THE OPTIMAL REPLACEMENT FOR ADDITIVE DAMAGE MODELS IN DISCRETE SETTING

A system receives shocks at successive random points of discrete time, and each shock causes a positive integer-valued random amount of damage which accumulates on the system one after another. The system is subject to failure and it fails once the total cumulative damage level first exceeds a fixed threshold. Upon failure the system must be replaced by a new and identical one and a cost is incurred. If the system is replaced before failure, a lower cost is incurred.On the basis of some assumptions, we specify a replacement rule which minimizes the longrun (expected) average cost per unit time and possesses the control limit property, Finally, an algorithm is discussed in a special case.

System Reduction Using an LQR-Inspired Version of Optimal Replacement Variables

Optimal ReplacementVariables(ORV)is amethod for approximating a large system of ODEs by one with fewer equations,while attempting to preserve the essential dynamics of a reduced set of variables of interest.An earlier version of ORV[1]had some issues,including limited accuracy and in some rare cases,instability.Here we present a newversion of ORV,inspired by the linear quadratic regulator problemof control theory,which provides better accuracy,a guarantee of stability and is in some ways easier to use.

Reduction of Linear Systems of ODEs with Optimal Replacement Variables

In this exploratory study,we present a new method of approximating a large system of ODEs by one with fewer equations,while attempting to preserve the essential dynamics of a reduced set of variables of interest.The method has the following key elements:(i)put a(simple,ad-hoc)probability distribution on the phase space of the ODE;(ii)assert that a small set of replacement variables are to be unknown linear combinations of the not-of-interest variables,and let the variables of the reduced system consist of the variables-of-interest together with the replacement variables;(iii)find the linear combinations that minimize the difference between the dynamics of the original system and the reduced system.We describe this approach in detail for linear systems of ODEs.Numerical techniques and issues for carrying out the required minimization are presented.Examples of systems of linear ODEs and variable-coefficient linear PDEs are used to demonstrate the method.We show that the resulting approximate reduced system of ODEs gives good approximations to the original system.Finally,some directions for further work are outlined.

Optimal periodic replacement policy for a warranted product subject to multi modes failure process

A complex product subjects to multiple failure modes such as minor and catastrophic failure with some probability.This paper investigates the effects of minor failure and catastrophic failure on the periodic replacement policy for a complex product supported by a warranty period.Cost models are developed and the expected optimal replacement policies are developed analytically such that long run expected life-cycle cost rate is minimized.Structural properties of the optimal replacement policies are derived for a product which fails with multiple failure modes and the failure rate is an increasing function of time.Finally,a numerical experiment is performed to show the important features of our study.

A Dynamic Memory Allocation Optimization Mechanism Based on Spark

Spark is a distributed data processing framework based on memory.Memory allocation is a focus question of Spark research.A good memory allocation scheme can effectively improve the efficiency of task execution and memory resource utilization of the Spark.Aiming at the memory allocation problem in the Spark2.x version,this paper optimizes the memory allocation strategy by analyzing the Spark memory model,the existing cache replacement algorithms and the memory allocation methods,which is on the basis of minimizing the storage area and allocating the execution area according to the demand.It mainly including two parts:cache replacement optimization and memory allocation optimization.Firstly,in the storage area,the cache replacement algorithm is optimized according to the characteristics of RDD Partition,which is combined with PCA dimension.In this section,the four features of RDD Partition are selected.When the RDD cache is replaced,only two most important features are selected by PCA dimension reduction method each time,thereby ensuring the generalization of the cache replacement strategy.Secondly,the memory allocation strategy of the execution area is optimized according to the memory requirement of Task and the memory space of storage area.In this paper,a series of experiments in Spark on Yarn mode are carried out to verify the effectiveness of the optimization algorithm and improve the cluster performance.

OPTIMAL GEOMETRIC PROCESS REPLACEMENT MODEL

In this paper, we study the geometric process replacement model as follows:the successivesurvival times of the system form a nonincreasing geometric process while the consecutive repairtimes of the system constitute a non-decreasing geometric process, and the system is replacedat the time of the Nth failure after its installation or last replacement. Based on the long-runaverage cost per unit time, we determine the optimal replacement policy N,show the uniquenessof the policy N and discuss its monotonicity.

Reliability analysis for a cold standby system under stepwise Poisson shocks

In this paper,a two-dissimilar-component cold standby repairable system maintained by a repairmanis 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 N∗is derived by minimising the average cost rate of the system.Numerical examples are presented to validate the theoretical results.