Random Working Times Research Articles

Random-time component reallocation and system replacement policy with minimal repair

The maintenance policies based on random working time guarantee the continuity of system functionality. This paper studies a random-time component reallocation and system replacement (RCS) policy, in which the random-time system replacement is to replace the system at the planned preventive time or the random working time, whichever comes first, the random-time component reallocation is to balance the degradation of components by reallocating components at random working time before system replacement, and minimal repair is implemented for failed components. To improve the efficiency and flexibility of RCS policy, we first establish an optimization model to minimize the expected system maintenance cost per unit time based on a given interval for random-time component reallocation, and analytical results are derived by comparing the proposed policy with the preventive component reallocation and random-time system replacement policy, and the simple random-time system replacement policy. Next, we construct another optimization model to maximize the interval length for the random-time component reallocation constrained by the threshold of the efficiency level of RCS policy. Numerical experiments demonstrate the performance of the RCS policy and provide guidance for the interval for the random-time component reallocation.

A generalized age-dependent minimal repair with random working times

Two extended preventive replacement models for systems that execute projects at random times are discussed in this paper. The system is subject to shocks at which the system experiences one of two kinds of failures whose probabilities depend on age. A type I failure will cause a minor failure of the system and is fixed by a minimal repair. A type II failure will lead to a catastrophic failure of the system, and a corrective replacement is required at such failure. First, we investigate a preventive replacement policy where the system is replaced at the m-th type I failure, or at the time instant when the n-th working project is completed, or at age τ, or at the first type II failure, whichever occurs first. In addition, we also investigate another preventive replacement model where the system is replaced preventively at the time instant when the n-th working project is completed, or at the m-th type I failure, or at age τ, whichever occurs last, and is replaced correctively at the first type II failure. We formulate the long-run expected cost rate for each replacement policy, and determine analytically the optimum preventive replacement policy. We also show that several previous replacement models in the literature are special cases of our models. Finally, a procedure for finding the optimum preventive replacement schedule is presented and some numerical examples are given illustrating the present policies.

Preventive replacement policies for parallel systems with deviation costs between replacement and failure

In order to balance the deviation time between replacement and failure, a new notion of cost named as deviation cost is taken into account for planning replacement policies. We firstly take up a standard parallel system with n identical units and model replacement policies that are done at planned time and at periodic times. Next, we model again the above replacement policies when the number of units is a random variable that has a Poisson distribution. Thirdly, replacement policies are planned preventively at the completion of random working times. Optimum number of units is scheduled for a total working interval that is constantly and randomly given. Finally, we give reliability functions of k-out-of-n systems for extensions of parallel systems. We give analytical discussions for the above replacement policies and illustrate numerical examples when the failure time of each unit has an exponential distribution.

Periodic replacement policies with shortage and excess costs

It has been proposed that if replacement time is planned too early prior to failure, a waste of operation cost, i.e., excess costs, would incur because the system might run for an additional period of time to complete critical operations, and if replacement time is too late after failure, a great failure cost, i.e., shortage cost, is incurred due to the delay in time of the carelessly scheduled replacement. In order to make the preventive replacement policies perform in a more general way, the above two variable types of costs are taken into considerations for periodic replacement policies in this paper. We firstly take up a standard model in which the unit is replaced preventively at periodic times. Secondly, the modeling approaches of whichever occurs first and last are applied into periodic and random models, and replacement first and last policies are discussed to find optimum periodic replacement times for a random working time. Furthermore, optimum working numbers are obtained for the extended models. We give analytical discussions of the above replacement policies, and finally, numerical examples are illustrated.

Extended age maintenance models and its optimization for series and parallel systems

In this paper, extended preventive replacement models for series and parallel system with n independent non-identical components are proposed. It is assumed that the system suffers from two types of failure. One is repairable (type-I) failure, at that time the system can be rectified by minimal repair. Another is non-repairable (type-II) failure, then the whole system is replaced. In the proposed models, the system is replaced at the planned time, at random working time, or at the time when type-II failure occurs, with options whichever occurs first or whichever occurs last. The average cost rate (ACR) function and the failure rate function (FRF) of the series and parallel system under the different cases are obtained respectively. Moreover, the optimal preventive replacement time of models based on minimization of the ACR function is obtained theoretically. Numerical examples are presented to evaluate the cost of the system and verify the performance of our results.

Generalized multi-parameter preventive replacement policy for systems with random processing times

This article addresses a multi-parameter preventive replacement policy for a stochastically deteriorating system with random working times and imperfect maintenance. The system is subject to two types of failures based on a random mechanism: type-I (repairable or minor) failure rectified by a minimal repair and type-II (non-repairable or catastrophic) failure removed by a corrective replacement. The replacement policy is a multi-criterion one regarding the system age, nature of failure, and number of continuously processed jobs. Under such a policy, the system undergoes the preventive replacement (PR) at a planned life-time T or at a certain number of working times N or at the nth type-I failure and the corrective replacement (CR) at any type-II failure, whichever occurs first. The optimal preventive replacement policy minimizing the mean cost rate is analyzed and determined numerically. The proposed model provides a general framework for analyzing a variety of maintenance policies.

