Reliability of a 2-Unit Standby Redundant System with Constrained Repair Time

This paper considers a 2-unit warm-standby redundant system with repair. The repair of a failed unit is constrained as follows: Associated with each failure of a unit is a random variable termed the Maximum-Repair-Time (MRT) of the failure. If the repair of a failed unit is not completed within the MRT, the unit is rejected for further use. Two types of failure stituations for the system are considered: 1) No allowed down time, and 2) Some allowed down time. Expressions for the Cdf of the Time to System Failure (TSF) and the mean TSF are derived by using Markov renewal processes.     

Reliability of a 2-Unit Priority-Standby Redundant System with Finite Repair Capability

This paper analyses the reliability of a 2-unit standby redundant system consisting of two dissimilar units. Unit 1 performs the desired system function whenever available for use. Unit 2 operates only during those periods when unit 1 is undergoing repair. Unit 1 can be repaired at most N times. Expressions for the Laplace-Stieltjes transform of the distribution of the Time to System Failure (TSF) and the mean TSF are derived.     

Reliability Considerations for a 2-Unit Redundant System with Erlang-Failure and General Repair Distributions

This paper considers the case of a 2-identical-unit redundant system with Erlang-failure and general repair distributions. Two cases are considered: 1) the failure of each unit is independent of the other; 2) when one unit fails, the failure distribution in the other unit changes. The Laplace transforms of the distribution of time to system failure and the explicit formula for the mean time to system failure are derived.     

A 2-Unit Repairable Redundant System with Switching Failure

The switch has two different failure modes: It switches an operating unit out of operation when it should not, and does not switch the standby in when it should. We consider a 2-unit warm-standby redundant system with two switching failure modes, and derive the stochastic behavior of system failure. Several reliability models are shown as special cases.     

Bayes Reliability Assessment of a 2-Unit Hot-Standby Redundant System

This study assesses the reliability of a 2-unit hot-standby redundant system with an imperfect switch. The prior knowledge of experts is used in the assessment through Bayes theorem. Bayes interval limits for the system reliability are presented. The predictive distribution of the first failure time of the system is formulated.     

Optimum Preventive Maintenance Policies for a 2-Unit Redundant System

Optimum preventive maintenance policies are discussed to maximize the availability for a 2-unit standby redundant system. The Laplace-Stieltjes transform of the pointwise availability and the steady-state availability are derived by applying a unique modification of the regeneration point techniques under the assumptions that all the distributions are arbitrary. A theorem gives the optimum preventive maintenance time which is a unique and finite solution of the equation under certain conditions. A numerical example is presented.     

Stochastic Behavior of 2-Unit Standby Redundant Systems with Imperfect Switchover

We discuss two models of 2-unit standby redundant systems with imperfect switchover. In Model I the switch assumes up and down states repeatedly, independently of the behavior of the main unit. We obtain the stochastic behavior of the system, i.e., the first-passage time distributions, the expected numbers of visits to a certain state, and the transition probabilities. In Model II the failure of the switch can be detected only when it is used.     

A 2-Unit Warm-Standby Redundant System With Delay and One Repair Facility

This paper introduces the Delay Times (preparing/waiting time for repair). The Laplace-Stieltjes transform of 1) The first-passage time distribution to system failure, 2) The s-expected number of system failures during (0, t], 3) The probability that the system fails at time t, are all derived for a 2-unit warm-standby redundant system by unique modification of a Markov Renewal process. Three examples are given     

Mean Time to System Failure for a 4-Unit Redundant Repairable System

The mean time-to-system-failure is derived for a system with 4-identical components, each of which has a constant failure rate and unspecified repair rate.     

Parametric Analysis of 2-Unit Redundant Computer Systems With Corrective and Preventive Maintenance

This paper shows the span of results which can be obtained by modeling a system's behavior by stochastic processes and demonstrates practical rules for employing Markov and semi-Markov models. The introduction summarizes several methods for reliability analysis and gives the advantages and drawbacks of four methods: Markov processes, semi-Markov processes, supplementary variables, the method of stages. The remainder deals with reliability and availability modeling of a 2-unit redundant computer system. There are a) two types of maintenance: corrective (c. m.) and preventive (p. m.), and b) two system parameters: coverage, and an increased failure rate when one unit is under repair or inspection. Approximate expressions for reliability, mean time to failure, and asymptotic availability show the effects of the system parameters as well as of the shapes of the Cdf's of the times related to maintenance actions. For c.m., Markov modeling is a good approximation. For p.m., Markov modeling is a rough approximation; one can go to semi-Markov models or to the method of stages. Lastly, an approximate expression is given for the mean inspection interval which maximizes reliability and availability for p.m.     

