Cold Standby Repairable System Research Articles

A new extended δ‐shock model with the consideration of shock magnitude

AbstractIn this article, a new ‐shock model that takes into account the magnitude of shocks is introduced and studied from reliability perspective. According to the new model, the system breaks down if either a shock after non‐critical shock occurs in a time length less than or a shock after a critical shock occurs in a time length less than where . The distribution of the system's lifetime is studied for both discrete and continuous intershock time distributions. It is shown that a new model is useful to describe a certain cold standby repairable system.

Availability and maintenance strategy under time-varying environments for redundant repairable systems with PH distributions

Systems commonly operate in time-varying environments which have essential impact on system performance, thus reliability modeling and maintenance strategy are faced with new challenges. In this study, a cold standby repairable system in a time-varying environment is investigated based on different operational levels and maintenance strategies, in which repairman's vacation and maintenance rules vary with environments. The evolution of dynamic environments is governed by a Markov process, and the successive vacation time is governed by Markovian arrival processes (MAPs). Using Phase-type (PH) distribution not only increases the flexibility of analytical properties because it can approximate to any probability distribution defined on a nonnegative real line, but also could effectively ensure the applicability of the model in engineering practice, specially all the lifetimes of components and maintenance time are subject to disparate PH distributions in diverse environments. By employing the matrix-analytic method, Kronecker operator theory and aggregated stochastic processes, some reliability indexes and the system average benefit are obtained respectively. Finally, an example of a redundant power supply is given to illustrate the validity and applicability of the proposed model.

A REPAIR REPLACEMENT PROBLEM FOR COLD STANDBY SYSTEM USING ALPHA SERIES AND GEOMETRIC PROCESS

The present paper studies a cold standby repairable system consisting of two identical components namely component 1, component 2 and onerepairman is studied. Assume that each component after repair is not 'as good as new' and also the successive working times form a decreasing a-series process, the successive repair time's form an increasing geometric process and both the processes are exposing to exponential failure law. Under these assumptions we study an optimal replacement policy N in which we replace the system when the number of failures of component 1 reaches N. It can be determined that an optimal repair replacement policy N* such that the long run average cost per unit time is minimized. It can also be derived an explicit expression of the long-run average cost and the corresponding optimal replacement policy N* can be determined analytically. Numerical results are provided to support the theoretical results

Analysis of the two-unit cold standby repairable system with damage and repair time dependency via matrix-exponential distributions

ABSTRACT In this paper, two-unit standby repairable system is studied via matrix-exponential distributions. The system under concern consists of one active and one standby components, and fails if either a damage size upon the failure of the active component is larger than a repair limit or the repair time of the failed unit exceeds the lifetime of the active unit, whichever happens first. Under the assumption that the damage size and repair time are statistically dependent, the Laplace transform of the system’s lifetime is obtained. The Laplace transform is shown to be rational under particular cases, and the reliability evaluation of the system is performed via well-known distributional properties of the matrix-exponential distributions. The problem of estimating the unknown parameters of the operation time and repair time distributions is also discussed based on system’s lifetime data.

Reliability assessment of a discrete time cold standby repairable system

This paper is concerned with the study of a discrete time repairable system consisting of one active and one standby component. The lifetime and repair time are assumed to have discrete phase-type distributions. The system’s lifetime is represented as a compound random variable. A matrix-based expression for the probability generating function of the system’s lifetime is obtained based on the phase characteristics of lifetime and repair time distributions. The probability generating function is then used to obtain the distribution of the system’s lifetime. Reliability and hazard rate functions are computed and evaluated for some particular choices of lifetime and repair time distributions. The limiting behavior of the hazard rates is also investigated.

A standby repairable system with rest of server between repairs

A cold standby repairable system of two identical units has been analyzed stochastically in detail by considering the idea of rest of the server between repairs. The unit has two modes – normal and complete failure. There is a single server who is allowed to take rest before starting repair of the unit which was waiting for the repair. The random variables associated with repair and rest time of the server follow arbitrary distribution with different probability density functions while the failure rate of the unit is considered as constant. The semi-Markov process and regenerative point technique are used to derive the expressions for mean time to system failure (MTSF), availability, busy period of the server due to repair, expected number of repairs and profit function. The profit analysis of the system model has been carried out for particular values of the parameters. The profit of the system model has also been observed for change in the revenue per unit time, change in the cost for which server is busy due to repair and change in the cost per repair per unit time.

一类修理工带休假的冷贮备可修系统的指数稳定性

一类修理工带休假的冷贮备可修系统的指数稳定性

Replacement Policy for Cold Standby Repairable System with Priority in Use by Using Arithmetico-Geometric Process

In this paper, we consider the arithmetico-geometric process (AGP) repair model. Here, the system has two nonidentical component cold standby repairable system with one repairman. Under this study, component 1 has given priority in use. It is assumed that component 2 after repair is as good as new, whereas the component 1 follows AGP. Under these assumptions, by using AGP repair model, we present a replacement policy based on number of failures, [Formula: see text], of component 1 such that long-run expected reward per unit time is maximized. For this policy, system can be replaced when number of failure of the component 1 reaches to [Formula: see text]. Working time of the component 1 is AGP and it is stochastically decreasing whereas repair time of the component 1 is AGP which is stochastically increasing. The expression for long-run expected reward per unit time for a renewal cycle is derived and illustrated proposed policy with numerical examples by assuming Weibull distributed working time and repair time of the component 1. Also, proposed AGP repair model is compared with the geometric process repair model.

