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In computer science community, garbage collection is a dynamic storage management technology to ensure the reliability of computer systems. In this paper, we consider two discrete garbage collection policies to meet the goal of time consumption for a generational garbage collector. That is, garbage collections occur at a nonhomogeneous Poisson process, (a) tenuring collection is triggered at the Nth minor collection preventively or at a threshold amount [Formula: see text] of surviving objects correctively, whichever takes place first, and (b), tenuring collection is triggered at the first collection when the amount of surviving objects has exceeded a threshold level [Formula: see text] and major collection is triggered at discrete times kT for a given T. Using the damage process and renewal theory, the expected cost rates are obtained, and their optimal policies for tenuring and major collections are discussed analytically and computed numerically.

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.

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.

When we consider the improvement of the functional performances that are released by the new updates of the products, it is an interesting problem to revisit the existing replacement polici...

It is always difficult to discuss the analytical formulas, in which optimum solutions of replacement policies satisfy, due to the mathematical complexity. This paper proposes several approximate ca...

Deep learning has made remarkable achievements in various domains. Active learning, which aims to reduce the budget for training a machine-learning model, is especially useful for the Deep learning tasks with the demand of a large number of labeled samples. Unfortunately, our empirical study finds that many of the active learning heuristics are not effective when applied to Deep learning models in batch settings. To tackle these limitations, we propose a density weighted diversity based query strategy (DWDS), which makes use of the geometry of the samples. Within a limited labeling budget, DWDS enhances model performance by querying labels for the new training samples with the maximum informativeness and representativeness. Furthermore, we propose a beam-search based method to obtain a good approximation to the optimum of such samples. Our experiments show that DWDS outperforms existing algorithms in Deep learning tasks.

Highlights • Random arrival times of mission durations are considered for replacement policies. • Random arrival times of mission durations are considered for minimal repairs. • Replacement first policies with mission durations are modeled. • Replacement last policies with mission durations are modeled. • Case illustrations are given via comparing of maintenance first and last policies., When a mission arrives at a random time and lasts for a duration, it becomes an interesting problem to plan replacement policies according to the health condition and repair history of the operating unit, as the reliability is required at mission time and no replacement can be done preventively during the mission duration. From this viewpoint, this paper proposes that effective replacement policies should be collaborative ones gathering data from time of operations, mission durations, minimal repairs and maintenance triggering approaches. We firstly discuss replacement policies with time of operations and random arrival times of mission durations, model the policies and find optimum replacement times and mission durations to minimize the expected replacement cost rates analytically. Secondly, replacement policies with minimal repairs and mission durations are discussed in a similar analytical way. Furthermore, the maintenance triggering approaches, i.e., replacement first and last, are also considered into respective replacement policies. Numerical examples are illustrated when the arrival time of the mission has a gamma distribution and the failure time of the unit has a Weibull distribution. In addition, simple case illustrations of maintaining the production system in glass factories are given based on the assumed data.

Periodic replacement models with minimal repairs have been studied extensively. In order to prevent high repair costs after failures, this paper considers the number of failures as another decision variable for replacement policies. We begin with the standard periodic replacement model, and then summarize several extended replacement models with number of failures, using the respective assumptions of whichever occurs first and last, and replacing over planned measure, respectively. Optimum policies of replacement times T, number of periodic times N, and number of failures K are discussed analytically. From the optimization of the integrated models of T, N and K, comparisons among these policies are made in analytical ways to determine which policy should be more economical.

This paper tries to trace our research history briefly from Barlow and Proschan to attain general replacement models. We begin with a random age replacement policy that is planned at a random time Y and call it as random replacement. When the distribution of Y becomes a degenerate distribution placing unit mass at T, age replacement is formulated. We obtain the general formulas for optimum replacement times. We next suppose the unit works for a job with random works, and replacement policies with N cycles are discussed. As follows, we combine age and random replacement models and discuss replacement first, replacement last, replacement overtime, replacement overtime first and replacement overtime last. By formulating the distributions of replacement times with n variables, general replacement models with n replacement times are obtained.

