Cunhua Qian

Optimal imperfect preventive maintenance policies for a used system

In some practical situations, it may be more economical to work a used system than do a new one. From this viewpoint, this article considers three basic preventive maintenance (PM) policies for a used system: the system with initial variable damage Y 0 begins to operate at time 0, and suffers damage due to shocks. It fails when the total damage exceeds a failure level K and corrective maintenance is made immediately. To prevent such failure, it undergoes PM at a planned time T, a shock number N and a damage level k, but maintenances are imperfect. However, failure rate of a used system maybe higher than that of a new one, so some maintenance is applied to the policies at each shock in the extended models. Using the theory of cumulative processes, expected cost rate models are obtained, optimal policies which minimise them are derived analytically and discussed numerically.

Optimal policies for cumulative damage models with maintenance last and first

From the economical viewpoint of several combined PM policies in reliability theory, this paper takes up a standard cumulative damage model in which the notion of maintenance last is applied, i.e., the unit undergoes preventive maintenances before failure at a planned time T, at a damage level Z, or at a shock number N, whichever occurs last. Expected cost rates are detailedly formulated, and optimal problems of two alternative policies which combine time-based with condition-based preventive maintenances are discussed, i.e., optimal TLâ Ž for N, ZLâ Ž for T, and NLâ Ž for T are rigorously obtained. Comparison methods between such maintenance last and conventional maintenance first are explored. It is determined theoretically and numerically which policy should be adopted, according to the different methods in different cases when the time-based or the condition-based PM policy is optimized.

OPTIMAL POLICIES FOR A DATABASE SYSTEM WITH TWO BACKUP SCHEMES

Abstract. This paper considers two backup schemes for a databasesystem: a database is updated at a nonhomogeneous Poisson processand an amount of updated les accumulates additively. To ensure thesafety of data, full backups are performed at time NT or when thetotal updated les have exceeded a threshold level K , and betweenthem, cumulative backups as one of incremental backups are made atperiodic times iT ( i =1 ; 2 ; ;N− 1). Using the theory of cumulativeprocesses, the expected cost is obtained, and an optimal number N of cumulative backup and an optimal level K of updated les whichminimize it are analytically discussed. It is shown as examples thatoptimal number and level are numerically computed when two costs ofbackup schemes are given. Keywords. Database, full backup, cumulative backup, cumulativeprocess, expected cost. 1. Introduction A database in a computer system is frequently updated by adding or deletingdata les, andisstoredinfloppydisksorothersecondarymedia. Evenhighreliablecomputers might sometimes break down eventually by severalerrorsdue to noises,human errors and hardware faults. It would be possible to replace hardware and

Optimal Backup Interval for a Database System with Full and Periodic Incremental Backup

This paper considers the following backup scheme for a database system: a database is updated at a nonhomogeneous Poisson process and an amount of updated files accumulates additively. To ensure the safety of data, full backup are performed at time NT=L or when the database fails, whichever occurs first, and between them, incremental backups are made at periodic times iT (i=1, 2, … , N-1) so as to make the backup efficiently. Using the theory of cumulative processes, the expected cost is obtained, and optimal number s N* of incremental backup which minimizes it are analytically discussed when incremental backup interval T or full backup interval L is given. Finally, it is shown as example s that optimal numbers are numerically computed.

Periodic and Random Inspection Policies for Computer Systems

Faults in computer systems sometimes occur intermittently. This paper applies a standard inspection policy with imperfect inspection to a computer system: The system is checked at periodic times and its failure is detected at the next checking time with a certain probability. The expected cost until failure detection is obtained, and when the failure time is exponential, an optimal inspection time to minimize it is derived. Next, when the system executes computer processes, it is checked at random processing times and its failure is detected at the next checking time with a certain probability. The expected cost until failure detection is obtained, and when random processing times are exponential, an optimal inspection time to minimize it is derived. Finally, this paper compares optimal times for two inspection policies and shows that if the random inspection cost is the half of the periodic one, then two expected costs are almost the same.

Comparisons of replacement policies with periodic times and repair numbers

Periodic replacement policies modeled with the history of minimal repairs have been studied extensively. However, in the viewpoint of cost rate, there is no literature to compare replacement polices which are carried out at some periodic times and at a predetermined number of repairs. In this paper, we compare these two types of replacement policies analytically from the optimizations of the integrated models. It will be shown that there always exists a degradation model when any bivariate replacement policy is optimized and this is just the best choice of the comparisons. Not only that, the approaches of whichever occurs first and last are applied to model the above two types of policies, which are named as replacement first and replacement last, respectively, and their comparisons are also made. In addition, we delay the policy at repair to periodic time for easier replacement, and the modified replacement model, which is named as replacement overtime, is compared with the original ones. Numerical examples are also given and agree with all analytical discussions.

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.

Generational Garbage Collection Policies

In the computer science community, the technique of garbage collection [5] is an automatic process of memory recycling, which refers to those objects in the memory no longer referenced by programs are called garbage and should be thrown away. A garbage collector determines which objects are garbage and makes the heap space occupied by such garbage available again for the subsequent new objects. Garbage collection plays an important role in Java’s security strategy, however, it adds a large overhead that can deteriorate the program performances. From related studies which are summarized in [5], a garbage collector spends between 25 and 40 percent of execution time of programs for its work in general, and delays caused by such garbage collection are obtrusive.

A Maintenance Policy for a Parallel System With Cascading Failure

This article considers an extended parallel system with cascading failure: Compared with the conventional parallel system with independent failure, the factor that cascading failure could reduce the reliability of the system due to redistribution of the workload. Reliability measures of the system are derived, using the theory of stochastic processes. To counteract the impact of cascading failure, a preventive maintenance policy is proposed. Further, this is applied to a dual active system. An optimal maintenance policy which minimizes the expected cost rate is derived. Finally, a numerical example is given and some discussions are made.

Comparison of Two Information Structures with Noise and Its Application to Bayes Decision Analysis

Abstract In order to raise the efficiency of Bayesian decision analysis, the comparison analysis of added information structure with noise are considered by using the correlation coefficient between two information structures. The entropy measures the indefiniteness of information system in information theory. Using the conditional entropy, we define the decrease of object’s uncertainty, and measure the volume of information content in the added information structures. An expression about correlation coefficient between two information structures is derived by considering the standardization of information content. Numerical illustrations are also presented. Such an analysis demonstrates that the correlation coefficient can be used to compare and appraise information structures with noise.