General Repair Time Distributions Research Articles

A stochastic model for cell survival after irradiation

This paper deals with the theory of cell survival after irradiation. It is based on the assumption that the cell is composed of two regions with different sensitivities and takes into account phenomena with general repair-time distribution different for each region. Expressions are obtained for the probability that the cell will be damaged and for the mean life time of the cell.

Reliability analysis of a two-unit cold standby redundant system with two operating modes

This paper considers a two unit cold standby redundant system subject to a single repair facility with exponential failure and general repair time distribution. Each unit can work in three different modes — normal, partial failure and total failure. There is a perfect switch to operate the standby unit on total failure of the operative unit. The system has been analysed to determine the reliability parameters e.g. mean time to system failure (MTSF), steady state availability, mean recurrence to a state and expected number of visits to a state, first two moments of time in transient state, by using the theory of Semi-Markov Process. Howard's reward structure has been super-imposed on the Semi-Markov Process to obtained expected profit of the system. A number of results obtained earlier are derived as particular cases.

Two repairable multistate devices with general repair-time distributions: Mitsuo Yamashiro. IEEE Trans. Reliab.R-30 (2), 204 (1981)

A survey of the research done on reliability of systems exhibiting two dual modes of failure, which are often called open and short, is given. Particular attention is paid to books and papers published after the 1977 review by Dhillon [32]. The present survey discusses the different terminology and approaches that appear in the literature and covers results concerning mainly the following topics: the optimal structure of the system, the optimal allocation of units, Markov and semi-Markov models of systems with repairable units and investigation of the structures of particular importance — series-parallel, k-out-of-n:G and logic circuits.

Two Repairable Multistate Devices with General Repair-Time Distributions

The system has two parallel redundant multistate devices with general repair-time distributions. The Laplace transforms of state probability and the mean time to system failure (MTSF) are obtained and a particular case is considered.

A multistate system with general repair time distribution : Mitsuo Yamashiro. IEEE Trans. Reliab.R-29 (5) 433 (December 1980)

A multistate system with general repair time distribution : Mitsuo Yamashiro. IEEE Trans. Reliab.R-29 (5) 433 (December 1980)

Analysis of a degraded multistate system with general repair-time distributions: Mitsuo Yamashiro. Microelectron. Reliab.20, 647 (1980)

Analysis of a degraded multistate system with general repair-time distributions: Mitsuo Yamashiro. Microelectron. Reliab.20, 647 (1980)

A Multistate System with General Repair Time Distribution

This paper deals with a multistate system with general repair time distribution. Laplace transforms of state probability for such a system are obtained and particular cases are discussed.

A Repairable Multistate Device with General Repair Time

This paper deals with a repairable multistate device with general repair time distribution. The Laplace transforms of state probability for such a device are obtained and a particular case is discussed.

Analysis of a degraded multistate system with general repair-time distributions

The system in this paper has good, degraded and (N−1)-failed states. Laplace transforms of state probability for such a system are obtained by using the supplementary variable method. A particular case is considered.

一般分布をもつ2-ユニット並列システム

This paper considers a two-unit paralleled system with general failure time and repair time distributions. The equations governing the behaviour of the system, without using regenerative (or cyclic) nature, have been derived by employing the method of supplementary variable. Then the problems of calculating the Laplace transform of the reliability of the system and the mean time to the first system failure are reduced to that of solved a well-known Fredholm integral equation, depending on the pdf's of the failure and repair time of units. In addition, the probability that repairman is idle at time t, the expected total idle time of repairman during the interval (O,t] , and the expected number of repair until the system failure occurs are shown.

Unavailability of components with inspection and repair

A general set of integral equations and solutions have been obtained for the unavailability of standby components. The model uses general failure time, test duration and repair time distributions. Random failures as well as contributions from human testing errors and true demands have been taken into account. Optimal testing/inspection intervals have been obtained for practical inspection policies.

Cost Analysis for 2-Unit Systems

For a 2-unit system with general repair and failure time distributions, the net profit has been studied as the difference between functions of the uptime and downtime. The mean number of products manufactured is also given.

Number of Repairs for a 2-Unit System

The number of repairs upto time t for a 2-unit cold-standby system with general repair and failure time distribution is studied. The number of failures upto time t is given as a dual case.

A Stochastic Model for Cell Survival after Irradiation

A theory of cell survival after irradiation has been developed based on a single compartment model of a living cell and taking into account a recovery phenomenon. The basis of the model is the assumption that once a cell is repaired, it will behave like a normal cell if irradiated further. Theoretical expressions for the probability of survival or damage of an irradiated cell at an arbitrary instant in time have been obtained for a constant damage rate and a general repair-time distribution. An application of these derived expressions has been made to experimental data.

Probabilistic analysis of a two-unit standby redundant system with repair efficiency and imperfect switch-over

A two-unit warm standby redundant system with exponential failure and general repair-time distributions is considered. There is a switch used to switch the standby unit to operate as and when operative unit fails. The probability that the switch operates successfully at the time of need is fixed. After each repair, a unit is examined to see if it meets repair specification. A unit meets specifications only on a fixed proportion of time. If a unit does not meet specification, it is sent to ‘ post-repair ’. The system has been analysed by studying the underlying semi-Markov chain and mean-time-to-system-failure (MTSF), expected number of visits to a state, steady-state availability, first two moments of time in transient states and time to absorption, absorption probabilities are obtained. In the sequence Howard's reward structure has been superimposed on the semi-Markov process to obtain expected profit of the system. Several earlier models are included as special cases.

Reliability and Availability of Two General Multi-Unit Systems

This paper considers k-unit systems with repair. Reliability and availability integral equations are set up using renewal theory. This paper treats a k-unit system with s-dependent failure rate and general repair time distribution, and a k-unit cold-standby system with Erlang failure time distribution and general repair time distribution.

On expected profit in a two-unit standby system with switch failure

A two-unit warm standby redundant system with switch failure, exponential failure-time and general repair time distribution is considered. Howard's reward structure has been superimposed on the semi-Markov process generated by the system to obtain expected profit that the system earns in steady state. Effect of switch behaviour on expected profit has also been studied. Several particular cases are included

Interrupted service queueing with arrivals and departures in batches of variable size and general repair time distribution

Dans I'article on etudie le comportement transitoire d'un systeme de fils d'attente dans lequel les arrivees et les departs se present en groupes de taille variable et le service est donne sous reserve de panne. Immediatement apres une panne le systeme est soumis a une reparation et le service recommence aussitot la reparation effectuee. Le temps de service et le temps de remise en route du systeme sont exponentiellement repartires. LAPLACE des fonctions generatices de la probabilite de la longueur de la file d'attente. Enfin quelques cas particuliers sont discutes.

Interrupted service queueing with arrivals and departures in batches of variable size and general repair time distribution

Interrupted service queueing with arrivals and departures in batches of variable size and general repair time distribution

Reliability Analysis of an n-Spare System with a Single Repair Facility

The reliability of standby systems with repair is investigated using semi-Markov processes. The systems are composed of n + 1 identical units having an exponential failure time distribution and of a single repair facility having a general repair time distribution. For these systems, the Laplace-Stieltjes transform of the system failure time distribution is derived in the form of generating functions. For indefinitely large n, asymptotic formulae of the mean time to system failure (MTSF) and limiting distributions of the system failure time are given. Under certain conditions, the system failure time distribution is shown to tend to be exponential as n increases. Numerical examples show that the asymptotic formulae of MTSF are good approximations, even for small n. The results can also be applied to the first passage time problem of the maximal queue size in the system M/G/1.