Reliability analysis for a cold standby system under stepwise Poisson shocks

ABSTRACT In this paper, a two-dissimilar-component cold standby repairable system maintained by a repairman is investigated. The system fails due to either intrinsic factors or external shocks. Assume that shocks arrive according to a stepwise Poisson process, the intensity of which varies with respect to the number of failures of the working component. Repair after failure is imperfect. Using the supplementary variable method and the vector Markov process theory, we obtain some important reliability index for the system. By the renewal reward theorem, an optimal replacement policy is derived by minimising the average cost rate of the system. Numerical examples are presented to validate the theoretical results.

Analysis of Reliability of A Two-Non-Identical Units Cold Standby Repairable System Has Two Types of Failure

Analysis of Reliability of A Two-Non-Identical Units Cold Standby Repairable System Has Two Types of Failure

Useful Inequalities for Upper and Lower Bounds for the Repairable Aging Cold Standby System

In this paper, we study a cold standby repairable system consisting of two non-identical components and a single repair facility with one repairman. It is assumed that, one of the two components is operating while the other is in cold standby and also two components follow a geometric process. Under these assumptions, at first we present Laplace-Stieltjes transform of the system lifetime and then we give some useful inequalities about the mean lifetime of the system.

An optimal age-replacement policy for a cold standby repairable system with priority in use and repair

ABSTRACTIn this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. Assume that Component 2 after repair is ‘as good as new’ while Component 1 after repair is not, but Component 1 has priority in use and repair. Under these assumptions, using a geometric process, we consider a replacement policy based on Component 1 age T as the system age under which the cold standby system is replaced when the system age reaches T. Our problem is to determine an optimal replacement policy T* such that the average cost rate of the system is minimised. The explicit expression of the average cost rate is derived, the corresponding optimal replacement policy T* can be determined analytically or numerically. Finally, a numerical example is given to illustrate the model developed, and some sensitivity analysis on the optimal solution is also conducted.

A geometric process repair model for a cold standby repairable system with imperfect delay repair and priority in use

ABSTRACTIn this article, a two-dissimilar-component cold standby repairable system with one repairman is studied. Assume that the repair after failure for each component is delayed or undelayed. Component 2 after repair is “as good as new” while Component 1 after repair is not, but Component 1 has priority in use. Under these assumptions, using a geometric process, we consider a replacement policy N based on the failure number of Component 1. An optimal replacement policy N* is determined by minimizing the average cost rate C(N) of the system. Finally, a numerical example is given to illustrate some theoretical results and the model applicability.

A cold standby repairable system with the repairman having multiple vacations and operational, repair, and vacation times following phase-type distributions

ABSTRACTThis paper studies a cold standby repairable system with two identical components and one repairman having multiple vacations applying matrix-analytic methods. The lifetime of the component follows a phase-type distribution. The repair times and the vacation times of the repairman are governed by different phase-type distributions, respectively. For this system, the Markov process governing the system is constructed. The system is studied in a transient and stationary regime, the availability, the reliability, the rates of occurrence of the different types of failures, and the working probability of the repairman are calculated, respectively. A numerical application is performed to illustrate the calculations.

Cold standby repairable system with working vacations and vacation interruption

Cold standby repairable system with working vacations and vacation interruption

An extended geometric process repair model for a cold standby repairable system with imperfect delayed repair

ABSTRACTThis paper proposes an extended geometric process repair model (EGPRM) to generalise the geometric process repair model (GPRM), and studies a repair–replacement problem for a cold standby repairable system consisting of two dissimilar components and one repairman. Assume that each component after repair in the system is not always successive degenerative, and the failure component in the system is not always immediately repaired. Under these assumptions, using the extended geometric process, we consider a replacement policy N based on the failure number of Component 2 under which the system is replaced when the failure number of Component 2 reaches N. Our problem is to choose an optimal replacement policy N* such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimised. The explicit expression of the average cost rate of the system is derived, and the corresponding optimal replacement policy N* can be determined by minimising the average cost rate of the system. Finally, a numerical example is given to illustrate some theoretical results and the model applicability.

Reliability analysis of a cold standby repairable system with repairman extra work

This paper deals with a cold standby repairable system with two identical units and one repairman who can do extra work in idle time. The authors are devoted to studying the unique existence and exponential stability of the system solution. C0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.

A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process

This paper studies a cold standby repairable system with working vacations and vacation interruptions. The repairman׳s multiple vacation, the working vacation policy and the vacation interruption policy are considered simultaneously. The lifetime of component follows a Phase-type (PH) distribution. The repair time in the regular repair period and the working vacation period are other two Phase-type distributions with different representations, and the successive vacation times are governed by a Markovian arrival process (MAP). For this system, a vector-valued Markov process is constructed. We obtain several important performance measures for the system in transient and stationary regimes applying the matrix-analytic method. Finally, a numerical example is given to illustrate the results obtained in the paper.

Reliability Measures of a Two-Unit Cold Standby Repairable System with Priority to Operation over Preventive Maintenance

main objective of present work is to carry out various important reliability measures of a twounit cold s tandby repairable system with priority to operation over preventive maintenance by using regenerative points technique and semiMarkov process. A single repair facility is pr ovided to conduct repair and maintenance of the system as and when required. All times distributions are exponential except the repair and preventive maintenance time distributions which are considered as general.

Discrete time cold standby repairable system: Combinatorial analysis

ABSTRACTIn this article, we obtain exact expression for the distribution of the time to failure of discrete time cold standby repairable system under the classical assumptions that both working time and repair time of components are geometric. Our method is based on alternative representation of lifetime as a waiting time random variable on a binary sequence, and combinatorial arguments. Such an exact expression for the time to failure distribution is new in the literature. Furthermore, we obtain the probability generating function and the first two moments of the lifetime random variable.