Stochastic behaviour of a maintained system with protection system

This paper deals with the analysis of a single unit system backed by a protection system (.P.S.). Both are subject to failure with exponential failure time distribution. Repair time of working unit, fault detection and inspection time of protection system are assumed to follow general distribution. The system has been investigated in detail by the help of semi-Markov process and several parameters of interest are obtained.     

Inspection frequency and availability of emergency equipment

A mathematical model has been developed which permits the investigation of the influence of human error during an inspection procedure on the availability of equipment used in emergency conditions. Two types of human error are considered: an error to detect failure of the equipment and an error which causes an inadvertent failure of the equipment during the inspection. The human reliability model based on THERP method is developed in the paper. Various levels of dependence between consecutive tastes are considered. An optimal inspection interval is found for exponential distribution of time to failure.     

A multi-component standby system subject to inspection and truncated normal failure time distribution

This paper investigates a stochastic model of a single server, two identical unit cold standby system. Each unit consists of n separately maintained independent components arranged in series. After each failure, an inspection is required to detect which component of the unit has failed. The failure time distribution of a unit is truncated normal while all the other time distributions are negative exponential. Using the regenerative point technique, we obtained various measures of system effectiveness to carry out the profit function analysis.     

Availability analysis of two-unit warm standby system with inspection time

This paper deals with two identical units warm standby system when a failure of unit is detected by actual inspection but a system down can be detected at any time without inspection. Where the lifetime distribution of unit is the bivariate exponential distribution and other distributions are arbitrary. The Laplace transform of the point-wise availability of the system and the steady state availability of the system are derived by using the supplementary variable method. Further, we discuss the optimum inspection period maximizing the steady state availability. A numerical example is presented.     

Optimal allocation of s-identical, multi-functional spares in aseries system

This paper considers the problem of allocating statistically-identical, multi-functional spares to subsystems of a series system. The objective is to maximize the system reliability for mission time T which can be deterministic or stochastic. Several problems which are conceptually similar to this one have been discussed in the literature in different contexts. An algorithm is provided for obtaining standby redundancy allocation, and sufficient conditions are derived for optimality of the resulting allocation for general T. The algorithm is equivalent to a simple allocation rule under the sufficient conditions. The allocation rule gives an optimal allocation for the special cases: the PDF's of component lifetimes are log concave (which implies increasing failure rate), and T is deterministic; the components have exponential failure times, and T follows a gamma distribution; and component lifetime distributions are general, and T follows an exponential or a mixture of exponential distributions. No simpler method is available for latter two cases     

Cost-benefit analysis of a single server three-unit redundant system with inspection, delayed replacement and two types of repair

This paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement at the time of failure of the active unit and a cold standby (stock) unit which can be replaced after a random amount of time. The type of the failure of operative or warm standby unit is detected by inspection only. The service facility plays the triple role of replacement, inspection and repair of a unit. Failure time distributions of operative and warm standby units are negative exponential whereas the distributions of replacement time, inspection time and repair times are arbitrary. The system has been studied by using regenerative points.     

Reliability and MTTF evaluation of a repairable complex system under waiting

This paper deals with the reliability and mean time to failure (MTTF) evaluation of a complex system under waiting incorporating the concept of hardware failure and human error. Failure rates of the complex system follow exponential time distributions, whereas repair follows a general repair time distribution. Laplace transforms of various state probabilities have been evaluated and then reliability is obtained by the inversion process. A formula for variance of time to failure has also been developed. A particular case is also given to highlight some important results. Moreover, various plots have been sketched at the end.     

An optimal inspection policy for a storage system with high reliability

A system such as missiles and spare parts of aircrafts has to perform a normal operation at any time when it is used. However, a system is in storage for a long time from the transportation to the usage and its reliability goes down with time. Such a system should be inspected and maintained at periodic times to hold a higher reliability than a prespecified value q. This paper suggests a periodic inspection of a storage system with two kinds of units where unit 1 is inspected and maintained at each inspection, however, unit 2 is not done. The system is replaced at detection of failure or at time when the reliability is below q. The total expected cost until replacement is derived and an optimal inspection time which minimizes it is discussed. Numerical examples are given when failure time distributions are exponential and Weibull ones.     

A two-unit priority standby system subject to random shocks and Releigh failure-time distribution

This paper deals with the cost-benifit analysis of a two-unit priority standby system subject to random shocks. The priority unit gets preference both for repair and operation over the ordinary unit and has three modes- Normal, Quasi-normal and Total-failure. The ordinary unit has only two-modes- Normal and Total-failure. The distributions of shock-time, repair-time of the ordinary unit and failure time of the priority unit are negative exponential. The distribution of the repair-time of the priority unit is taken to be general while the time to failure of ordinary unit follows Releigh distribution. Various characteristics related to system effectiveness have been obtained by using the regenerative point technique.     

An inspection model with generally distributed restoration and repair times

In classical inspection models, it is assumed that the inspection time and the restoration time are either zero or fixed, and the production facility never breaks down. However, in real production, the production system is subject to random failures and the repair and restoration times are usually random. In this paper, we will study the effect of the exponential failure time and generally distributed restoration and repair time on the optimal inspection interval of a production unit subject to deterioration. Treating the process as a semi-regenerative process (SRP) and analyzing the SRP by Markov renewal theory, the formula for the long-run expected average cost per unit time and formulae for the steady-state probabilities of the SRP are obtained in an explicit form. The optimal inspection interval is obtained by minimizing the average cost function.     

