failure formulae are developed for some particular cases. Selective plots are shown to demonstrate the impact of critical human error on system availability and reliability.     

Analysis of a two unit standby redundant fail-safe system

This paper evaluates reliability and fail-safety of a two unit cold standby fail-safe redundant system. Three modes of failure—(1) failure due to human error, (2) failure due to unit faults and (3) failure due to switchover faults—are considered. The complete failure states of the system are divided into two categories, fail-safe state and fail-dangerous state. Several fail-safety measures of interest to a fail-safe system designer are defined and evaluated, such as safety function, safety ratio and danger ratio.     

Cost analysis of a 2-unit standby redundant electronic system with critical human errors

In this paper, investigations have been carried out for the evaluation of availability and expected profit during the operable stage of a standby redundant, electronic system, incorporating the concept of human failure. The system can be in any of the three states: good, degraded and failed. One repair facility is available for the repair of a unit in failed or degraded state. The system cannot be repaired when it fails due to critical human errors. The repair of the system in any state follows general distribution. To make the system more applicable to practical life problems, time dependent probabilities have been evaluated so as to forecast the expected profit and the operational availability of the system at any time.     

Reliability analysis and optimization applications of a two-unit standby redundant system with spare units

Consider a two-unit standby redundant system with two main units, one repair facility, and n spare units. When the main unit has failed and the other is under repair, a spare unit takes over the operation and if it fails, it is replaced by a new one until the repair of the failed unit is completed. The system fails when the last spare unit fails while one main unit is under repair and the other has failed. In this paper, we derive expressions for 1) the distribution function of the first time to system failure, 2) the probability that the total number of failed spare units during the time interval (0,t] is n and 3) the mean of the total number of failed spare units in (0,t] and its asymptotic behaviour. Introducing costs incurred for each failed main unit and each failed spare unit, the expected cost per unit of time of the system was also derived. Finally an optinmization problem is discussed in order to compare the expected cost of the system with both main units and spare units with that of spare units only, and particular cases are considered.     

Optimal planned maintenance with salvage cost for a two-unit standby redundant system

This paper considers the optimal spare ordering policies for a cold standby redundant system with two dissimilar units. Especially, the planned maintenance schedule with salvage cost is discussed. The failure time distributions for respective units are assumed to be arbitrary. By applying the expected cost per unit time in the steady-state and the stationary availability as criteria of optimality, the optimal ordering policy minimizing or maximizing each criterion is obtained under some economical and/or physical assumptions. Finally, numerical examples are presented, and the effect of the failure time distributions for the optimal ordering policy is examined in detail.     

Stochastic behaviour of a standby redundant system with three modes

This paper discusses the stochastic behaviour of a two-unit cold standby redundant system in which each unit works in three different modes-normal, partial failure and total failure. Failure-time distributions of units are exponential, whereas repair-time distributions are arbitrary. Explicit expressions for the Laplace-Stieltjes transforms of the distribution function of the first passage time, mean time to system failure and steady state availability of the system are obtained. A few particular cases are discussed.     

A k-out-of-N:G redundant system with cold standby units and common-cause failures

This paper presents a k-out-of N:G redundant system with M cold standby units, r repair facilities and common-cause failures. The constant failure rates of the operating and cold standby units are different. Failed system repair times are arbitrarily distributed. The system is in a failed state when (N+M?k+1) units failed or a common-cause occurred. Laplace transforms of the state probabilities, the availability of the system and the system steady-state availability are derived.     

Comparative reliability analysis of simplex and redundant systems

This paper presents the comparative reliability analysis of simplex and selective redundant configurations. System configurations such as k-out-of-n units, bridge, series-parallel and parallel-series are compared with the simplex system when the unit failure rate is constant and time dependent. Comparative reliability plots are shown for different reliability networks and failure time distributions. As expected, the detailed investigation shows that the system mean-time-to-failure may be a misleading indicator of performance for mission-oriented systems.     

A new algorithm for performance analysis of communication systems

An algorithm is proposed for generating in order the most likely states of a probabilistic system, thus allowing a more-rapid procedure than previously available for analyzing the performance of communication networks with stochastically failing components. The algorithm improves the algorithm reported by Y. F. Lam and V.O.K. Li (ibid., vol.COM-34, no.5, p.496-7, May 1986), in terms of both storage requirements and execution efficiency