Analysis of a k-out-of-n unit system with two types of failure and preventive maintenance

A k-out-of-n unit system is analysed with two types of failure: (1) failure due to change in operating characteristics and (2) catastrophic failure. Preventive maintenance of the system is allowed at random epochs. All transition rates are taken to be general. Several measures of reliability useful for system designers and operations managers have been obtained by using regenerative point technique with Markov renewal process. Some important results obtained earlier are shown as particular cases.     

Two unit redundant system with adjustable failure rate, critical human error (CHE) and inspection

The present paper deals with the analysis of a two unit redundant system with adjusting failure rate of the operative unit and critical human error (CHE). A single repair facility is used and after each repair the unit is sent for inspection to decide whether the repair is perfect or not. Using the regenerative point technique with a Markov renewal process, several reliability characteristics of interest have been obtained.     

Probabilistic analysis of a two-unit cold standby redundant system subject to failure of controlled weather device

This paper studies stochastic analysis of a two-unit cold standby system taking into account failure of a weather condition device. All failure times and time to repair the weather condition device have a negative exponential distribution, whereas repair rates of the operating unit are general. The regenerative points technique in Markov renewal processes (MRP) is applied to obtain several 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…     

Stochastic analysis of a redundant system with two types of failure

This paper deals with the analysis of a system model consisting of two units, in which one is operative and the other is on cold standby. The failure of an operative unit may be caused by a machine as well as by random shocks which occur after a certain interval of time.Using the regenerative point technique in Markov renewal processes, several effective measures of reliability are obtained.     

Analysis of a two-unit parallel redundancy with an imperfect switch

A parallel redundant system of two identical units is studied when the switchover from repair to on-line is defective. It is assumed that there is a single repair facility and that either unit has priority over the switching device while queuing for repair. The reliability and availability functions are obtained explicitly when the units have a constant failure rate. The method of extension to cover the case of dissimilar units with non-constant failure rates is also indicated.     

Reliability of a 2-Unit Standby Redundant System with Constrained Repair Time

This paper considers a 2-unit warm-standby redundant system with repair. The repair of a failed unit is constrained as follows: Associated with each failure of a unit is a random variable termed the Maximum-Repair-Time (MRT) of the failure. If the repair of a failed unit is not completed within the MRT, the unit is rejected for further use. Two types of failure stituations for the system are considered: 1) No allowed down time, and 2) Some allowed down time. Expressions for the Cdf of the Time to System Failure (TSF) and the mean TSF are derived by using Markov renewal processes.     

Two unit repairable redundant standby system

The Laplace-Stieltjes (LS) transform for the distribution of time to first system failure (TFSF), transition probability, availability and mean time to system failure have been derived for two unit repairable redundant standby system with perfect as well as imperfect switchover condition. General expressions for computing various reliability performance indices have been obtained by using Markov Renewal techniques considering general distributions for time to failure and time to repair for the units.     

Reliability Analysis of a Two-Unit Standby-Redundant System with Preventive Maintenance

We consider a standby-redundant model of two units, where we assume that one unit is operative and the other unit is in standby at time t = 0. If the operative unit fails, a unit in standby is put into preventive maintenance policy of the operative unit to maintain our the preventive maintenance policy of the operative unit to maintain our system with high reliability. Our concern for the system is the time to the first system-down. The Laplace-Stieltjes transform of the time distribution to the first system-down and the mean time to the first system-down are derived by applying the relationship between Markov renewal processes and signal flow graph. Further, the behavior after the system-down is investigated by using the results of Markov renewal processes. Finally, numerical examples are presented for the k-Erlang failure time distributions. The optimal preventive maintenance time is discussed.     

Time-varying failure rates in the availability and reliabilityanalysis of repairable systems

This paper combines time varying failure rates and Markov chain analysis to obtain a hybrid reliability and availability analysis. However, combining these techniques can, depending on the size of the system, result in solutions of the Markov chain differential matrix equations that are intractable. This paper identifies solutions that are tractable, These form the analytical baseline for the reliability and availability analysis of systems with time varying failure rates. Tractable solutions were found for the 1-component 2-state and the 2-component 4-state configurations. Time varying failure rates were characterized by a general polynomial expression. Constant, linear, and Weibull failure rate functions are special cases of this polynomial. The general polynomial failure rate provides flexibility in modeling the time varying failure rates that occur in practice     

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.     