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. 1 2017 Elsevier Ltd This paper was made possible by Qatar National Research Fund (No. PDRA1- 0116-14107 ) and National Natural Science Foundation of China (No. 71371097 ). Scopus

It would be of interest to formulate the general replacement models, combing the constant and random policies to satisfy the commonly planned and randomly needed replacement times. This paper takes up age and periodic replacement models again to formulate their general models when replacement actions are also conducted at random times $$Y_i~(i=1,2,\ldots ,n)$$ . The classic approach of whichever occurs first and the newly proposed approach of whichever occurs last are used for such general models, whose models are named as replacement first, modified replacement first, replacement last and modified replacement last, respectively. We compare all of the replacement models analytically and numerically to find which policy should be selected from the viewpoint of cost. It is shown that the modified replacement policies with combined approaches of whichever occurs first and last are more economical than others. In addition, the replacement models with different replacement costs are extended for further studies.

Compared with the oil hydraulic systems, cavitation is more serious in water hydraulic systems due to the higher saturated vapor pressure of water. Poppet valve is one of important hydraulic components and cavitation is easy to happen due to the sharp pressure drop caused by throttling. This paper presents a numerical investigation into the flow force and cavitation characteristics inside water hydraulic poppet valves. Three kinds of typical structures of poppet valves are selected in the research. The effects of geometric parameters and backpressure of the poppet valves on flow characteristics, cavitation and flow force have been analyzed. Considering the axisymmetric structure of the valves, a half of 2D mixture model is selected and a two-phase mixture model is adopted in the calculation. The accuracy of the numerical models has been validated by comparing the simulation results with the experiment data. The results reveal that two-stage throttle valve (TS valve) can effectively suppress the occurrence of cavitation while the flow force of TS valve is much bigger than that of other valves. By comparing the simulation results under two different boundary conditions (including with backpressure and without backpressure), it seems that cavitation could slightly decrease the flow force.

Age replacement models are fundamental to maintenance theory. This paper summarizes our new perspectives and hods in age replacement models: First, we optimize the expected cost rate for a required availability level and vice versa. Second, an asymptotic model with simple calculation is proposed by using the cumulative hazard function skillfully. Third, we challenge the established theory such that preventive replacement should be non-random and only corrective replacement should be made for the unit with exponential failure. Fourth, three replacement policies with random working cycles are discussed, which are called overtime replacement, replacement first, and replacement last, respectively. Fifth, the policies of replacement first and last are formulated with general models. Sixth, age replacement is modified for the situation when the economical life cycle of the unit is a random variable with probability distribution. Finally, models of a parallel system with constant and random number of units are taken into considerations. The models of expected cost rates are obtained and optimal replacement times to minimize them are discussed analytically and computed numerically. Further studies and potential applications are also indicated at the end of discussions of the above models.

This paper takes up the reliability and preventive replacement problems for a K-out-of-n system, where K is a stochastic parameter provided. Firstly, we consider the case when K is predefined as constant numbers as is done with the traditional method, and obtain the system reliability R(t), mean time to failure (MTTF), and replacement policies, in which the number n of units for replacement and replacement time T of operation are, respectively, optimized. Secondly, we focus on the above discussions again when K cannot be predefined constantly, but it is a random variable with an estimated probability function. Furthermore, we give approximate computations in an easier way for MTTF, optimal number n and replacement time T, respectively. This paper was made possible by a Postdoctoral Research Award PDRA1-0116-14107 from the Qatar National Research Fund (a member of The Qatar Foundation). Scopus

