Study of Optimal Frequency to the Repairable System Due to Failure Finding Interval to Maximize Availability System

This research article is based on a study of optimal frequency to the repairable system due to the failure finding interval to maximize as well as minimize the availability of some components devices. We studied together maintenance and corrective actions that carried out item of failure and periodic failure finding designed to check whether a system is still working. The model is proved as well as useful application in detecting the problem related to finding failure tasks of different scheme devices by maximization. The model formulated and the numerical application to the relevant mathematical model have been discussed to demonstrate the article quality. Therefore based on probability analytic development, the optimal maintenance policy is then obtained as solution of an optimization problem in which the maintenance cost rate is the objective function and the risk of corrective maintenance is the constraint function. Finally, the solution to the optimal device in the considered development model has been well adjusted due to derivation to the experimental observation rather than theory which will be taken into consideration in the next applied practical design research related and the system device provided that, the proactive device agreed with using the exponential distribution to the survive distribution function which can not be considered as valid.

Reliability Analysis of a Cold Standby Repairable System with Repairman Extra Work

This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one 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.

Markov repairable systems with stochastic regimes switching

Compared with the classical Markov repairable system, the Markov repairable system with stochastic regimes switching introduced in the paper provides a more realistic description of the practical system. The system can be used to model the dynamics of a repairable system whose performance regimes switch according to the external conditions. For example, to satisfy the demand variation that is typical for the power and communication systems and reduce the cost, these systems usually adjust their operating regimes. The transition rate matrices under distinct operating regimes are assumed to be different and the sojourn times in distinct regimes are governed by a finite state Markov chain. By using the theory of Markov process, Ion channel theory, and Laplace transforms, the up time of the system are studied. A numerical example is given to illustrate the obtained results. The effect of sojourn times in distinct regimes on the availability and the up time are also discussed in the numerical example.

Availability Analysis of Parallel Repairable System with Omitted Failures

The new model for parallel repairable system is introduced, and it is based on the practice problems of maintenance and the idea of Ion-Channel modeling. In the new model, repair times that are sufficiently short （less than some critical value） do not result in system failure, and such a repair interval is omitted from the downtime record. Usually, the underlying process is Markov process if the durations of working and repair time have the negative-exponential distributions, but the new system has not the Markov properties, which is worth to study. The reliability indexes such as instantaneous availability and steady-state availabilities for the new system are given through probability analysis. A numerical example is given to illustrate the results.

A Two-Unit Cold Standby Repairable System with One Replaceable Repair Facility and Delay Repair: Some Reliability Problems

This paper considers a two–unit same cold standby repairable system with a replaceable repair facility and delay repair .The failure time of unit is assumed to follow exponential distribution , and the repair time and delay time of failed unit are assumed to follow arbitrary distributions , whereas the failure and replacement time distributions of the repair facility are exponential and arbitrary . By using the Markov renewal process theory, some primary reliability quantities of the system are obtained.

REPAIRABLE SYSTEM AVAILABILITY MODEL WITH RESPECT TO LIFE DISTRIBUTION OF SPARE PARTS

The failed components of repairable systems are replaced with spare parts that may have different failure distributions from those of the components that have failed. The spare parts may be either the same as new, better than new, or worse than new. This is the reality in maintenance engineering. Repair with better spare parts is defined as ＂super repair＂. The failure distributions of the spare parts affect the availability of the components and their systems. A novel model is proposed to describe the availability of repairable systems across their operating time, at the level of their components, on the assumption that the failed components are immediately replaced. The model functions with arbitrary failure distributions of spare parts. It can be used to compute the availability of components and systems not only under perfect and imperfect repair but also under super repair.

Existence and Uniqueness of the Dynamic Solution of a Series-Parallel Repairable System Consisting of Three-Unit with Multiple Vacations of a Repairman

We investigate a series-parallel repairable system consisting of three-unit with multiple vacations of a repairman. By using C0-semigroup theory of linear operators in the functional analysis, we prove that the system is well-posed and has a unique positive dynamic solution.