Availability analysis of a robot with safety system

This paper presents availability analysis of a system composed of a robot and its associated safety system. The failed robot system is repairable and its associated repair rates could be constant or non-constant. The supplementary variable and Markov techniques were employed to obtain expressions for steady state availability, state probabilities, and Laplace transform of the state probabilities. Various plots are presented.     

Stochastic analysis of a 2-unit standby system with two failure modes and slow switch

This paper considers the cost-benefit analysis of a one-server two unit system subject to two different failure modes and slow switch. The failure rates of the units are constant. The repair times and the switchover time are assumed to be arbitrarily distributed. The server repairs the units and puts the standby unit into operation. Detailed analysis of the system is done by using regenerating point technique and results are obtained for mean time to system failure, steady state availability, busy period of a repair man, expected number of visits by the repair man and expected profit earned by the system.     

Approximated reliability of r-out-of-n(F) system with common cause failure and maintenance

In modern industries very high reliability system are needed. To improve the reliability of system, the component redundancy and maintenance of component or system play an impotant role and must be studied. This paper presents a reliability model of a r-out-of-n(F) redundant system with maintenance and Common Cause Failure. Failed component repair times are arbitrarily distributed. The system is in a failed state when r units failed because of the combination of single element failure or CCF(Common Cause Failure). Laplace transformation of reliability is derived by using analysis of Markov state transition graph. By using the analyzed MTBF, we compute MTBF of r-out-of-n(F) system. The MTBF with CCF is saturable even if repair rate is large.Approximated reliability of the r-out-of-n(F) system with maintenance and Common Cause Failure O.SummaryThe paper presents a reliability model of a r-out-of-n(F) redundant system with maintenance and Common Cause Failure. Failed component repair times are arbitrarily distributed. The system is in a failed state when r units failed because of the combination of single element failure or Common Cause Failure. Laplace transformation of reliability is derived by using analysis of Markov state transition graph. By analyzing this mean visiting time equations, we compute MTBF and shows computational example. The MTBF with CCF is saturable even if repair rate is large. In general the maintenance overcomes MTBF bounds, But the repair method not overcome the MTBF saturation when the system has Common Cause Failure.     

Stochastic behaviour of a two-unit paralleled system

This paper deals with a two-unit paralleled system with a single repair facility. Most papers on this subject assumed that at least one of the life time and repair time distribution is exponential. However the above assumption is violated by this paper. Then the various state probabilities (densities) have derived by employing the method of supplementary variables. We obtain the stochastic behaviour from these probabilities; (1) the long-run availability, (2) the idleness probability for the repair crew, and (3) the expected number (per unit time in long run) of system failures. Also comparison between the constant failure rate and non-constant failure rate is shown by numerical example.     

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.     

Reliability analysis of non-maintained parallel systems subject to hardware failure and human error

This paper presents four newly developed Markov models to evaluate reliability and mean time to failure of non-maintained parallel systems with hardware failure and human error. The first three models represent two-unit, three-unit and four-unit non-maintained parallel systems, respectively, whereas the fourth model generalises the analysis to a non-maintained n-unit parallel system. System state probability equations and mean time to failure expressions are developed for all four models.     

Reliability analysis of a complex system with a deteriorating standby unit under common-cause failure and critical human error

This paper presents a stochastic model representing two units and one as a standby unit with critical human error and common cause failure. The deteriorating effect of the standby unit on the system is studied. Repair times of the failed system are arbitrarily distributed while all other transition time distributions are negative exponential. The analysis is carried out using supplementary variable techniques and various measures of system effectiveness such as pointwise availability, steady-state availability, MTTF and variance of the time to failure of the system are obtained.     

Inspection policy for two-unit parallel redundant system

This paper deals with a single-server two-unit parallel redundant system with non-negligible inspection time. We shall assume that a failure of a unit or the system failure is detected by inspection only. We consider two inspection policies and under each inspection policy the stationary availability is derived by applying Piecewise Markov Process. Optimum inspection schedule is discussed to maximize the stationary availability of the system. A numerical example is presented.     

A repairable system with N failure modes and one standby unit

In this paper, we deal with a repairable system with N failure modes and one stanby unit. Laplace transforms of state probability for such a system are obtained by using the supplementary variable method. A particular case is considered.