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.     

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 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.     

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.     

Reliability analysis of a two state repairable parallel redundant system under human failure

In this paper, the investigations have been carried out for the MTTF and reliability analysis of a repairable two-unit redundant electronic equipment having two states under human failures. The two-unit repairable parallel redundant system suffers two types of failures; viz; unit failure and human failure. Human failure brings the system to a complete failure stage. There is only one server who is always available. Laplace transforms of the probabilities of the complex system being in up and down states have been derived and have been inverted to obtain time dependent probabilities. Two graphs have also been given in the end.     

Availability and MTTF analysis of a three-state parallel redundant multi-component system under critical human failures

This paper deals with the availability and mean time to failure of a single server complex system made up of two classes A and B under critical human errors. Sub-system A has two identical components arranged in parallel whereas B has N non-identical components arranged in series. The complex redundant system has three states, viz. good, degraded, failed and suffers two types of failures, viz. unit failure and failure 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 have been obtained along with steady state behaviour of the equipment. A numerical example has also been appended in the end to highlight the important results. There is only one repair facility, which is availed only when the system is in failed state due to failure of sub-system B.     

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).     

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.     

Cost analysis of a multi-component parallel redundant complex system with overloading effect and waiting under critical human error

The cost analysis of a multi-component parallel redundant complex system is considered, incorporating the concept of overloading effect and waiting time for repair under critical human error. Failure and waiting times follow an exponential time distribution, whereas repair time follows a general distribution. Using the supplementary variable technique, Laplace transforms of the probabilities of the complex system being in various states have been computed. Some graphs have been plotted to highlight the main results.     

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.     

Cost analysis of a two-unit electronic parallel redundant system with overloading effect

A two-unit parallel redundant repairable electronic system with exponential failure-time distribution and overloading effect is considered. The system is to be in any of the three states: good, degraded and failed. One repair facility is available when the system is either in degraded or failed state. 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 operational availability of the system at any time. Using supplementary variable technique, Laplace transforms of various state probabilities have been evaluated. Making use of Abel's theorem, various time independent probabilities have been computed. Also the overloading effect for the expected profit on the operational availability of the complex system has been studied.     

Reliability and MTTF analysis of a non repairable parallel redundant complex system under hardware and human failures

This paper deals with the evaluation of point-wise availability and M.T.T.F., of a two-unit standby redundant electronic equipment, incorporating the concept of human failures. Single service facility is available for the service of constant failure. Using the supplementary variable technique, general equations are set up for deriving the above two measures. In addition, steady state availability is also derived and some important graphs have been sketched in the end.     

Availability, MTTF and cost analysis of a three-state parallel redundant multi-component system under critical human failures

This paper deals with the availability, MTTF and the cost analysis of a single server complex system consisting of two classes A and B with three possible states, viz. good, degraded, failed and suffers two types of failure, viz. unit failure and failure due to critical human errors.Sub-system A has two dissimilar units arranged in parallel whereas sub-system B has three non-identical units arranged in series. Failure and repair times have exponential and general distributions respectively. There is only one repair facility when the system is in failed state due to failure of sub-system B. Several parameters of interest are obtained using the supplementary variable method. A numerical example has been appended. Five graphs have also been given in the end.     

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.     

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.     

An approximation analysis for the availability of a parallel redundant system with general distributions

This paper presents an approximation method for deriving the availability of a parallel redundant system with general distributions. The system discussed is composed of two identical units. A single service facility is available for the performance of preventive maintenance(PM) and repair. The failure times, repair times and PM times are assumed to be arbitrarily distributed. The presented method formulates the problem of the availability analysis of a parallel redundant system as a semi-Markov process which represents the state transitions of one specified unit in the system. This method derives the availability easily and accurately. Further, when all the distributions are exponential, the availability obtained by this method is exact.     

Reliability consideration on a compound redundant system with repair

This paper considers a standby-redundant system consisting of 2 systems, in which one is main and the other is its standby-redundant system. These systems also consist of 2 subsystems connected in series.A feature of this system is that the system has 2 switching devices connecting subsystems, in addition to one connecting main and standby systems, in order to utilize surviving subsystem. In this consideration it is assumed that all the units are repairable.We shall obtain the system reliability, the mean time to system failure, the steady state availability, and examine numerically the effects of this model to the usual one without particular switching devices.     

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.