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.     

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.     

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 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.     

Multi-state device redundant systems with common-cause failures and one standby unit

This paper presents two mathematical models. Model I represents a two identical unit active redundant system whose units may fail in either of the two mutually exclusive failure modes. Similarly, model II represents a two non-identical unit active parallel system whose units either fail or survive. In addition, models I and II comprise the occurrence of common-cause failures and one standby unit. Systems are only repaired when all the system units fail (including the standby unit). System repair times are arbitrarily distributed. Laplace transforms of the state probability equations are developed.     

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.     

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.     

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].     

Availability analysis of a two-unit cold standby system with two switching failure modes

We consider a 2-unit cold standby redundant system with two switching devices—transfer switch and connect switch. The system is analysed under the assumption that each unit works in three different modes—normal, partial failure and total failure. Failure time distributions of units and connect switch are exponential, whereas repair time distributions are general. At any instant after use the transfer switch fails with probability q = 1?p. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated. A few particular cases are discussed.     

A repairable system with N failure modes and K standby units

This paper presents a repairable system with N failure modes and K standby units. Laplace transforms of state probability for such a system are obtained by using the supplementary variable method. Two particular cases are considered.     

Availability of the crystallization system in the sugar industryunder common-cause failure

Some results from an analytic study of reliability and availability of the crystallizer system in sugar plants are presented. The analytic model was developed in a study of an actual plant. The crystallizer system consists of five basic repairable subsystems in series. Each subsystem is considered as being: good, reduced, or failed. Some subsystems can fail together due to a common cause. The model is based on the Chapman-Kolmogorov equations. Steady-state availability and various state probabilities are derived using Laplace transforms. The usefulness of the study is demonstrated through illustrations     

Switch failure in a two duplex unit standby system

A two duplex unit standby system with an imperfect switch and subject to preventive maintenance is discussed. It is assumed that switch is available at the time of need with probability p(= 1−q). The failure time of a duplex unit is taken to be negative exponential whereas the repair time distributions of duplex unit and switch and the time taken for preventive maintenance action, respectively, are assumed to be arbitrarily distributed. The analysis is carried out by using the regenerative point technique, and some particular cases are discussed.     

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.     

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.     

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.     

Effect of intermittent repair in a two unit redundant system with standby failure

A two-unit standby redundant system with exponential failure time distribution of the operative unit is considered. It is assumed that failure of the standby unit is detected only at the time of use and is available with a known probability. Repair facility is also available at the time of need with a known probability. Repair and preoccupation times are general. Stochastic behaviour of the system has been studied by Semi-Markov process and parameters of interest eg. MTSF, steady state availability, expected profit have been obtained. Expected profit of this model is compared with that of an earlier model and a condition on extra incurred cost is obtained.     

Availability analysis of a standby complex system having imperfect switch-over device

Availability for a system composed of four subsystems in series having standby in one subsystem is considered in this paper. The system is in series with an imperfect switch-over device which switches the standby unit as and when a working unit fails.     

A general repairable system with N failure modes and k standby units

A repairable system with N failure modes and k standby units is studied under quite general conditions. Laplace transforms of the transition probabilities of the system are obtained by using semi-Markov techniques. A particular case is discussed.     

A k-out-of-N:G redundant system with cold standby units and common-cause failures

This paper presents a k-out-of N:G redundant system with M cold standby units, r repair facilities and common-cause failures. The constant failure rates of the operating and cold standby units are different. Failed system repair times are arbitrarily distributed. The system is in a failed state when (N+M?k+1) units failed or a common-cause occurred. Laplace transforms of the state probabilities, the availability of the system and the system steady-state availability are derived.     

Analysis of a two unit standby system with partial failure and two types of repairs

A two dissimiliar unit standby system is analysed. The priority unit can either be in normal or partial operative mode. When the unit fails from the partial mode, it undergoes minor repair and the unit becomes operative with different failure rate. If this unit fails again, it goes to major repair after which it works as good as new. The standby unit while in use is either operative or failed. This non priority unit fails without passing through the partial failure mode and undergoes only one type of repair with different repair time distribution. Failure and repair time distributions are negative exponential and general respectively. Regenerative technique in MRP is applied to obtain several reliability characteristics of interest to system designers.