A generalized multi-standby multi-failure mode system with various repair facilities

We consider a system of (m + 1) non-identical units—one functioning and m standby. Each unit of the system has the following states: normal, N types of partial failures and corresponding to them N types of total failures. There are k distinct major repair facilities and one on the spot repairman. One unit can pass from one state to another with known probability and then the time of staying in this state has a general distribution. The system starts to work at t = 0 and fails when the (m + 1)th unit after a total failure is finally rejected. Using semi-Markov techniques we obtain Laplace transforms of transition probabilities. Considering particular cases we derive known results for systems which have been defined in the past.     

Cost-benefit analysis of single server n-unit imperfect switch system with delayed repair

This paper deals with the cost-benefit analysis of a single-server n-unit system with an imperfect switch where failures of the items (units or the switch) are not detected unless either inspected by the server or when the system is down. Initially, one unit is put into operation (the switch is working at t = 0) and n − 1 units are kept as cold standbys. A failed unit is replaced by a standby if the switch and a standby are available. The server visits the system at random to check for the failed item and the check is instantaneous. When the system is down, either because of want of the standby or failure of the switch, the server is called for, and is assumed to arrive instantaneously. The revenue as well as the cost of repair are arbitrary functions of time. The expected net gain in (0, t) is evaluated assuming that all the life-time distributions are exponential and all the repair time distributions are arbitrary.     

A 1-out-of-N: G system with common-cause failures and critical human errors

A system which has N operating units and r repair facilities with common-cause failures and critical human errors is presented. The system is of 1-out-of-N: G nature. Failure rates are constant and the repair rate is arbitrary. Mathematical formulation is carried out using the supplementary variable technique. Lagrange's method for partial differential equations is employed to solve the governing equations. Various probabilities, system parameters and special cases are discussed.     

A k-out-of-N:G redundant system with dependent failure rates and common-cause failures

This paper presents a k-out-of-N: G redundant system with dependent failure rates, common-cause failures and r repair facilities. The failure rates of the components increase as the number of components failed increases, while the repair rates are constant. Common-cause failure is not considered in Model I. In Model II the common-cause failures are involved. Steady-state probabilities and steady-state availability are derived.     

A reliability model for a k-out-of-N:G redundant system with multiple failure modes and common cause failures

The paper presents a reliability model of a k-out-of-N:G redundant system with M mutually exclusive failure modes and common cause failures. Failed system repair times are arbitrarily distributed. The system is in a failed state when (N−k+1) units failed or a common cause failure occurred. Laplace transforms of the state probabilities and the availability of the system are derived. Finally, the system steady-state availability is also reported.     

A priority multi-component system with spares

A system with n similar components in series with constant failure rates and m spares in warm standby supported by a single repair facility is studied. The repair time distributions of on-line and standby failures are taken to be different and arbitrary. Two models, one with pre-emptive repeat priority and another with non-pre-emptive priority are discussed. Equations for the reliability and availability functions are obtained for both cases and earlier results are recovered as special cases of the non-pre-emptive model.     

Estimation of parameters of a model of a complex repairable system

This paper deals with estimation of parameters of a model of a complex repairable system with 3ne unit on operation and the remaining (N − 1) units as inactive standbys and having a repair facility. Various operating characteristics, namely, reliability, availability, mean time to failure of the system, s-expected numbers of repairs in (0, t], s-expected numbers of failures of the system in (0, t] are estimated under two censoring schemes namely, the type-I censoring and type-II censoring schemes.     

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.     

Reliability and profit analysis of two single-unit models with three modes and different repair policies of repairmen who appear and disappear randomly

Cost-benefit analysis of a single-unit system with three possible modes of the unit—normal (N), partial failure (P) and complete failure (F)—is carried out. The paper consists of two models: in model 1, the unit goes under repair (if a repairman is available) the moment it fails partially, whereas in model 2 the unit goes under repair at complete failure. The repairman appears in, and disappears from, the system randomly. A comparison between these two models after calculating MTSF and profit has also been made.     

