Stochastic behaviour of a three-state complex repairable system with three types of failures

This paper deals with the operational availability of a three-state complex repairable system consisting of n distinct units arranged in series. Single service facility is available for three types of failures of the complex system. A mathematical model for the complex system under severe restrictions has been developed for exponential failures and general repairs. Laplace transforms of various state probabilities have been evaluated and availability is then obtained by the inversion process. Few graphical illustrations are also given in the end so as to explain the practical utility of the model.     

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.     

A time-dependent availability measure for a repairable systemsubject to catastrophic failures

Attention is given to a repairable system which is subject to catastrophic failures while it is in operation or under repair. The topic of investigation is the time-dependent point availability measure of the system, which is obtained in terms of the repair and failure time distributions and in the form of convolution integrals that are readily evaluated by means of known computational algorithms. Also derived are expressions for this measure that are useful for estimating the parameters of the model according to the data available. An application of the model is considered     

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.     

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.     

Reliability prediction for repairable redundant systems

It is assumed that the mean time to failure and mean repair time are known for each of the subsystems of a system. The subsystems conform to the usual exponential failure (and repair) laws and their behaviors are mutually independent. The system includes redundant subsystems in active standby status. Whenever, after a system failure, repair of a failed subsystem re-establishes an adequate configuration, the system as a whole is returned to active status while repair of other failed subsystems (if any) continues. Under this set of assumptions, equations are developed which permit prediction of mean time to failure and mean down time for the system. The development differs somewhat from the use of birth-and-death equations which has been customary for similar problems in the past.     

Optimal allocation for a repairable system

A system is composed of n series subsystems. Each subsystem consists of some same type of parallel or cold stand-by components. These components are repairable. We discuss the optimal allocation of this system under various constraints, and give some procedures for solution of this problem.     

The number of working periods of a repairable Markov system duringa finite time interval

In reliability analysis, continuous parameter homogeneous irreducible finite Markov processes are used to model repairable systems with time-independent transition rates between individual states. The state space is then partitioned into the set of up states and the set of down states. The number of completed repair events during a finite time interval is an important (undiscounted) cost measure for such a system; it can be expressed in terms of the number of working periods during the same time interval. This paper derives a closed-form expression for the PMF of this latter quantity. The tool used is a recent result on the joint distribution of sojourn times in finite Markov processes. The MatLab implementation of the Markov model of a 2-unit parallel power transmission system is used to demonstrate the utility of the formula. The quantity examined is the number of completed repairs during a finite time interval. The method is viable in this case whereas the more usual randomization technique is not     

Excess repair time for a repairable system

In this paper we deal with a repairable system and the topic of investigation is the total of all excess repair times—an excess repair being that repair the duration of which exceeds a given constant τ. The mean of this total excess repair time to the mean of the total repair time in (0, t), provides a useful measure of overtime repair. We also derive expressions for the distribution function of the time to the instant of the beginning of the first excess repair.     

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.     

Calculating the failure frequency of a repairable system

Failure frequency is an important parameter of a repairable system. Combining the techniques of cut set, tie set and exclusive manipulation, a general formula has been derived in this paper. It can give the exact result at any point of time for systems whose component failure and repair times are arbitrarily distributed.     

Long-run availability of a repairable parallel system

We analyze the long-run availability of a two-unit parallel system sustained by a cold standby unit and attended by two identical repairmen. The system satisfies the usual conditions (i.i.d. random variables, perfect repair, instantaneous and perfect switch, queueing). Each operative unit has a constant failure rate and a general repair time distribution. We use Hokstad's supplementary variable method to construct a system of simultaneous partial differential equations. We present a first-order numerical scheme and an iterative algorithm for the solution of the equations. A particular but important numerical example (Weibull repair), illustrated by computer-plotted graphs, motivates the proposed approximation.     

Generalised availability measures for a two-unit intermittently used repairable system

This paper obtains generalised availability measures as defined by Baxter, J. appl. Prob.18, 227–235 (1981), for a two-unit cold stand-by intermittently used redundant repairable system. Regenerative point technique of Markov Renewal Process has been employed to obtain these measures. A particular case is also considered.     

Performance-related reliability measures for a repairable two-unit gracefully degrading system

The system analysed is a two-unit gracefully degrading system with repair. After each repair, the unit is tested to see if the repair meets certain predefined specifications. If it does, the unit is put to operation, otherwise it goes to post-repair. The failure-time and testing-time distributions are exponential whereas all other distributions are arbitrary. The technique of embedded SMP is employed to obtain several system performance parameters, namely, MTFF (mean time to first failure), availability, computational availability, expected number of visits to a certain state etc.     

An exponential SRGM with a bound on the number of failures

An exponential software reliability growth model (SRGM) incorporating a situation where more than one failure can be attributed to one fault/error has been proposed. Different model parameters have been estimated and an optimal release policy which minimizes the software cost, subject to achieving a given level of reliability, has been discussed. Finally, a numerical example illustrating the applicability of the model and a few practical situations where this model can be applied are also given.     

Availability analysis of a repairable standby human-machine system

This paper presents a model representing a two units active and one unit on standby human-machine system with general failed system repair time distribution. In addition, the model takes into consideration the occurrence of common-cause failures. The method of linear ordinary differential equation is presented to obtain general expressions for system steady state availability for failed system repair time distributions such as Gamma, Weibull, lognormal, exponential, and Rayleigh. Generalized expressions for system reliability, time-dependent availability, mean time to failure, and system variance of time to failure are also presented. Selected plots are presented to demonstrate the impact of human error on system steady state availability, reliability, time-dependent availability, and mean time to failure.     

Generalised availability measures for a multi-unit repairable system with standby failure

This paper obtains generalised availability measures, e.g. interval reliability, joint interval reliability, joint availability and expected number of system failures etc. for a multi-component system with deterioration in storage. We discuss here two such models under different assumptions. Regenerative point technique of Markov Renewal Process has been employed to obtain the aforesaid measures. This paper further unifies the treatment as employed to simple and two-unit standby redundant systems earlier [4,5,6].     

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.