Probability analysis of a 2-out-of-n: F system with common cause failure, multiple failure and dependent failure

We analyze 2-out-of-n:F system with Common Cause Failure (CCF), Multiple Failure (MF) and Dependent Failure(DF) by using the method of extended Markov state transition and 2-dimensional Laplace transition method. Computing the system availability, we studied the effect of repair in the CCF, MF and DF environment. we introduced the new steady state availability by using the results of the Laplace transformed availability. We apply basic relation of 2-dimensional Laplace transformation for the new availability analysis. Then we apply this transformation at different differential equations. The result of this analysis is to get the fixed quantity of system availability according to the repair rate change     

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.     

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

A reliability analysis of a k-out-of-N: G redundant system with multiple critical errors and r repair facilities in the presence of chance, is dealt with in this paper. The system is in a failed state when k units have failed or one of any multiple critical errors has occurred. Failed system repair times are arbitrarily distributed. The formulae for reliability function in terms of a Laplace transform, steady-state availability and mean time to failure are derived.     

A k-out-of-N:G redundant system with cold standby units and common-cause failures

This paper presents a k-out-of N:G redundant system with M cold standby units, r repair facilities and common-cause failures. The constant failure rates of the operating and cold standby units are different. Failed system repair times are arbitrarily distributed. The system is in a failed state when (N+M?k+1) units failed or a common-cause occurred. Laplace transforms of the state probabilities, the availability of the system and the system 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.     

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.     

Availability analysis of systems with two types of repair facilities

This paper presents two mathematical models of repairable systems. Failed systems repair times are arbitrarily distributed. Two types of repair facilities are needed to repair a failed system. Laplace transforms of the state probability equations are developed.     

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.     

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.     

Unified availability modeling: A redundant system with mechanical,electrical, software,human and common-cause failures

This paper presents availability analysis of a two identical unit redundant system. Each unit can fail in n-mutually exclusive failure modes. The system can fail due to a common-cause failure. Failed system repair times are arbitrarily distributed.A special case example is presented. This example is concerned with a two identical unit redundant system whose unit can fail due to occurrence of electrical, mechanical, human or software failure. Laplace transforms of the state probability equations are developed.     

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.     

Reliability of a Consecutive-k-out-of-n:F System for Markov-Dependent Components

We examine a consecutive-k-out-of-n:F system, where the probability of failure of a component depends upon the state, (good or failed) of the preceding component; ie, the states of the components form a Markov chain. We compute the reliability of such a system, via a recurrence relation.     

Common-cause failures and critical human errors in repairable and non-repairable systems

This paper presents a reliability analysis of a k-out-of-N:G redundant system with common-cause failures, critical human errors and r repair facilities. The system is in a failed state when common-cause failures or critical human errors occurred or k units failed. When less than k units failed, the failed units are to be repaired. If the whole system is in a failed state, it cannot be repaired. Laplace transorms of state probabilities and system reliability are derived. Various versions of mean time to failure of a system are also reported.     

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.     

Two 1-Server n-Unit Systems with Preventive Maintenance and Repair

This paper deals with the availability and reliability analysis of two different 1-server n-unit systems with preventive maintenance and repair. Initially, one unit operates and the remaining n - 1 units are kept as cold standbys. In the first system the time to failure and the time to preventive maintenance of a unit are arbitrarily distributed. In the second system, each unit consists of 2 components connected in series. When a unit fails, the failed component is taken up for repair while the other waits for preventive maintenance. Explicit expressions for the Laplace transform of the mean down-time of the system in [0, t] and for the mean time to system failure are obtained. Steady-state availability of the system is also discussed. A few special cases have been studied.     

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 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 general standby system with constant human error and arbitrary system repair rates

This paper presents a mathematical model for performing reliability and availability analyses of a general standby system with constant human error and common-cause failure rates. In addition, system repair times are assumed arbitrarily distributed. Markov and supplementary variable techniques were used to develop equations for the model. The method of linear ordinary differential equation is developed to obtain the general expressions of the steady state availability. The Laplace transform technique was used to obtain the system time-dependent availability, reliability and mean time to failure expressions.     

Operational behaviour of a three state standby redundant electronic equipment under critical human errors

This paper deals with the operational behaviour of a cold-standby redundant system incorporating the concept of three states, with four types of failures, namely major unit failure, minor unit failure, partial failure due to critical human errors and complete failure due to critical human errors, under only one repair facility. Failure and repair times for the complex system follow exponential and general distributions, respectively. Repair is undertaken only when the system is either in degraded state or in failed state. Laplace transforms of the probabilities of being in various states as well as in up and down states are computed, along with the steady state behaviour of the system. A particular case of such a system has also been appended to highlight the important results.     

Cost analysis of a two unit, three state standby redundant complex system with two types of repair facilities under waiting

This paper deals with the cost analysis of a two unit, three state standby redundant complex system, incorporating the concept of two types of repair facilities, viz. minor and major repair. The concept of waiting time for the major repair of the failed system has also been introduced. The system can suffer from two types of failures, namely catastrophic and partial. Failure and waiting times of units follow exponential time distribution, whereas repair of units follows general time distribution. Using the supplementary variable technique, Laplace transforms of probabilities of the complex system being in various states have been computed. In addition, using Abel's lemma, steady state behaviour has also been examined. Some important graphs have been sketched at the end to highlight the important results.