A note on the cost analysis of an n-unit system with spares

This paper deals with the cost analysis of a non-repairable standby system consisting of (n + m) identical units; n-units are needed for the system to function, while the remaining m units are warm standbys. The online and standby units have different constant failure rates. There is no facility for repair. Functions expressing the probability that in (0, t) there are i on-line failures and j standby failures and thereby the reliability of the system. MTTF and the expected profit are obtained. Finally, a numerical example with graphs is also given to highlight important results like the reliability of the system, MTTF and the expected profit.     

Optimal replacement policy (N, n) for a parallel system with common cause failure and geometric repair time

The purpose of this article is to present an improved replacement model for a parallel system of N identical units, by bringing in common cause failure (CCF), maintenance cost and repair cost per unit time additionally, and to develop a procedure to obtain the optimal redundant units N^* and optimal number of repairs n^* with the conditions that the system is allowed to undergo at most a prefixed number of repairs before to be replaced and the successive reapir times after failures constitute a non-decreasing Geometric process. Several conditions for the existence of the optimal N^* and n^* is stated and the results are illustrated by a numerical example.     

Approximate analysis of n-unit cold-standby systems

In this paper, a n-unit cold-standby system with a single repair facility is analysed using two approximate methods namely, cutting and clustering the state space. It has been assumed that the failure rate is constant and the repair time is arbitrarily distributed. A mathematical model is developed using semi-regenerative phenomena and systems of convolution integral equations satisfied by various state probabilities corresponding to different initial conditions are obtained. Explicit expressions for the expected number of failures and expected number of repair completions in an interval [0, t] are obtained. An iterative numerical method is used to solve the systems of integral equations obtained and a comparative study has been carried out between exact and approximate solutions.     

Cost-benefit analysis of a multi-unit parallel trichotomous system with random shocks

This paper deals with the analysis of profit function of an n-unit parallel trichotomous system subject to random shocks. Failure times are assumed to follow negative exponential distributions with different parameters whereas the repair time distributions are taken to be general. Several reliability characteristics of interest to system engineers/designers as well as operation managers have been evaluated using the supplimentary variable technique.     

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     

Reliability of imperfect switching of cold stanby systems with multiple non-critical and critical errors

Reliability and availability analysis of having k active, N cold standby units with repair facilities and multiple non-critical and critical errors while the switching mechanism subjected to failure is presented. Failed (active and/or by any one of the multiple non-critical errors) units will be repaired at a constant repair rate. The system is in a failed state when any one of the multiple critical errors has occurred, (N + 1) units have failed or there is a failure of switching mechanism. A failed system will be repaired with repair times arbitrarily distributed. The expressions for reliability and steady-state availability are given.     

Reliability of a 2-Unit Standby Redundant System with Repair, Maintenance and Standby Failure

A repairable 2-unit warm-standby system with repair and preventive maintenance is discussed. Two models are presented. In each of the models the mean time to system failure and the steady state availability are calculated. Some numerical calculations illustrate the results.     

Optimal repair stage for K-out-of-N systems

Optimization studies on reliability systems is currently a fascinating area of research. In recent investigations, optimization techniques have been extended to cover even more complex reliability systems with larger applicational scope. In this paper, we study a complex system in terms of a K-out-of-N system (for example, occuring in mass transmission and computer networks) with provision for a repair facility. We develop an optimization procedure to help identify the Optimal Repair Stage for the system under certain conditions. The applicational use of the theoretical results is illustrated through numerical work, specifically the negative exponential law governing stochastic repair times.     

An n-unit standby redundant system with r repair facilities and preventive maintenance

Identifying suitable regeneration points the availability and reliability of an n-unit warm standby system with r repair facilities, in which the operating online unit is subjected to preventive maintenance are obtained. A numerical example is provided to illustrate the results obtained. Based on the numerical result, an optimal PM policy is also derived.