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.     

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.     

A Modified Block Replacement Policy Using Less Reliable Items

A modified block replacement policy is examined with the purpose of excluding the wastefulness caused by the property that almost new items might be sometimes replaced at planned replacement times under the ordinary block replacement policy. This modified policy can be stated as follows: 1) Operating items are replaced by new items at times kT (k = 1,2,...), 2) If operating items fail in [(k - 1)T, kT - v), they are replaced by new items, and in [kT - v, kT), they are replaced by less reliable items than new items. Numerical comparisons between the proposed policy and the ordinary block replacement policy are carried out for Weibull distribution.     

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.     

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 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.     

Two-unit redundant system with inspection and adjustable rates

A two-unit redundant system is studied, in which one unit is operative and the other is a warm standby which replaces the operative failed unit instantaneously. To increase system availability, the failure rate of the operative unit and the repair rate of the failed unit adjust automatically according to the state of the standby unit. Also, after repair of the operative failed unit it is sent for inspection to decide whether the repaired unit is perfect or not. If the repaired unit is found to be imperfect, it is sent for post repair. Using a regenerative point technique in the Markov renewal process, several reliability characteristics of interest to system designers and operation managers are obtained.     

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.     

Analysis of a three-unit redundant system with two types of repair and inspection

This paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement of a failed operative unit and a cold standby which takes a random amount of time to become operative/warm. After each repair a unit is sent for inspection to decide whether the repaired unit is perfect or imperfect. If the repaired unit is found to be imperfect then it goes for post-repair. Using the regenerative point technique in the Markov renewal process several reliability characteristics of interest to system designers and operation managers are obtained.     

Approximate method for the discretisation of continous linear multivariable systems

The letter describes the application of transform theory to the problem of determining the discrete equivalent x{(k+1)T} = ?(T)x(kT)+?(T)u(kT) of the linear continuous multivariable system x? = Ax+Bu     

Multi-standby system with repair and replacement policy

This paper investigates the mathematical model of a system composed of (m + 1) non-identical units—one functioning and m standbys. Each unit of the system has four possible states—normal, partial failure, total failure and repair facility—the last one meaning that the totally failed unit is being attended to at the repair facility where it might be either repaired or eventually rejected and replaced. The normal and partial failure states are up states while the other two are down states. The system breaks down when the (m + 1)th unit after total failure is finally rejected and no standby remains to replace it. Several reliability characteristics of interest to system designers as well as operations managers have been computed. Results obtained earlier are verified as particular cases.     

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 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 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.     

Comparison of two stochastic models for two-unit series system with cold standbys

Reliability characteristics are compared for two stochastic models of a system that has two non-identical units, arranged in series, each unit with its identical cold standby. The same set of assumptions is used for both models, except that in model 2 both of the standby units replace the failed operative unit instantaneously whereas in model 1 an operative failed unit is replaced by its corresponding standby unit (i.e. only one unit is replaced in this case). A single repair facility is available to repair the failed unit. Failure and repair time distributions are assumed to be negative exponential.     

Reliability of a 2-Unit Priority-Standby Redundant System with Finite Repair Capability

This paper analyses the reliability of a 2-unit standby redundant system consisting of two dissimilar units. Unit 1 performs the desired system function whenever available for use. Unit 2 operates only during those periods when unit 1 is undergoing repair. Unit 1 can be repaired at most N times. Expressions for the Laplace-Stieltjes transform of the distribution of the Time to System Failure (TSF) and the mean TSF are derived.     

Reliability and availability analysis for two non-identical unit parallel systems with common cause failures and human errors

This paper presents three models with common cause failure and human error analysis of a two non-identical unit parallel system. The difference between models I and II is that, in model I the failed system is repaired back to its normal operating state whereas in model II it is not so. Similarly, the basic difference between models II and III is that, in model II it is possible for the partially failed system to be restored to its normal operating state and in model III it is not so. The system reliability, time dependent system availability, steady-state system availability and mean-time to failure are developed for the above models. The problem is discussed with a numerical example.     

A simple ordering policy with linear lifetime for a unit

In this paper optimum ordering policies of a one-unit system where each failed unit is scrapped and each space is only provided after a lead time by an order with a deterministic linear lifetime for the unit is considered. The optimum ordering policy minimizing the expected cost per unit time in the steady state is discussed by introducing the two types of constant lead times along with ordering costs and downtime cost. The problem concludes with a numerical example minimizing the expected cost function.     

Systems in reduced efficiency and alternating periods

We discuss here 2-unit systems working in alternating periods of normal and abnormal periods. The system consists of two units L₁ and L₂. In a normal period only the failure of the unit L₂ causes system failure. If the unit L₁ fails in this period the system works in reduced efficiency. In an abnormal period the failure of any one of the two units produces a complete failure of the system. This is model I. In model II the failure of L₂ causes a failure of the system irrespective of the periods. On the failure of unit L₁ in a normal period the system works in reduced efficiency as in model I. But in an abnormal period when the unit L₁ fails the system does not fail immediately. It is able to work for a certain short period, called the sustenance period. In an abnormal period a failed unit cannot be repaired. If the sustenance period expires, the system is considered as a total failure. If in the meanwhile the system enters the normal period it continues to work in reduced efficiency. The normal and abnormal periods alternate. The reliability of these two models are discussed using the Markov renewal technique. Certain particular cases are analysed.