Reliability and maintainability of a multicomponent series-parallel system with simultaneous failure under preemptive repeat repair discipline

This paper considers a system consisting of two subsystems connected in series with a single repair facility. One sybsystem is K-out-of-N:G system consisting of N identical units, while the other consists of M different units connected in series. The life-times of the active units depend on each other in having simultaneous failure of all the operating units and repair times are distributed quite generally. The system breaks down if more than (N−K+1) units in parallel group are simultaneously in the failed states or if any failure occurs in the series group or if simultaneous failure occurs. The availability and reliability function of the system are obtained simultaneously. Explict expressions for the steady state availability of the system and the mean time to the first system failure are obtained.     

Reliability and maintainability of a multicomponent series-parallel system under several repair disciplines

This paper considers a system consisting of two subsystems connected in series with a single repair facility. One subsystem is K-out-of-N:G system consisting of N identical units, while the other consists of M different units connected in series. The life-times of the active units depend on each other in having simultaneous failure of all the operating units and repair times are distributed quite generally. Initially all the units are operating. The system breaks down if more than (N-K+1) units in the parallel group are simultaneously in the failed states or if any failure occures in the series group. The availability and reliability function of the system under several repair disciplines are obtained simultaneously. We use a suitable transformation to deduce the reliability from the availability function. Explict expressions for the steady-state availability of the system and the mean time to system failure under several repair disciplines are obtained. Finally some properties of the steady-state availability for each repair discipline are given.     

Reliability model of series-parallel systems

Markov models are used to obtain closed form solutions of the reliability of a series-parallel system. The system consists of two identical equipment in series. Each equipment has one component. To improve equipment reliability, extra component is connected in parallel with the original one. Therefore; each equipment is considered as 2-component fault-tolerant one. The component has a Poisson failure, and a repair of contant rate. The system fails if at least one equipment is out of order.     

Reliability analysis of a multicomponent system in a multistate Markovian environment

Consider a system which operates in a randomly changing environment. The changes of environmental levels are described by a Markov process with finite states. The system consists of several units and one repair facility, the repair time of a failed unit has an arbitrary distribution. We obtain the system reliability functions, availabilities and failure frequencies.     

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 optimization of series-parallel systems using a genetic algorithm

A problem-specific genetic algorithm (GA) is developed and demonstrated to analyze series-parallel systems and to determine the optimal design configuration when there are multiple component choices available for each of several k-out-of-n:G subsystems. The problem is to select components and redundancy-levels to optimize some objective function, given system-level constraints on reliability, cost, and/or weight. Previous formulations of the problem have implicit restrictions concerning the type of redundancy allowed, the number of available component choices, and whether mixing of components is allowed. GA is a robust evolutionary optimization search technique with very few restrictions concerning the type or size of the design problem. The solution approach was to solve the dual of a nonlinear optimization problem by using a dynamic penalty function. GA performs very well on two types of problems: (1) redundancy allocation originally proposed by Fyffe, Hines, Lee, and (2) randomly generated problem with more complex k-out-of-n:G configurations.     

Reliability approximation of a Markov queueing system with server breakdown and repair

This paper considers the reliability approximation of the queueing system PH/PH/1 with server breakdown and repair, where the life time of the server has the exponential distribution, and its repair time has the phase type distribution. First, we obtain the steady availability and steady failure frequency of the server. Then, we get the reliability function of the server, its probability density function and its Laplace-Stiltjes transform, which also gives an effective approximation of the reliability function of the server, where the error of the approximation can be easily bounded and is uniform in t. Finally, we discuss a special case and we can show that the reliability approximation has a wider application to various Markovian queueing systems with a repairable server.     

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.     

Reliability system with two types of repair facilities

This paper deals with two identical unit cold stand-by systems. Two types of repair facilities, having a considerable difference in their costs, are used to repair the units. Repair of type 2 facility, a costlier one, is always available, while for repair of type 1 facility one has to wait for some time. If this waiting time exceeds some given maximum time, one has to call costly repair i.e. repair of type 2 facility.The system has been analysed to determine the reliability measures viz. MTSF, steady state availability, expected number of repairs etc., by using theory of semi-Markov processes and regenerative processes. Integral equations are set up for deriving these measures. These equations are solved with the help of Laplace transform technique. A cost equation is derived. The condition for maximizing the profit is also derived. Certain particular cases are analysed.     