Reliability matrix solution to multiple mechanism prediction

We present a method for predicting the failure rate and thus the reliability of an electronic system by summing the failure rate of each known failure mechanism. We use a competing acceleration factor methodology by combining the physics of failure for each mechanism with its own effect as observed by High/Low temperature and High/Low voltage stresses. Our Multiple High Temperature Overstress Life-test (M-HTOL) method assumes that the lifetime of each failure mechanism follows constant rate distribution whereby each mechanism is independently accelerated by its own stress factors. Stresses include temperature, frequency, current, and other factors that can be entered into a reliability model. The overall failure rate thus, also follows an exponential distribution and is described as the standard FIT (Failure unIT or Failure in Time). This method combines mathematical models for known failure mechanism and solves them simultaneously for a multiplicity of accelerated life test results to find a consistent set of weighting factors for each mechanism. The result of solving the system of equations is a more accurate and a unique combination for each system model by proportional summation of each of the contributing failure mechanisms.     

Bayes credibility estimation of an exponential parameter for randomcensoring and incomplete information

A Bayes interval estimation for an exponential parameter Θ in a model of random censoring with incomplete information is investigated. The instant of item failure is observed if it occurs before a randomly chosen inspection time and the failure was signaled; otherwise, the experiment is terminated at the instant of inspection. An explicit expression for the posterior PDF (probability distribution function) of the parameter is derived, and a normal approximation to it based on Taylor expansion near the maximum likelihood estimate is suggested. The results of an extension simulation showed that the reparametrization Θ₁=log Θ appreciably increases the accuracy of the normal approximation. Highly accurate highest posterior density intervals for Θ₁ are derived in a closed form for a normal prior for Θ₁ or, equivalently, for the lognormal prior on Θ     

Estimation in a random censoring model with incomplete information:exponential lifetime distribution

Analysis of methods and simulation results for estimating the exponential mean lifetime in a random-censoring model with incomplete information are presented. The instant of an item's failure is observed if it occurs before a randomly chosen inspection time and the failure is signaled. Otherwise, the experiment is terminated at the instant of inspection during which the true state of the item is discovered. The maximum-likelihood method (MLM) is used to obtain point and interval estimates for item mean lifetime, for the exponential model. It is demonstrated, using Monte Carlo simulation, that the MLM provides positively biased estimates for the mean lifetime and that the large-sample approximation to the log-likelihood ratio produces accurate confidence intervals. The quality of the estimates is slightly influenced by the value of the probability of failure to signal. Properties of the Fisher information in the censored sample are investigated theoretically and numerically     

Reliability Sampling Plans Under Progressive Type-I Interval Censoring Using Cost Functions

This paper gives a reliability sampling plan for progressively type I interval censored life tests when the lifetime follows the exponential distribution. We use the maximum likelihood method to obtain the point estimation of the parameter of failure time distribution. We provide an approach to establish reliability sampling plans which minimize the total cost of life testing under given consumer's and producer's risks. Some numerical studies are investigated to illustrate the proposed approach.      

Analysis of two-unit-standby redundant system with administrative delay in repair

A two-unit cold standby redundant system is analysed under the assumption that administrative time is spent in locating the repairman and getting him available at the system location. The administrative time distribution is assumed to be exponential and whereas the repair and failure time distribution are exponential and arbitrary. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated.     

Failure distributions for local vs. global and replicate vs.standby redundancies

The paper begins with an arbitrary single-output, discrete-signal, irredundant system consisting of interconnected computing units each of which has the same exponential distribution for failure time. Then it presents several corresponding redundant designs that compute the same function, derives their distributions for failure time, and illustrates them with quantitative examples. None of the straight replicative designs very much improves the original distribution for failure time; nor do the releasing designs do better. The standby designs do best, even after the standby management-system failure distribution is factored into the system failure distribution. Replicate releasing designs, as a group, are better than straight replicate designs; and standby designs are best     

Stochastic behavior of a two-unit cold standby redundant system subject to random failure

The present paper deals with a stochastic model of a two-unit cold standby redundant system subject to random failure. The random failure occurs at random times which follow an exponential distribution. Using a regenerative point technique in the Markov-renewal process, several reliability characteristics are obtained. The mean time to system failure function is studied graphically.     

Stochastic behaviour of a two-unit cold standby redundant system with administrative delay and two types of repairs

In this paper we consider a two-unit cold standby redundant system in which each unit works in three modes—normal, partial failure and total failure with two types of repairs (major and minor) after partial failure mode, with administrative delay to locate expert repair man for major repair. The administrative time distribution is assumed to be exponential, whereas the repair and failure time distributions are exponential and arbitrary. The technique of regenerative processes is applied to obtain various reliability characteristics of interest to system designers.     

A Two-Unit Cold Standby Repairable System with One Replaceable Repair Facility and Delay Repair: Some Reliability Problems

1 Model and Assumption In reliability analysis of repairable systems, it is usually assumed that the repair facility neither fails nor deteriorates as well as the repairman is instantaneously available. So that the repair is started immediately upon the failure of a unit provided that he is not busily repairing another unit. However, in actual practice, the repair facility in a repairable system is subject to failure and can be replaced (or can be repaired) after it fails, and certain delay ac…     

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.