Model for Failure Point Process of a Repairable System and Application

A engineering system is usually repairable, and failure process of a repairable by a failure point process. The power law model is a commonly used approach to model syst the em is often described failure point process. This paper introduces the concept and model for the failure process of repairable system. The method of parameter estimation is developed, and failure observations are fitted into a power-law model by using the least square method. Two applications of the pressent model are discussed according to the practical failure data of the central cooling system of a nuclear power plant. One application is determining the optimal overhaul time, and the other is evaluating the quality of maintenance. This paper provides references for the overhaul decision making and maintenance quality evaluation in reality.

Reliability Analysis of Some Typical Repairable Systems with Arbitrary Repair-Time Distribution

In this paper, reliability of some typical non-Markov repairable systems, including series systems, m-out-of- n or majority vote systems, and n : m cross-strapping standby redundant systems with general repair-time distribution, are studied by applying the generalized Markov renewal process (GMRP). The stochastic behavior of the typical systems is analyzed here. Formulas for mean time to first system failure, MTBF, MTTR, and availability are then developed.

Instantaneous Reliability Index of a Typical Repairable System

A two-state system was taken as an example to show the method that we derived for analyzing the instantaneous reliability index,which was an important issue in the field of reliability.The paper first described the system as an abstract Cauchy problem by choosing suitable operators and state spaces.Then,with the TrotterKato theorem and strong continuous semi-group theorem,the method of solving the instantaneous reliability index of the repairable system was constructed.The convergence of the method was also proved in theory in this paper.To show the effectiveness of this method,some numerical examples were given at the end of the paper.

Grey Repairable System Analysis

In this paper, we systematically discuss the basic concepts of grey theory, particularly the grey differential equation and its mathematical foundation, which is essentially unknown in the reliability engineering community. Accordingly, we propose a small-sample based approach to estimate repair improvement effects by partitioning system stopping times into intrinsic functioning times and repair improvement times. An industrial data set is used for illustrative purposes in a stepwise manner.

Four Common Properties of Repairable Systems Calculated with the Boltzmann-Like Entropy

Gnedenko, the father of the modern Reliability Theory, first derived some fundamental properties of reliable systems following rigid deductive logic. This paper shares the deductive method and infers four principal properties of repairable/maintainable systems using the Boltzmann-like entropy. In particular we calculate the reparability function and next discuss the physical meanings of the formal results. Lastly we comment on the broad range of applications and researches which can relate to this study.

Asymptotic Stability of a Series-Parallel Repairable System Consisting of Three-Unit with Multiple Vacations of a Repairman

We study a series-parallel repairable system consisting of three units with multiple vacations of a repairman. We first show that all points on the imaginary axis except zero belong to the resolvent set of the operator and zero is an eigenvalue of the operator, and then we prove that the semigroup generated by the operator is irreducible. By combining these results with our previous result we deduce that the dynamic solution of the system converges strongly to its steady-state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.

Resilience-Oriented Load Restoration Method and Repair Strategies for Regional Integrated Electricity-Natural Gas System

The rising frequency of extreme disaster events seriously threatens the safe and secure operation of the regional integrated electricity-natural gas system(RIENGS).With the growing level of coupling between electric and natural gas systems,it is critical to enhance the load restoration capability of both systems.This paper proposes a coordinated optimization strategy for resilience-enhanced RIENGS load restoration and repair scheduling and transforms it into a mixed integer second-order cone programming(MISOCP)model.The proposed model considers the distribution network reconfiguration and the coordinated repair strategy between the two systems,minimizing the total system load loss cost and repair time.In addition,a bi-directional gas flow model is used to describe the natural gas system,which can provide the RIENGS with more flexibility for load restoration during natural gas system failure.Finally,the effectiveness of the proposed approach is verified by conducting case studies on the test systems RIENGS E13-G7 and RIENGS E123-G20.