The generalized age maintenance policies with random working times

The purpose of this paper is to investigate the generalized age maintenance policies for a system with random working times. When the system fails, it is subject to one of two types of failures with age-dependent probability: type I failure can be removed by minimal repair and type II failure must be rectified by replacement. First, the system is preventively replaced before type II failure at time T or at the completion of Nth working projects, whichever occurs first. Two modified models, where the system is preventively replaced before type II failure at time T or at the completion of Nth working projects, whichever occurs last, and it is preventively replaced at the first completion of the working project over time T or at the completion of Nth working projects, whichever occurs first, are considered. By introducing costs due to repairs, maintenance and replacement, the expected cost per unit time is derived as a criterion of optimality and the optimal policy that minimizes that cost is discussed analytically.

A geometric process model for deteriorating operating system with periodic and random inspections

In this paper, we consider a deteriorating operating system which executes a job with random working times. It is assumed that the working times form a geometric process. In Model 1, the system is checked at periodic times and also at every completion of working times to detect the failures. In Model 2, we extend Model 1 by further assuming that a preventive repair is taken when the failure is not found by periodic inspection. For both models, the explicit expressions of the total expected cost until the detection of the failure are obtained. The optimal periodic inspection policies are computed numerically.

Optimal preventive policies for imperfect maintenance models with replacement first and last

ABSTRACTThis paper proposes preventive replacement policies for an operating system which may continuously works for N jobs with random working times and is imperfectly maintained upon failure. As a failure occurs, the system suffers one of the two types of failures based on some random mechanism: type-I (repairable or minor) failure is rectified by a minimal repair, or type-II (non repairable or catastrophic) failure is removed by a corrective replacement. A notation of preventive replacement last model is considered in which the system is replaced before any type-II failure at an operating time T or at number N of working times, whichever occurs last. Comparisons between such a preventive replacement last and the conventional replacement first are discussed in detail. For each model, the optimal schedule of preventive replacement that minimizes the mean cost rate is presented theoretically and determined numerically. Because the framework and analysis are general, the proposed models extend several existing results.

OPTIMAL RANDOM BACKUP POLICIES FOR A DATABASE SYSTEM

Some systems work for a job with random working and processing times, and are checked at periodic and random times. When a failure occurs, we execute the backup operation to the latest checking time. First, the expected costs with periodic and random backups are formulated, and comparisons between periodic and random policies are made. Next, we focus on the backup policies when the system is checked at the Nth interval of working times, two total expected costs are obtained and optimal numbers N* which minimize them are derived analytically. Finally, one modified backup model in which failures are detected only at checking times is proposed and two expected costs are obtained.

AGE AND PERIODIC REPLACEMENT MODELS WITH OVERTIME POLICIES

This paper proposes two modified replacement policies which combine random replacement with standard age and periodic policies, where units undergo replacement at the first completion of some random working time over a planned time T, which are called replacement overtime. The expected cost rates of age and periodic replacement overtime polices are obtained, and optimal policies which minimize them are discussed analytically. Comparisons between such two overtime policies and standard age and periodic replacements are made in detail. When two costs for replacement overtime and standard age or periodic policies are the same, it is shown as estimated previously that the standard replacements are better than their overtime policies. Furthermore, two modified replacement overtime costs are discussed and computed numerically when such new policies would be better than the standard age and periodic replacements.

Optimum preventive maintenance policies for systems subject to random working times, replacement, and minimal repair

This paper proposes, from the economical viewpoint of preventive maintenance in reliability theory, several preventive maintenance policies for an operating system that works for jobs at random times and is imperfectly maintained upon failure. As a failure occurs, the system suffers one of two types of failure based on a specific random mechanism: type-I (repairable) failure is rectified by a minimal repair, and type-II (non-repairable) failure is removed by a corrective replacement. First, a modified random and age replacement policy is considered in which the system is replaced at a planned time T, at a random working time, or at the first type-II failure, whichever occurs first. Next, as one extended model, the system may work continuously for N jobs with random working times. Finally, as another extended model, we might consider replacing an operating system at the first working time completion over a planned time T. For each policy, the optimal schedule of preventive replacement that minimizes the mean cost rate is presented analytically and discussed numerically. Because the framework and analysis are general, the proposed models extend several existing results.

Optimal maintenance policies for cumulative damage models with random working times

PurposeThe purpose of this paper is to consider maintenance policies for an operating system which works at random times for jobs. Each job causes some damage to the system and these damages are additive, and the system fails when the total damage has exceeded a failure level K.Design/methodology/approachUsing techniques of cumulative damage models, the maintenance is made at the N‐th completion of working time for the first model and at a damage level Z with a limit number of working times N for the second model.FindingsThe system is maintained at the first completion of the working time over time T for the third model. The system fails with probability p(x) when the total damage is x and undergoes minimal repair at failure for the fourth model. The expected cost rates are obtained and optimal maintenance policies are discussed analytically and computed numerically.Originality/valueThe paper discusses four maintenance policies for an operating system which works at successive random times for jobs, where the system fails due to damage that can be additive caused by jobs.

