Reliability and availability analysis of a system with warm standby and common cause failures

This paper presents reliability and availability analyses of a two unit parallel system with warm standby and common-cause failures. The standby and switching mechanisms are subject to failure. The failed system repair times are assumed to be arbitrarily distributed. Expressions for Laplace transforms of system state probabilities, steady state system availability, system reliability, and mean time to failure are developed.     

Some applications of semi-regenerative processes to two-unit warm standby system

We deal with a two-unit warm standby system with a single repair facility; a failure of an operating unit can be detected immediately but a failure of a warm standby unit can not be observed until the system is inspected. According to whether the operation of the system is stopped or not during each inspection, we consider two models. We describe the stochastic behavior of the system as a semi-regenerative process, and the pointwise availability and the steady state availability of the system are derived applying the limit theorem of semi-regenerative processes. Further, we shall discuss the optimum interinspection time maximizing the steady state availability for Model 1.     

Reliability analysis of a complex system with a deteriorating standby unit under common-cause failure and critical human error

This paper presents a stochastic model representing two units and one as a standby unit with critical human error and common cause failure. The deteriorating effect of the standby unit on the system is studied. Repair times of the failed system are arbitrarily distributed while all other transition time distributions are negative exponential. The analysis is carried out using supplementary variable techniques and various measures of system effectiveness such as pointwise availability, steady-state availability, MTTF and variance of the time to failure of the system are obtained.     

Analysis of a repairable redundant system with delayed replacement

The paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement at the time of failure of the active unit and a cold standby (stock) unit which can be replaced after a random amount of time. Failure time distributions of operative and standby units are exponential whereas all repair times follow arbitrary distributions. The system has been studied in detail by applying the results from the theory of semi-Markov process and mean-time-to-system-failure, steady-state availability, expected number of visits to a state, second moment of time in an up-state and expected profit of the system have been obtained.     

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.     

Effect of intermittent repair in a two unit redundant system with standby failure

A two-unit standby redundant system with exponential failure time distribution of the operative unit is considered. It is assumed that failure of the standby unit is detected only at the time of use and is available with a known probability. Repair facility is also available at the time of need with a known probability. Repair and preoccupation times are general. Stochastic behaviour of the system has been studied by Semi-Markov process and parameters of interest eg. MTSF, steady state availability, expected profit have been obtained. Expected profit of this model is compared with that of an earlier model and a condition on extra incurred cost is obtained.     

Two models for two-dissimilar-unit cold standby redundant system with partial failure and two types of repairs

This paper deals with the availability function and the mean time to the first failure for two models of a cold standby redundant system with two different types of repair. Each model consists of two dissimilar units. In the first model, the operative unit has two modes of operation, normal mode and partial failure mode. The standby unit has one mode of operation, normal mode. In the second model, each unit has three modes of operation, normal mode, failure mode and total failure mode. Both models are analyzed by the semi-Markov process technique, assuming that the failure time and repair time distributions are general and arbitrary. Some reliability measures of interest to system designers as well as operations managers have been obtained. Moreover, we give computer programs for calculating the MTSF for each model (see Appendix).     

Cost analysis of a two dissimilar-unit cold standby redundant system subject to inspection and two types of repair

This paper deals with the cost analysis of a two dissimilar-unit cold standby redundant system subject to inspection and two types of repair where each unit of the system has two modes, normal and failed. It is assumed that the failure, repair, replacement and inspection times are stochastically independent random variables each having an arbitrary distribution. The cold standby unit replaces the failed operative unit after a random amount of time. An inspection is required to decide whether it needs type I (minor repair) or type 2 (major repair). In this system the repairman is not always available with the system, but is called whenever the operative unit fails. The system is analysed by the semi-Markov process technique. Some reliability measures of interest to system designers as well as operations managers have been obtained. Pointwise availability, steady-state availability, busy period by a server and the expected cost per unit time of the system are obtained. Certain important results have been derived as particular cases.     

Availability analysis of two-unit warm standby system with inspection time

This paper deals with two identical units warm standby system when a failure of unit is detected by actual inspection but a system down can be detected at any time without inspection. Where the lifetime distribution of unit is the bivariate exponential distribution and other distributions are arbitrary. The Laplace transform of the point-wise availability of the system and the steady state availability of the system are derived by using the supplementary variable method. Further, we discuss the optimum inspection period maximizing the steady state availability. A numerical example is presented.     