A 2-Dissimilar-Unit Redundant System With Repair And Preventive Maintenance

This paper presents the stochastic behaviour of a 2-dissimilar--unit cold-standby redundant system with repair and preventive maintenance. The Laplace-Stieltjes transform of (i) The first-passage time distribution to system failure, (ii) The expected number of system failures during (0, t], (iii) The probability that the system fails at time t, are all derived by using unique modifications of a Markov renewal process. Three examples are given.     

Probabilistic Analysis of a 2-Unit Cold-Standby System with a Single Repair Facility

The reliability and the availability characteristics of a 2-unit cold standby system with a single repair facility are analyzed under the assumption that the failure and the repair times are both generally distributed. System breakdown occurs when the operating unit fails while the other unit is undergoing repair. The system is characterized by the probability of being up or down. Integral equations corresponding to different initial conditions are set up by identifying suitable regenerative stochastic processes. The probability of the first passage to the down-state starting from specified initial conditions is obtained by the same method. An explicit expression for a Laplace Transform of the probability density function (pdf) of the downtime during an arbitrary time interval is obtained when the repair time is exponentially distributed. A general method is suggested for the calculation of the moments of the downtime when the repair time is arbitrarily distributed.     

Time Dependent Solution of a Complex Standby Redundant System under Preemptive Repeat Repair Discipline

The system has two classes of components. Each component in one of the classes is essential to operation. Components in the other class are helpful but not essential. The Laplace transforms of various state probabilities have been obtained; a particular case has been derived.     

An Optimal Maintenance Policy for a 2-Unit Parallel System with Degraded States

The system consists of two identical units in parallel with good, degraded, and failed states. We discuss a maintenance policy that maximizes the expected net profit-rate from the system over an infinite time span. General equations which describe the system behavior under a certain maintenance policy are derived. The optimal maintenance policy can be determined by solving those equations.     

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.     

Mission Reliability for a 1-Unit System with Allowed Down-Time

This paper considers a 1-unit system; the unit is repaired upon failure. The failure and repair rates need not be constant. The system fails if the unit is not repaired within a fixed time, or if the number of failures during the mission exceeds a fixed number. As a special case, that number is allowed to be ``infinite.' The Laplace transforms of the reliability and mean time to system failure are derived; they are not easily solved. The special case of constant failure and repair rates is treated. The results are compared with those of Calabro.     

Unreliability of a Standby System with Repair and Imperfect Switching

We evaluate and analyze a model of a 2-unit standby system with repair and imperfect switching. The model determines the cumulative probability that system failure occurs in a time interval 0 to T. In order to cope with arbitrary failure-time and repair-time distributions, a ``step by step' method is used which for practical purposes yields a sufficiently accurate result. The model results in explicit expressions which are very suitable for computer implementation. A simple illustrative example is given.     

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.     

Analysis of 7 Models for the 2-Dissimilar-Unit, Warm Standby, Redundant System

The paper is in 2 parts. In all models the failure rates are constant, but repair rates need not be constant. The method of supplementary variables is used for solving the models. Part I considers the effect of priorities on reliability and availability for 4 basic models; 1) priority in both repair and operation; 2) priority in repair; 3) priority in operation; 4) no priority. Models 1 and 2 treat 2 repair disciplines: a) preemptive-repeat, b) preemptive-resume. We obtain 1) Laplace transforms of availability and reliability and 2) explicit expressions for steady state availability and for mean time to system failure. The effect of priority assignment to maximize steady state availability is discussed. Part II considers the effect of having different repair rates, depending on whether the failure was from standby or from operation. We obtain 1) Laplace transforms of availability and reliability and 2) explicit expressions for mean time to system failure.     

A Two-Unit Cold Standby Repairable System with One Replaceable Repair Facility and Delay Repair: Some Reliability Problems

1 Model and Assumption In reliability analysis of repairable systems, it is usually assumed that the repair facility neither fails nor deteriorates as well as the repairman is instantaneously available. So that the repair is started immediately upon the failure of a unit provided that he is not busily repairing another unit. However, in actual practice, the repair facility in a repairable system is subject to failure and can be replaced (or can be repaired) after it fails, and certain delay ac…