It has been modeled for several replacement policies in literatures that the whole life cycle or operating interval of an operating unit should be finite rather than infinite as is done with the traditional method. However, it is more natural to consider the case in which the finite life cycle is a fluctuated parameter that could be used to estimate replacement times, which will be taken up in this article. For this, we first formulate a general model in which the unit is replaced at random age U, random time Y for the first working number, random life cycle S, or at failure X, whichever occurs first. The following models included in the general model, such that replacement done at age T when variable U is a degenerate distribution, and replacement done at working numbers N summed by number N of variable Y, are optimized. We obtain the total expected cost until replacement and the expected replacement cost rate for each model. Optimal age T, working number N, and a pair of (T, N) are discussed analytically and computed numerically. 1 2017 Taylor & Francis Group, LLC. Scopus

Open-circle sea water hydraulics, utilizing surrounding water as a working medium, has become more and more popular in submersible. Axial piston pump with port valves is used frequently in the open-circle water hydraulic system. Port valve is one of the important parts in this type pump. However, there are few literatures about the effect of the port valves’ materials on the noise characteristic of the water pump. In this study, the effect of materials on the noise of the pump was researched through experimental and theory simulation methods. The influences of three kinds of plastics (Polyetheretherketone (PEEK), Polytetrafluoroethylene (PTFE), Aliphatic polyamides (NYLON)) and one kind of anti-corrosion stainless steel (316 L) are compared. The noise of the pump with the different materials port valve seat ranges from high to low as the order: 316 L>NYLON>PEEK>PTFE. The differences would contribute to the collision between valve spool and seat, which is identified by the simulating results. The experimental results showed that the difference of noise between PEEK and PTFE is small. In addition, the lifespan and volumetric efficiency are also taken into considering. The PEEK is selected to use in the seawater pump for a large submersible.

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.

To improve the safety of the launch and recovery of the deep-sea remotely operated vehicle (ROV) under harsh sea states, the passive heave compensator is usually equipped. Through dynamic modeling and performance analysis of the compensation system, it can provide theoretical reference for the design and operation of the system. Firstly, the geometrically exact beam element was used to obtain the two-dimensional nonlinear finite element model of umbilical cable, and the continuous dynamics model of the compensator was built and discretized to one finite element, and then inserted as the first element of the whole model. The Newmark method was used to solve the total finite element model numerically. Finally, the performance of the passive heave compensation system under different effects such as the ship heave period, the stroke of the compensator, the working depth of ROV and the sea current speed were analyzed. The results show that the condition of smaller ship heave period, the longer stroke of heave compensator, under the critical depth and the less sea current speed will produce the better performance of passive heave compensation, and the performance for cable tension is better than that for cage heave motion.

Water hydraulic variable ballast system (WHVBS) is a competitive mechanism to realize the hovering system which is one of the most popular ways to expand the maneuvering capability of AUVs. However, the WHVBSs equipped in AUVs almost were on–off type without controlling the flow rate of the in/out ballast water, which limits the hovering performance of the AUVs operated in complex underwater environment. In this paper, three novel types of WHVBS, which supports one or two low cost means to control the flow rate of ballast water, have been proposed to improve the performance of an AUV hovering system. A torpedo-like AUV equipped with WHVBS was used as a simulation platform to verify the effectiveness of the proposed WHVBSs. Numerical simulation results support the idea that compared with the commonly used on–off type WHVBS, the WHVBSs introduced flow rate control can significantly improve the hovering performance of the AUV, especially in the situations with unfavorable sea wave disturbances. Additionally, the statistics on water usage of different WHVBSs in numerical simulation indicated that the novel WHVBSs have the potential to extend the mission duration of AUV.

Natural waters are becoming more and more popular working or lubricating medium used in hydraulic system instead of the traditional oil in some underwater apparatus due to its environmental friendliness. A novel tribopair consisting of WC-10Co-4Cr coating and Si 3 N 4 have been exhibited excellent tribological properties under silt-laden natural waters and showed potential application in open-circuit type water hydraulic system. Before applying this tribopair in more water lubrication apparatus, there is necessary to study the synergistic effects of corrosion and abrasion of the cemented carbide coating under natural silt-laden waters. In this study, friction behaviours, abrasion, corrosion and its synergistic effects in the material loss were researched under lubrication in natural sea and river water. The results exhibit that the tribopair owns excellent friction and wear resistance behaviours under the natural silt-laden waters no matter in free corrosion or electrochemical protection. Although the abrasion increased by corrosion no matter for the coating or Si 3 N 4 , the abrasion is the main failure mechanism and the proportion of corrosion descends with sliding velocity and applied load.

