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 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 two dissimilar unit multi-component system with correlated failures and repairs

This paper investigates a two non-identical unit cold standby system model. Each unit is composed of n independent components arranged in a series configuration. A single repairman is available to repair a failed unit. The priority in operation is being given to the first unit, while in repair the priority is given to the second unit. The failure and repair times of the ith and jth component for the first and second unit, respectively, are jointly distributed as bivariate exponentials (B.V.E.) with different parameters. Using a regenerative point technique, various reliability characteristics have been analysed.     

Analysis of a two server-two unit cold standby system with correlated failures and repairs

This paper studies a two (non-identical) unit cold standby system with correlated failures and repairs. The system has two types of server—regular (not perfect) and expert. The regular repairman is always available with the system while the expert repairman is called when it is needed. The joint distributions of failure and repair times are taken to be bivariate exponential (B.V.e.). Important reliability characteristics useful to system managers are obtained.     

A two-unit cold standby system with allowed down-time and correlated failures and repairs

This paper considers the stochastic behaviour of a two-unit cold standby system with allowed down-time and a single repair facility to repair the failed unit. It is assumed that the repair and failure times of a unit are associated with each other in some way or other and their joint distribution is bivariate exponential.     

A two-unit cold standby system with three modes and correlated failures and repairs

The economic parameters are studied for a two-unit cold standby system with three modes and failure and repair times having bivariate exponential density as their joint distribution. The system is studied at suitable regenerative epochs to obtain these economic parameters. Explicit results have also been obtained for the case when failure and repair times are independent. Two important parameters of the system, i.e. MTSF and availability, have been studied graphically to observe the effect on them of correlation.     

Profit analysis of two-unit standby system with rest period for the operator and correlated failures and repairs

This paper analyses a two-unit cold standby system with the provision of rest for the operator. After working a random amount of time, the operator needs to rest for a random amount of time and during the rest period the system comes down, but does not fail. Also, the failure and repair times of each unit are assumed to be correlated, by taking their joint density as a bivariate exponential. The system is observed at suitable regenerative epochs to obtain various reliability characteristics of interest to system designers as well as operations managers. Numerical results pertaining to a particular case are also presented.     

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.     

A two unit priority redundant system with three modes and correlated failures and repairs

This paper considers a two dissimilar units priority redundant system with three modes. One of the units has a priority operative mode and the other has a priority repair mode. Assuming that the joint distribution of failure and repair times is exponentially bivariate, some reliability characteristics useful to system managers have been obtained. Results for a system with two similar units are obtained as a particular case.     

Cost analysis of a three-state repairable redundant complex system under various modes of failures

In this paper investigations have been carried out for the availability and mean time to failure analysis of a three unit repairable electronic equipment having three states; viz; good, degraded and failed under critical human errors. The three states three units repairable electronic equipment suffers two types of failures; viz; unit failure and failure due to critical human errors. Entire system can fail due to critical human errors. The 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 are obtained along with steady state behaviour of the equipment. A numerical example has also been appended to highlight the important results. Three graphs have also been given in the end. There is only one repair facility, which is availed only when the system is in either degraded or failed state due to unit failure.     

A bulk queueing system with random failures and two phase repairs

The paper studies a queueing system with bulk arrivals and bulk departures wherein the service channel is subject to random failures and the repairs are performed in two phases. Units wait until both phases of repairs of the service channel are complete. The probability generating functions of the queue length have been obtained for the various states of the system and the corresponding results for the steady state have been derived. Two particular cases have been discussed and the mean queue length has been obtained explicitly. Finally depenedence of the mean queue length on failure and repair parameters have been shown graphically.     

Cost analysis, availability and MTTF of a three state standby complex system under common cause and human failures

The paper deals with the pointwise availability, steady state availability, MTTF and variance of the time to failure of 3 state, 1-out-of-2 unit systems with cold standby, under common cause and human failures. The cost function analysis is also to get the expected gain over the time. Several graphs are presented to interpret the results.     

K-out-of-N:G system with multiple correlated failures

In this paper we consider a K-out-of-N:G system subject to multiple correlated failures. One repair facility is available. The method of the supplementary variables is used to obtain the Laplace transform (LT) of the pointwise availability, LT of the pointwise reliability, the mean time to the first system failure (MTSF) and the steady state availability.     

Network reliability with arc failures and repairs

Arc repair probabilities are incorporated into network calculations for directed networks with independent arc failures. A discrete-time Markov chain with one absorbing state is constructed for the problem. The transition probability matrix is used to determine the probability of source-to-sink conductivity in a given time interval, the mean time to source-to-sink connectivity, the fraction of time a node is blocked, and the fraction of time the network is blocked (disconnected). Blockage probabilities aid in repair-crew allocation to the nodes of the network     

Cost analysis of a three-state parallel redundant complex system

This paper deals with the cost analysis of a three state system consisting of two independent units in parallel redundancy. The failure and repair times for the system follow exponential and general distributions respectively. The Laplace-transforms of various state probabilities have been derived and steady state behaviour of the system has also been examined. A few particular cases have also been discussed at the end to highlight the utility of the model.     

N-unit parallel redundant system with multiple correlated failures

This paper deals with mathematical models of an N-unit parallel redundant system with one repair facility and multiple correlated failures. These models are generalized on the basis of the results obtained previously and related to a system subject to a process of single failures and double and N-unit correlated failures. The method of the supplementary variable in two models differing by the repair policy is used. We obtain the following results: for both models the stationary availability, and for the second model the Laplace transform (L.T.) of the system reliability, L.T. of the pointwise a vailability, and the mean time to system failure (MTSF).     

Probabilistic analysis of a pulverizer system with common-cause failures

This paper presents a newly developed mathematical stochastic model to represent ‘n’ number of active redundant pulverizers with a cold standby pulverizer. The active redundant pulverizers may also fail due to common-cause failures. Failed system repair times are arbitrarily distributed. Laplace transforms of the state probability and point-wise availability equations are developed. In addition, the Laplace transforms of the state probability equations of three special case models for n=2, n=4 and n=5 are presented. For constant failure and repair rates and n=2 (with one standby) steady state system availability plots are shown.     

Modeling and analysis of correlated software failures of multiple types

Most software reliability models assume independence of successive software runs. It is a strict assumption, and usually not valid in reality. Goseva-Popstojanova & Trivedi (2000) presented an interesting study on failure correlation among successive software runs. In this paper, by extending their results, a software reliability model is developed based on a Markov renewal process for the modeling of the dependence among successive software runs, where more than one type of failure is allowed in general formulation. Meanwhile, the cases of restarting with repair, and without repair, are considered. Although such a model is more complex than the traditional approach based on reliability growth, it incorporates more information about the failures, and system structure. A numerical example is also shown to illustrate the procedure, and provide some comparison.     

Stochastic behaviour of a three-state complex repairable system with three types of failures

This paper deals with the operational availability of a three-state complex repairable system consisting of n distinct units arranged in series. Single service facility is available for three types of failures of the complex system. A mathematical model for the complex system under severe restrictions has been developed for exponential failures and general repairs. Laplace transforms of various state probabilities have been evaluated and availability is then obtained by the inversion process. Few graphical illustrations are also given in the end so as to explain the practical utility of the model.