Cost analysis of a three-state repairable redundant complex system under various modes of failures

In this paper investigations have been carried out for the availability and mean time to failure analysis of a three unit repairable electronic equipment having three states; viz; good, degraded and failed under critical human errors. The three states three units repairable electronic equipment suffers two types of failures; viz; unit failure and failure due to critical human errors. Entire system can fail 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 are obtained along with steady state behaviour of the equipment. A numerical example has also been appended to highlight the important results. Three graphs have also been given in the end. There is only one repair facility, which is availed only when the system is in either degraded or failed state due to unit failure.     

Stochastic behaviour of a repairable system operating under fluctuating weather

A repairable system which operates under fluctuating weather conditions is considered. There are 3 types of weathers: normal, abnormal 1 and abnormal 2. Weather changes from normal to abnormal 1 and abnormal 2 at exponential rates. Failure time distribution of the system from normal weather is exponential whereas it is general from abnormal states. Repair time distributions are different and general. The model is analysed by the help of SMP technique and reliability parameters viz MTSF, steady-state availability, absorption probabilities etc. are obtained.     

Stochastic analysis of a repairable system with three units and two repair facilities

This paper investigates the availability characteristics and the reliability of a three-dissimilar-unit repairable system with two different repair facilities. Under some practical assumptions, we obtain the explicit expressions of the state probabilities of the system and then the explicit expressions of the following performance measures of the system: (1) the pointwise and steady-state availability; (2) the pointwise and steady-state failure frequency; (3) the pointwise and steady-state renewal frequency; and (4) the reliability and the mean time to system failure.     

Stochastic behaviour of a standby redundant system with three modes

This paper discusses the stochastic behaviour of a two-unit cold standby redundant system in which each unit works in three different modes-normal, partial failure and total failure. Failure-time distributions of units are exponential, whereas repair-time distributions are arbitrary. Explicit expressions for the Laplace-Stieltjes transforms of the distribution function of the first passage time, mean time to system failure and steady state availability of the system are obtained. A few particular cases are discussed.     

An optimal replacement policy for a three-state repairable system with a monotone process model

In this paper, a deteriorating simple repairable system with three states, including two failure states and one working state, is studied. Assume that the system after repair cannot be "as good as new", and the deterioration of the system is stochastic. Under these assumptions, we use a replacement policy N based on the failure number of the system. Then our aim is to determine an optimal replacement policy N/sup */ such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. An explicit expression of the average cost rate is derived. Then, an optimal replacement policy is determined analytically or numerically. Furthermore, we can find that a repair model for the three-state repairable system in this paper forms a general monotone process model. Finally, we put forward a numerical example, and carry through some discussions and sensitivity analysis of the model in this paper.     

Bayes prediction for the number of failures of a repairable system

After observing a repairable system for some time, one may wish to predict the number of failures of the system in some fixed future interval. Such a prediction depends on the: (1) assumed model for the failure process; and (2) length of the interval. The authors use a Bayes approach to obtain point and interval predictions for the number of failures in a future interval. Two situations are discussed: (1) the power law process (PLP) governs failure times during the period of observation, but in the future interval the homogeneous Poisson Process (HPP) governs the failure times; and (2) the failure process is the PLP. A rationale and an example of each situation is presented. They discuss the use of informative and noninformative priors for the parameters of the failure process. The Bayes approach can incorporate both sources of uncertainty: (1) the number of failures in the future interval is random, so even if the parameters of the failure process are known, the number of failures that would occur in a future interval would still not predict with certainty; and (2) the parameters of the failure process are not known and must be estimated from the observed data     

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.     

On the transient behaviour of a repairable system with a warm standby

In this paper, a two-unit active standby system is analysed to evaluate various measures of system performance under the assumption that the failure and repair times follow arbitrary distributions. Systems of integral equations satisfied by various state probabilities corresponding to different initial conditions have been written using the supplementary variable technique and state-space method. A particular case is analysed numerically under the assumption that the failure and repair times of both the units follow normal distributions.     

Stochastic behaviour of a two-unit (dissimilar) hot standby system with three modes

A hot standby system composed of two non-identical units is analysed under the assumption that each unit works in three possible modes—normal, partial failure and total failure. For each unit the failure time distribution is negative exponential and the repair time distribution is arbitrary. Breakdown of the system occurs when both the units are in total failure mode. There is only one repair service and when both the units are in the same mode, priority is given to the first unit in the matter of operation as well as repair. Several reliability characteristics of interest to system designers and operations managers have been evaluated.     

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.     

A repairable multistate system with several degraded states and common-cause failures

In this paper, we deal with a system with several degraded states and common-cause failures. Laplace transforms of state probability for such a system are obtained and a particular case is considered.     

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.     

Stochastic behaviour of a two-unit cold standby system with three modes and allowed down time

This paper discusses the stochastic behaviour of a two-unit cold standby redundant system under two very general sets of conditions: (i) each unit of the system having three different modes of working—normal, partial failure and total failure; (ii) breakdown of the system occurring when with both the units in total failure mode, the system is not regarded as failed (the system fails only when the breakdown does not terminate within the allowed down time). Failure-time distributions of units are exponential, whereas repair time distributions are arbitrary. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated.     

Reliability analysis of a repairable parallel system with standby involving human error and common-cause failures

This paper presents two analytical models of special multiple-state devices with repair. The failure rates are constant and the repair rates between failure states are constant, while the repair rate times between failure state and good state are arbitrarily distributed. Laplace transform of the state probabilities and steady-state availability are derived.     

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 non-identical three-state units redundant system with common-cause failures and one standby unit

This paper presents a mathematical model for predicting a two non-identical three-state active units redundant system with common-cause failures and one standby unit. The units may fail in either of two mutually exclusive failure modes or by the occurrence of common-cause failures. System is only repaired when all the units fail (including the standby unit). The failure rates of units are constant and system repair times are arbitrarily distributed. Laplace transforms of the state probabilities are derived.     

Estimation of parameters of a model of a complex repairable system

This paper deals with estimation of parameters of a model of a complex repairable system with 3ne unit on operation and the remaining (N − 1) units as inactive standbys and having a repair facility. Various operating characteristics, namely, reliability, availability, mean time to failure of the system, s-expected numbers of repairs in (0, t], s-expected numbers of failures of the system in (0, t] are estimated under two censoring schemes namely, the type-I censoring and type-II censoring schemes.