The tribopairs of water hydraulic plunger pumps are usually operated under severe conditions, due to the poor lubrication of water and silt suspended in natural water. It is essential to identify the desired engineering materials and material combinations for designing water pumps. As the candidate materials of tribopairs, the tribological characteristics of different Al2O3-TiO2 coatings combined with Si3N4 ceramics under silt-laden water and tap water lubrication were investigated. The Al2O3-TiO2 coatings with different weight percentages of TiO2 in a wide range from 3 to 100% were tested. The tribological characteristics of the various couple pairs were researched using a ring-on-ring test rig. The microstructures of the contact surfaces were analyzed with a scanning electron microscope before and after the test to study the wear mechanism. The experimental results indicate that the friction coefficient of the Al2O3-TiO2/Si3N4 tribopairs increases with an increase in the percentage of TiO2 conte...

To make effective use of a running system, this paper proposes that, when replacement times could be scheduled at a planned time $T$ of operation, and at a number $N$ of minimal repairs, the newly proposed approach of whichever occurs last should be employed into optimizations for policy consideration. The replacement policy with the classical approach of whichever occurs first is also used to make comparison with the approach of whichever occurs last. Further, using the overtime technique, a replacement scheduled at time $T$ in this paper is modified to be done at the first failure after $T$ has arrived, to avoid probable interruptions for running jobs. That is, the system is replaced at failure $N$ before time $T$ , or at the first failure after $T$ has arrived, whichever occurs first, and last, respectively. The policies acting on the approaches of first and last with minimal repairs are analyzed in detail, and their expected cost rates are formulated. Optimal solutions for separate and bivariate $T$ and $N$ are obtained and compared analytically.

Natural water is widely used as working or lubricating medium instead of the traditional oil. Hard materials have potential application to solve the abrasive wear caused by the silt suspending in natural water and poor lubrication of water. As the candidate materials can worked in water, the tribological characteristics of the tribological properties of high velocity oxy-fuel (HVOF) spraying WC–10Co–4Cr coating combined with sintered Si 3 N 4 were investigated under different natural water lubrication, including natural silt-laden and filtered water from sea and river. In addition, distilled water was used as typical water lubricants to study the effect on the tribological behaviours. The tribological results of the tribopair exhibit excellent friction and wear resistance behaviours under the natural waters. The average steady-state friction coefficients of the tribopair under natural water are below 0.009, whilst the average wear rates under all natural waters are below 9 × 10 − 12 cm 3 /(N·m) for both materials. The results indicate that the WC–10Co–4Cr/Si 3 N 4 tribopair owns wider applicability to different natural waters. The water hydraulic components with this tribopair can work in different water areas in word, even unfiltered natural waters as pressure medium.

This paper discusses preventive replacement policies for an independent damage process, in which successive shocks occur at random times, and the independent damages caused by shocks are random variables. It is assumed that a unit fails when the damage has exceeded a prespecified level [Formula: see text]. We consider three models: Model 1: the unit is replaced at the [Formula: see text]th shock for damage [Formula: see text], at damage [Formula: see text], or at time [Formula: see text], whichever occurs first. Model 2: the unit is replaced at the [Formula: see text]th shock for damage [Formula: see text], at damage [Formula: see text] or at shock [Formula: see text], whichever occurs first. Model 3: the unit is replaced at the [Formula: see text]th shock for damage [Formula: see text], at damage [Formula: see text], at shock [Formula: see text] or at time [Formula: see text], whichever occurs first. We obtain the expected cost rates for each model and discuss analytical optimal [Formula: see text] and [Formula: see text] to minimize their expected cost rates. Numerical examples are given when the damage has an exponential distribution and shocks occur at a gamma distribution.