Two-unit redundant system with inspection and adjustable rates

A two-unit redundant system is studied, in which one unit is operative and the other is a warm standby which replaces the operative failed unit instantaneously. To increase system availability, the failure rate of the operative unit and the repair rate of the failed unit adjust automatically according to the state of the standby unit. Also, after repair of the operative failed unit it is sent for inspection to decide whether the repaired unit is perfect or not. If the repaired unit is found to be imperfect, it is sent for post repair. Using a regenerative point technique in the Markov renewal process, several reliability characteristics of interest to system designers and operation managers are obtained.     

Reliability and availability analysis of two-unit warm standby microcomputer systems with self-reset function and repair facility

Reliability and availability analysis of systems having one active unit and one warm standby unit with self-reset function and one maintenance facility is presented. Two failure models are discussed. The failure unit is repaired through self-reset or maintenance according to different failure models. The state transition diagram and equation are described. The formulae for reliability and steady-state availability are given.     

On a two dissimilar unit cold standby system with switchover time and proper initialization of connect switching

This paper investigates the stochastic behaviour of a two dissimilar unit cold standby system with connect switching. The connect switch keeps this system in good connection with other systems. The standby unit takes random switchover time to assume the operative state when the operative unit fails. The failure times of the units and connect switch and the repair times of the units are assumed to have different arbitrary distributions. The mean waiting times in the states of the system and expression for the steady state availability of the system are obtained. The results obtained by Kumar and Lal and Laprie [1, 2] are derived from the present results as special cases.     

Availability analysis of a repairable standby human-machine system

This paper presents a model representing a two units active and one unit on standby human-machine system with general failed system repair time distribution. In addition, the model takes into consideration the occurrence of common-cause failures. The method of linear ordinary differential equation is presented to obtain general expressions for system steady state availability for failed system repair time distributions such as Gamma, Weibull, lognormal, exponential, and Rayleigh. Generalized expressions for system reliability, time-dependent availability, mean time to failure, and system variance of time to failure are also presented. Selected plots are presented to demonstrate the impact of human error on system steady state availability, reliability, time-dependent availability, and mean time to failure.     

Two unit repairable redundant standby system

The Laplace-Stieltjes (LS) transform for the distribution of time to first system failure (TFSF), transition probability, availability and mean time to system failure have been derived for two unit repairable redundant standby system with perfect as well as imperfect switchover condition. General expressions for computing various reliability performance indices have been obtained by using Markov Renewal techniques considering general distributions for time to failure and time to repair for the units.     

A two-unit duplicating standby system with correlated failure-repair/vbreplacement times

This paper considers the stochastic analysis of a two-unit (original and duplicate) cold standby system model with preventive maintenance and replacement of the failed duplicate unit. The failed duplicate unit is non-repairable but its replacement is considered with an identical duplicate unit which is available instantaneously. Joint distributions of failure and repair/replacement times of original/duplicate units are bivariate exponential with different parameters. Various reliability characteristics of the system model under study are obtained by using regenerative point technique. Mean time to system failure and steady state availability have also been studied through graphs.     

A two unit series system with correlated failures and repairs

This paper investigates a stochastic model of a system having two identical units, each with two components, arranged in series configuration. Upon failure of a component of the unit, the standby unit replaces the failed unit instantaneously. It is assumed that the joint distribution of the repair and failure times of a component are bivariate exponential. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated and relevant results obtained earlier are verified as a particular case. The MTSF and availability have also been studied through graphs.     

A cold standby system with arrival time of server and correlated failures and repairs

This paper presents the analysis of a two unit cold standby system with random arrival time of a server. The failure and repair times of each unit are assumed to be correlated and their joint density is taken as bivariate exponential. Using the regenerative point technique, various reliability characteristics of the system have been obtained. The behaviour of MTSF and steady state availability have also been studied through graphs.     

Probabilistic analysis of a two-unit system with a warm standby subject to preventive maintenance and a single service facility

The object of this paper is to carry out the availability and the reliability analysis of a two-unit system with a warm standby having a single service facility for the performance of preventive maintenance and repair. The failure times, the repair times, the inspection times and the preventive maintenance times of the main unit and of the standby one are assumed to be arbitrarily distributed. The system is characterized by the probability of its being in the up or the down state. Explicit expressions for the mean down time of the system and for the mean time to system failure are obtained. Some previous results are derived from this work as special cases.     

A reliability physics model for dissimilar two-unit standby system with single repair facility

In this paper, the reliability and availability analysis of a repairable dissimilar two-unit standby system is carried out using stress-strength failure model. Single repair facility with the time taken to repair a unit being either deterministic or random has been considered. The analysis is carried out for arbitrary stress, strength and repair time distributions.