Reliability measures for two-unit systems with a dependent structure for failure and repair times

This paper deals with reliability measures for two-unit systems with a repair facility assuming that the failure times and the repair time follow a trivariate exponential distribution of Marshall and Olkin, J. Amer. Statist. Assoc., 1967, 62, 30–44. The case where the system down-time is observed, is also discussed. The system reliability and system mean-time before failure are evaluated for standby and parallel systems. When the down-time is observed the system availability, steady-state availability and the system mean down-time are evaluated for standby, parallel and series systems.     

Reliability of a 3-unit cold redundant system with Weibull failure

Redundancy technique is applied to increase the reliability of a system where maintenance or repair is either not possible or is too costly. Reliability of a cold redundant system is always higher than a hot one. Moreover the increase in reliability due to adding of a unit in sequence can always be exactly determined.Literature is full of derivation of reliability expressions of a cold redundant system whose units obey exponential failure density. Due to extreme difficulty in evaluation of integrals involving Weibull density function, few attempts on derivation of reliability of redundant systems have been made. We have here derived reliability of a simple case of a 3-unit cold standby system whose units obey Weibull failure density.     

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

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

CHE failure in a two-unit standby system with slow switch, repair and post repair

A mathematical model of a two-unit cold standby system with critical human errors (CHE) and slow switch is investigated. The CHE leads to complete system failure, and repair and post-repair are needed before the system can be put back into operation. Slow switch means that on failure of the operative unit the switch puts the standby unit into operation after a random time. Failure time and switchover time distributions are negative exponential whereas all the repair and post repair time distributions are general. Using a regenerative point technique, we obtain various reliability characteristics which can be used to carry out the cost-benefit analysis. In a particular case, the behaviour of the cost function is also studied graphically.     

Complex system maintainability verification with limited samples

Complex system maintainability verification is always a challenging problem due to limited sample sizes. Consequently, conducting maintenance experiments in a laboratory environment is an appropriate way to obtain data for maintainability verification. In maintenance experiments, faults are seeded in the equipment and maintenance activities are implemented to record repair time. In this process, two problems arise when laboratory experimental data (in-lab data) are used together with field data during the operational test and evaluation stage. The first problem is the verification of segmental maintenance data and the second one is the combination of in-lab data and field data for integrative maintainability verification. Regarding the problems mentioned above, this paper proposes a suitable methodology to solve them. Firstly, the idea of segmentally weighted verification is adopted and the segmentally weighted verification (SWV) method is proposed to realize in-lab data verification. Secondly, the Dempster-Shafer (D-S) evidence theory based integrative verification method is presented to solve the problem of in-lab and field data combination. A case study concerning radar system maintainability verification is presented as an example of the implementation of complex system maintainability verification in industry.     

Reliability evaluation of a TMR computer system with multivariate exponential failures and a general repair

A Triple Modular Redundant (TMR) computer system is discussed under the assumptions of the multivariate exponential lifetimes and a general repair distribution. Analysis of an extended Markov Renewal Process (MRP) enables us to formulate a stochastic model and give some reliability measures which are quite useful to evaluate the TMR computer system.     

Periodic replacement with minimal repair at failure and general random repair cost for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for the multi-unit system which have the specific multivariate distribution. Under such a policy an operating system is completely replaced whenever it reaches age T (T > 0) at a cost c₀ while minimal repair is performed at any intervening component failures. The cost of the j-th minimal repair to the component which fails at age y is g(C(y),c_j(y)), where C(y) is the age-dependent random part, c_j(y) is the deterministic part which depends on the age and the number of the minimal repair to the component, and g is an positive nondecreasing continuous function. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the component. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited.     

Reliability,maintainability and cost-effectiveness: A bibliographical note

In a system, the level of performance is highly dependent on the reliability and maintenance, which are in turn constrained by the cost. In this note, a short overview on reliability and maintainability is given, and the influence of system cost is outlined. Finally, a list of books on reliability and maintainability is complied.     

Reliability evaluation of a phased mission system with time varying redundancy and failure probability

An attempt is made to derive the closed-form mathematical expression of a phased mission system reliability. A system is considered, where failure probability of a component and number of added redundancy change during the mission time. Several performance measures are also suggested.     

Analysis of a two-unit parallel redundant system with phase type failure and general repair

Explicit expressions for the Laplace transform of the reliability and availability of a general two-unit parallel redundant system are obtained. The mean time to system failure and steady state availability are deduced as special cases. Some particular cases of our result are also obtained.     

A two (multicomponent) unit parallel system with standby and common cause failure

This paper investigates the mathematical model of a system composed of two non-identical active parallel units and one cold standby. A unit has N components, each having a constant failure and repair rate. These vary from component to component. Several reliability characteristics of interest to system designers as well as operations managers have been computed. Results obtained earlier are verified as particular cases.