The main purpose of this paper is to propose several new maintenance policies that can be performed at suitable middle times for trivariate preventive maintenance scenarios. Firstly, characteristics and limitations for the approaches of whichever occurs first and whichever occurs last are analyzed, and their respective maintenance models, which are called first maintenance and last maintenance, are given directly. Secondly, a combined approach of first and last is employed and middle maintenance is proposed. Thirdly, the aforementioned policy is modified to be performed at discrete working cycles, using the method of overtime maintenance. Finally, a new approach of whichever occurs middle is proposed for modelings. We give the analyses of how to formulate the middle maintenances and obtain their expected maintenance cost rates, using the technique of cumulative damage models. Numerical examples are given to compare the optimal policies among first, last, and middle maintenances. Finally, a potential application of middle maintenance is provided for future studies. Copyright © 2015 John Wiley & Sons, Ltd.

When a unit is running successive works with cycle times, it would be uneconomical or impractical to do maintenances during any working cycle. This paper firstly reviews two replacement models proposed in literatures as follows: (1) replacement is done over a planned time T at the completion of the working cycle, which is called over-time replacement, and (2) replacement is done over damage level Z at the completion of the forthcoming working cycle, which is called over-level replacement. From the viewpoint of replacement cost savings, we secondly focus on comparisons of over-time replacement and its standard age-based policy, over-level replacement and its standard condition-based policy. Furthermore, modified over-time and over-level replacement costs are obtained to specify critical points at which these new replacements, rather than their standard polices, would save more replacement costs. Discussions in this paper are given analytically and computed numerically. 2015, Springer Science+Business Media New York. Scopus

The random age replacement policies discussed in literatures are helpful to complete the nonstopping works with random working cycles, however, maintenance policies are more easily performed at periodic times in real applications. For such a viewpoint, this paper proposes that age replacement policies are planned at periodic times while considering the random working cycles. Using the modeling approaches of replacement first and last policies, we discuss two models such that the unit is replaced at periodic times [Formula: see text] and working cycles [Formula: see text], whichever occurs first and whichever occurs last. The expected cost rate models are obtained and their optimal solutions for [Formula: see text] and [Formula: see text] are discussed. The comparisons between the policies of [Formula: see text] and [Formula: see text], and replacement first and last are made from the point of cost. Numerical examples are illustrated when the failure time has a Weibull distribution.

It has been assumed in most maintenance models that (i) the number of units for a parallel system can be predefined precisely, (ii) maintenance cost after failure should be avoided, and (iii) age replacement can always be performed at its optimized times. However, these assumptions are challenged from practical perspectives in this paper. For this purpose, shortage and excess costs, which claim that replacement done too early before failure involves a waste of operation, are introduced into replacement models, such as replacement plans with time T or distribution G(t) for constant n or random N of units. Furthermore, the number N of working times and the number n of available units for a scheduled replacement time T are discussed. For each model, the expected replacement cost for one cycle and expected replacement cost rate for a long run are optimized, and numerical examples are given. 2016 Elsevier Ltd. All rights reserved. This work is partially supported by Postdoctoral Research Award PDRA1-0116-14107 from the Qatar National Research Fund, and Ministry of Science and Technology of Taiwan MOST 103-2221-E-030 -008 . Scopus