Modeling Expected Failure Considering Repair Time and Degradation: A Rail System Case Study

The repeated failures of any equipment or systems are modeled as a renewal process. The management needs an assessment of the number of future failures to allocate the resources needed for fast repairs. Based on the idea of expectation by conditioning, special Volterra-type integral equations are derived for general types of repairs, considering the length of repair and reduced degradation of the idle object. In addition to minimal repair and failure replacement, partial repairs are also discussed when the repair results in reduction of the number of future failures or decreases the effective age of the object. Numerical integration-based algorithm and simulation study are performed to solve the resulting integral equation. Since the geometry degradation in different dimensions of a rail track and controlling and maintaining defects are of importance, a numerical example using the rail industry data is conducted. Expected number of failures of different failure type modes in rail track is calculated within a two-year interval. Results show that within a two-year period, anticipated occurrences of cross level failures, surface failures, and DPI failures are 2.4, 3.8, and 5.8, respectively.

Numerical Simulation to Reliability Analysis of Fault-Tolerant Repairable System

In the traditional method for the reliability analysis of fault-tolerant system,the system structure is described by means of binary decision diagram (BDD) and Markov process,and then the reliability indexes are calculated.However,as the size of system augments,the size of state space will increase exponentially.Additionally,Markov approach requires that the failure and repair time of the components obey an exponential distribution.In this study,by combining dynamic fault tree (DFT) and numerical simulation based on the minimal sequence cut set (MSCS),a new method to evaluate reliability of fault-tolerant system with repairable components is proposed.The method presented does not depend on Markov model,so that it can effectively solve the problem of the state-space combination explosion.Moreover,it is suitable for systems whose failure and repair time obey an arbitrary distribution.Therefore,our method is more flexible than the traditional method.At last,an example is given to verify the method.

Uncertain multiobjective redundancy allocation problem of repairable systems based on artificial bee colony algorithm

Based on the uncertainty theory, this paper is devoted to the redundancy allocation problem in repairable parallel-series systems with uncertain factors, where the failure rate, repair rate and other relative coefficients involved are considered as uncertain variables. The availability of the system and the corresponding designing cost are considered as two optimization objectives. A crisp multiobjective optimization formulation is presented on the basis of uncertainty theory to solve this resultant problem. For solving this problem efficiently, a new multiobjective artificial bee colony algorithm is proposed to search the Pareto efficient set, which introduces rank value and crowding distance in the greedy selection strategy, applies fast non-dominated sort procedure in the exploitation search and inserts tournament selection in the onlooker bee phase. It shows that the proposed algorithm outperforms NSGA-II greatly and can solve multiobjective redundancy allocation problem efficiently. Finally, a numerical example is provided to illustrate this approach.

Multi-Point and Multi-Interval Availabilities for Markov Repairable Systems with History-Dependent Up and Down States

A Markov repairable system with history-dependent up and down states is presented. The state space of the repairable system is divided into three sets, which are up states, down states and changeable states.Using aggregated stochastic processes, we can get the multi-interval availability and multi-point availability for the Markov repairable system. Finally, numerical examples are given to illustrate the obtained results.

Reliability Analysis of Multi-State Repairable System with Dynamic Transition Probabilities

Inadequate maintenance decisions lead to incremental overall costs. In order to minimize costs in maintenance of the multi-state repairable system, we model a preventive maintenance(PM) scheme of the multistate repairable system using non-Markov process. The periodically decreasing reliability model of the non-Markov dynamic system with dynamic transition probabilities is established to satisfy the probability change. The diesel engine system is taken as an example to illustrate the model. The reliability of the diesel engine is analyzed and its PM scheme is worked out. RENO software is used to simulate the diesel engine system. The maintenance cost of components and the optimal PM interval data of the system are obtained by using the minimal average cost as the objective function. The adaptability of PM is judged, and the optimal PM scheme is presented.

Reliability Evaluation of Two-Stage Directed Semi-Markov Repairable Network Systems

A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc. The availability of the system is discussed by using Markov renewal theory, Laplace transform and probability analysis methods. A numerical example is given to illustrate the results obtained in the paper.