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.

ANALYSIS ON A TYPE OF SERVICING MACHINES MODEL WITH REPAIRABLE SERVICE STATION

This paper deals with a type of servicing machines model, which service station has a life time of the kth Er-langian distribution and can be repaired just like a new one. The cyclic time and the inefficiency quantities of this system in equilibrium are obtained.

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.

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.

Availability Equivalence Factors of a General Repairable Parallel-Series System

The availability equivalence factors of a general repairable parallel-series system are discussed in this paper considering the availability function of the system. The system components are assumed to be repairable and independent but not identical. The life and repair times of the system components are exponentially distributed with different parameters. Two types of availability equivalent factors of the system are derived. The results derived in this paper generalize those given in the literature. A numerical example is introduced to illustrate how the idea of this work can be applied.

A REPLACEMENT MODEL FOR QUEUEING SYSTEM WITH REPAIRABLE ELECTRICAL EQUIPMENT OF AUTOMATIC STEEL ROLLING

The optimal replacement model for the repairable queueing system con-sisting of single electrical equipment of automatic steel rolling is studied. Assumingthat the equipment after repair is not “as goed as new” , by using geometric pro-cess, we take the n

RELIABILITY ANALYSIS FOR A REPAIRABLE PARALLEL SYSTEM WITH TIME-VARYING FAILURE RATES

To solve a real problem:how to calculate the reliability of a system with time-varying failure rates in industry systems,this paper studies a model for the load-sharing parallel system with time-varying failure rates,and obtains calculating formulas of reliability and availability of the system by solving differential equations.In this paper,the failure rates are expressed in polynomial configuration.The constant,linear and Weibull failure rate are in their special form.The polynomial failure rates provide flexibility in modeling the practical time-varying failure rates.

Reliability Analysis of Repairable Systems Using Stochastic Point Processes

In order to analyze the failure data from repairable systems, the homogeneous Poisson process (HPP) is usually used. In general, HPP cannot be applied to analyze the entire life cycle of a complex, re-pairable system because the rate of occurrence of failures (ROCOF) of the system changes over time rather than remains stable. However, from a practical point of view, it is always preferred to apply the simplest method to address problems and to obtain useful practical results. Therefore, we attempted to use the HPP model to analyze the failure data from real repairable systems. A graphic method and the Laplace test were also used in the analysis. Results of numerical applications show that the HPP model may be a useful tool for the entire life cycle of repairable systems.

The Linear Stability of a Solution of a Parallel Redundant Repairable System

In this paper,the solution of a parallel redundant repairable system is investigated.by using the method of functional analysis.Especially,the linear semigroups of operator theory on Banach space,we prove the existence of the strictly dominant eigenvalue,and show the linear stability of solution.

Warranty Cost Model Based on Optimal Preventive Maintenance Operations for Repairable Products

Most warranty cost models based on preventive maintenance operations are assumed that products improve at each preventive maintenance （PM） operation and the failure rate is reduced to the failure rate of new products or to some specified level. To make warranty cost models more suitable to real operations, a modeling method of the PM warranty cost was proposed with the situation where each PM operation slowed the rate of product degradation. A warranty cost model was built on PM operations. On the basis of the cost model, both without and with reliability limit PM warranty policy, algorithms were presented to derive the optimal PM number and the optimal PM interval with an objective of minimizing expected total warranty cost over a t＇mite warranty period. Finally, to demonstrate the feasibility of the presented modeling method, Weibuil distribution cases were tested by numerical simulations. The simulation results indicate that the proposed modeling method is feasible and valid for resolving the optimal solution of the product warranty cost.

Repairable Configuration Optimization Model under Two-Echelon Inventory

Spares inventory configuration optimization is an effective way to improve readiness and reduce life cycle cost of equipment.Through analyzing two-echelon spares support system,the METRIC model basic theory was used.An inventory configuration optimization model of two-echelon spares support system was proposed which took the spares expected shortfall as the object and made the minimum repairable parts expected shortfall instead of the maximum spares supportability as the objective function.Marginal efficiency analysis algorithm was applied to optimizing the spares configuration and generating a rational spares inventory configuration.Finally,several examples are given to verify the model.

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.

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.

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.

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.

Nonlinear Mixed-Effects Models for Repairable Systems Reliability

Mixed-effects models,also called random-effects models,are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject,but also to describe the variation among different subjects.Nonlinear mixed-effects models provide a powerful and flexible tool for handling the unbalanced count data.In this paper,nonlinear mixed-effects models are used to analyze the failure data from a repairable system with multiple copies.By using this type of models,statistical inferences about the population and all copies can be made when accounting for copy-to-copy variance.Results of fitting nonlinear mixed-effects models to nine failure-data sets show that the nonlinear mixed-effects models provide a useful tool for analyzing the failure data from multi-copy repairable systems.

Operator Semi-group of Density Evolution Equation for a Repairable Redundant System with Two Same Components

For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.

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.