Nowadays selecting the most suitable robot is a difficult task for manufacturing firms due to increase in production demands and availability of various robot models. Robot evaluation and selection can be regarded as a multiple criteria decision-making (MCDM) problem and three key issues are the assessment of robots, the determination of criteria weights and the prioritisation of alternatives. This paper aims to propose an integrated model based on hesitant 2-tuple linguistic term sets and an extended QUALIFLEX approach for handling robot selection problems with incomplete weight information. The new model can not only manage uncertain and imprecise assessment information of decision-makers with the aid of hesitant 2-tuple linguistic term sets, but also derive the important weights of criteria objectively when the weight information is incompletely known. Moreover, based on the extended QUALIFLEX algorithm, the priority orders of robots can be clearly determined and a more reasonable and credible solution can be yielded in a particular industrial application. Finally, a robot selection case study is carried out, and comparative experiments indicate the practicality and effectiveness of the proposed integrated linguistic MCDM approach. 2016 Informa UK Limited, trading as Taylor & Francis Group. This work was partially supported by the National Natural Science Foundation of China [grant number 71402090]; the Project funded by China Postdoctoral Science Foundation [grant number 2015T80456]; the Program for Young of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning [grant number QD2015019]; Chen Guang project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation. Scopus

Preventive replacement policy conducted at a routine time [Formula: see text] has been surveyed extensively in literatures. Another two random replacement times [Formula: see text] and [Formula: see text] for time [Formula: see text] are jointly considered in this paper. We formulate the models of replacement first, replacement last and replacement middle, which are based on the respective assumptions of whichever occurs first, whichever occurs last and whichever occurs middle. Next, we modify replacement first and replacement last by using whichever occurs first and last jointly. Furthermore, we give the model of replacement overtime when the assumptions of whichever occurs first, whichever occurs last and replacing the unit over time [Formula: see text] are simultaneously considered. Comparisons among these replacement models are made to find which policy is more economical than the other.

It has been proposed in recent literatures that if replacement time is planned too early prior to failure time, 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 the 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. The above notion of shortage and excess costs are taken into consideration for the replacement first, replacement last and replacement overtime models in this paper. We obtain the expected cost rates and their optimum replacement times. Comparisons among these optimum times are made analytically and numerically.

A new periodic damage model is proposed in this paper, where the damage produced by shocks is only measured at periodic times, without considering the stochastic shocks and the cumulative process of damage in discrete times. We model five replacement policies for the periodic damage models using three approaches of whichever triggering event occurs first, whichever triggering event occurs last, and replacing over a planned measure, which are named as replacement first, replacement last, over-damage replacement, over-damage replacement first, and over-damage replacement last, respectively. In analytical ways, we obtain their optimum replacement policies to minimize the expected cost rates and compare them to find which model is more economical. Finally, numerical examples are given to illustrate the validity of the presented models. This paper was made possible by PDRA Grant # PDRA1-0116-14107 from the Qatar National Research Fund (a member of The Qatar Foundation), and NPRP 4-631-2-233 Scopus

It has been commonly known in a Database Management System that constant plans of incremental/differential backup schemes are set up and their full backups should be done to balance the costs of data backup and failure recovery. In this paper, we consider a database system that is running for 24/7 and has several random busy states of updates, and we suppose that incremental/differential backups are implemented after each update and full backups are triggered at constant time [Formula: see text] and random updates [Formula: see text]. That is, models with decision variables of [Formula: see text] and [Formula: see text] for full backups with random incremental/differential backups are considered. We obtain the expected costs of data backup and failure recovery and the expected cost rates for full backups. Optimum solutions to minimize the expected cost rates are discussed in analytical ways. Furthermore, full backups that are made at time [Formula: see text] and updates [Formula: see text] are considered as constant and random modes respectively and compared analytically. For the discussions, numerical examples in exponential cases are given.

Hydraulic transformer can improve the transmission efficiency of the hydraulic system. As the manual hydraulic transformer cannot achieve automatic control and remote control in the hydraulic system, to meet this challenge, the electro-hydraulic servo plate-inclined plunger hydraulic transformer (EHHT) was proposed in this paper. First, through analyzing the principle of the EHHT, the structure of EHHT is designed based on the theoretical analysis; Secondly, the mathematical model and simulation model of output pressure were created. Finally, the fuzzy control strategy was designed and tested on the experiment bench. Both the simulated and experimental results show that the control strategy can effectively improve the pressure control performance of hydraulic transformer and the theoretical analysis is correct.