Optimal redundant systems for works with random processing time

This paper studies the optimal redundant policies for a manufacturing system processing jobs with random working times. The redundant units of the parallel systems and standby systems are subject to stochastic failures during the continuous production process. First, a job consisting of only one work is considered for both redundant systems and the expected cost functions are obtained. Next, each redundant system with a random number of units is assumed for a single work. The expected cost functions and the optimal expected numbers of units are derived for redundant systems. Subsequently, the production processes of N tandem works are introduced for parallel and standby systems, and the expected cost functions are also summarized. Finally, the number of works is estimated by a Poisson distribution for the parallel and standby systems. Numerical examples are given to demonstrate the optimization problems of redundant systems.

Reliability-based design optimization for box-booms considering strength degradation and random total working time

Box-booms are widely used in some cranes. The strength of box-booms would continuously deteriorate with the use of time. In this paper, gamma process is employed to describe strength degradation when dealing with the overall stability of the box-boom. Furthermore, the total working time is not deterministic but random because of the random arrivals of tasks and the random working time of every task. By accounting for strength degradation and the random total working time, a time-dependent reliability-based design optimization (RBDO) model for the box-boom is proposed. An engineering case is used to illustrate the proposed model.

Optimization Problems of a Parallel System With a Random Number of Units

This paper considers a parallel system with a random number of units according to a Poisson distribution. The fracture of an aircraft fuselage with multiple site damage serves as a real world application for this problem. The mean time to failure is obtained. Using this result, an optimal number of units and replacement time for the system which minimize the expected cost rates are derived analytically, and numerically, when the failure time has a Weibull distribution. It is of interest that these results also give good approximations to those of the system with a constant number of units. Further, similar discussions for a scheduling problem of a job with random working times are made, when a parallel system is provided.

Optimal random replacement models with continuously processing jobs

AbstractIn some practical situations, it would be impossible to conduct a replacement action for an operating system during the middle of a job and might be wise to wait until the completion of its operation. First, this paper considers age replacement policies for a system, which continuously works for multiple jobs with random working times. Next, the system can undergo minimal repairs upon failures and is replaced at the first completion of the working time over a planned time T. Finally, when a job incurs some damage to the system, the replacement model over time T is applied. The expected cost rates for these modified models are derived, and the optimal maintenance policies, which minimize the expected cost rates are obtained analytically. Copyright © 2012 John Wiley & Sons, Ltd.

Numerical Model of Wave Flume

Based on the finite volume method, the Navier-Stokes equations was used as the governing equations to develop a new module of the wave generating and absorbing function. The wave generating was introduced as the man-made source terms into the momentum equations, which was suitable for the volume of fluid method (VOF). Within the numerical wave flume, the reflected waves from the construction could be absorbed effectively. The absorbing section arranged at the end of the wave flume was for absorbing the incident wave, which allows for random and effective working time within the reletively smaller computation domain. Consequently, the computation efficiency was greatly improved. Finally, the validity of the absorbing section arranged at the front and end of the wave flume was investigated individually.

A summary of periodic and random inspection policies

Some systems work for a job with random working times. It would be useful for such systems that they are checked at the completion of working times to detect their failures, which is called a random inspection policy. Two inspection policies, where a system is checked at periodic or successive times and also at every completion of working times, are considered. The total expected costs until the detection of failure are obtained, and when the random working time is exponential, optimal inspection policies which minimize them are derived analytically. Furthermore, the inspection policy where the system is checked only at every completion of N th working time is proposed. Finally, as one of modified random inspection models, the backup model where the system goes back to the latest checking time when it has failed is taken up and analyzed, by using the inspection policy.

OPTIMAL BACKWARD AND BACKUP POLICIES IN RELIABILITY THEORY

We are sometimes faced with the problem of searching for the actual failure time of a unit when it has failed until time t0. This is called a backward time problem of how much time we go back to search for the failure time from time t0, and is solved by using the reversed failure rate. This paper proposes an extended model of multiple backward trials in which we find the actual failure time from time t0. Another problem is that when an operating unit fails, we have to go back to the newest checking time and reconstruct it as recovery techniques, which is called a backup policy. This paper takes up three backup policies where the unit is checked at periodic, successive and random working times, and discusses analytically their optimal policies. Finally, it would be important to keep a record of operational behavior of a unit when its failure is detected, which is called traceability. This paper compares two models with traceability and without traceability, and proposes three traceability models where the unit operates for a finite interval, and is checked at periodic and successive times. Optimal policies for each model are discussed by using backup techniques.