Reliability and availability analysis of a k-out-of-N:G redundant system with repair in the presence of chance of multiple critical errors

The paper presents a reliability and availability analysis of a k-out-of-N:G redundant system with repair facilities in the presence of chance of multiple critical errors. The system is in a failed state when N−k+1 units have failed or any one of the multiple critical errors has occurred. Failed units and failed system will be repaired with constant repair rate to state with N−k+1 failed units. Laplace transforms of the state probabilities, the reliability and the availability of the system are derived. The system steady-state availability is also given.     

Reliability analysis of a k-out-of-N:G parallel redundant system with multiple critical errors

This paper presents a reliability and availability of a k-out-of-N:G parallel redundant system with multiple critical errors while failed unit is not repaired. The system is in a failed state when a critical error occurred or k units have failed. Failed system repair times are arbitrarily distributed. Laplace transforms of state probabilities and reliability of the system are derived. The steady-state availability is also given.     

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 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.     

Reliability and availability analysis of warm standby systems in the presence of chance with multiple critical errors

This paper presents a reliability and availability analysis of k active, N warm standby units in the presence of chance with M multiple critical errors. The system is in a failed state when (N + 1) units have failed (active and/or warm standby units have failed) or one of the multiple critical errors has occurred. Failed units are not repaired but a failed system will be repaired with repair times arbitrarily distributed. The expressions for reliability, availability and steady-state availability are derived.     

Stochastic analysis of a warm standby system with repair in the presence of chance of multiple critical errors

The paper presents a stochastic analysis of a k active and N warm standby system with r repair facilities in the presence of chance of multiple critical errors. The system is in a failed state when N+1 (active and/or warm) units have failed or any one of the multiple critical errors has occurred. Failed units will be repaired with constant repair rate. The failed system due to critical errors will be repaired with constant repair rate to state with N+1 failed units. Laplace transforms of the reliability and the availability and the steady-state availability of the system are given.     

Availability and frequency of warm standby systems in the presence of chance with multiple critical errors

This paper presents the availability and frequency of encountering different state of k active, N warm standby units in the presence of chance with M multiple critical errors. The system is in a failed state when one of any multiple critical errors has occurred or when (N+1) units have failed. Failed units are not repaired. However, failed system will be repaired with constant repair rates. The expressions for steady-state availability and frequencies of down- and up-states are derived.     

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.     

Cost analysis of an electronic repairable redundant system with critical human errors

In this paper, an electronic system consisting of two subsystems connected in series has been considered. One subsystem consists of two identical units connected in parallel while the other subsystem has only one unit. The system is to be in any of the three states: good, degraded and failed. The system suffers two types of failures, viz; unit failure and failure due to critical human error. The system can be repaired when it fails due to the failure of the units in the subsystems and cannot be repaired when it fails due to critical human errors. The repair for 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.     

Stochastic analysis of k-out-of-N:G redundant systems with repair and multiple critical and non-critical errors

Probabilistic analysis of k-out-of-N:G redundant systems with repair facilities and multiple critical and non-critical errors is presented. Failed unit (active and/or by any one of the multiple non-critical errors) will be repaired with the same constant repair rate. The system is in a failed state when any one of the multiple critical errors has occurred or (N − k + 1) units have failed. Failed system will be repaired with repair times arbitrarily distributed. The formulas for reliability and steady-state availability are given.     

Reliability bounds and direct computation of the reliability of a consecutive k-out-of-n:F system with Markov dependence

We propose bounds and direct computation of the reliability of a consecutive k-out-of-n:F system, in the case where each component can have only two states (good or failed) and the sequence of the states of the components forms a Markovian chain. Some interesting deterministic properties are also given.     

Common-cause failure analysis of a k-out-of-n:G system with repairable units

A newly developed generalized expression for the mean time to failure of a k-out-of-n: G system composed of repairable units and subject to common-cause failures is presented. Also, reported are some special case system reliability and variance of time to failure formulas.     

Reliability analysis of a two-unit redundant system with a replaceable repair facility

This paper considers a two-unit redundant system where the repair facility is subject to failure and can be replaced by a new one when it fails. By using Markov renewal theory we obtain some reliability quantities of the system and the repair facility, respectively.     

Optimal redundancy of K-out-of-n:G system with two kinds of CCFs

This paper considers the problem of optimal redundancy of K-out-of-n:G systems. The model highlights the occurrence of two types of common-course failures, namely, lethal and non-lethal CCFs, in addition to random failures. The optimum number of redundant components (n^*) in K-out-of-n: G systems are derived with two types of CCF. The optimization is approached by a minimization of the mean cost rate (C₁(n^*)) which is established to be finite and unique. Numerical evidence indicates the reduction of optimal redundancy with two types of CCF when compared to random failures alone.     

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.     

Consecutive k-out-of-n:F system with sequential failures and a single repair

This paper presents a solution for determining the mean time to system failure of a consecutive k-out-of-n:F system with a single repair. The components of the system are subject to sequential failures. The mean time to system failure is evaluated by making use of the relation between the reliability function and the probability of the first passage time to system failure. The Laplace transform of the first passage time to system failure is obtained as a ratio of two determinants.     

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.     

Non-parametric inferences on system availability with a reference of k-out-of-m systems

The availability of a system is an important characteristic which includes both reliability and maintainability. It is generally not feasible to make assumptions regarding the failure and repair time distributions of a system at its early stage of designing. Thus, the present paper deals with a non-parametric analysis of the system availability. Bayesian availability analysis is also given using conjugate priors. Further, at the initial designing stage, the operational or experimental data on the complete system is either non-existent or costly to realise. Therefore, the operational experience on the subunits or components has been used for analysing the availability of a k-out-of-m system.     

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 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.