Optimal release time for software systems considering cost, testing-effort, and test efficiency

In this paper, we study the impact of software testing effort & efficiency on the modeling of software reliability, including the cost for optimal release time. This paper presents two important issues in software reliability modeling & software reliability economics: testing effort, and efficiency. First, we propose a generalized logistic testing-effort function that enjoys the advantage of relating work profile more directly to the natural flow of software development, and can be used to describe the possible testing-effort patterns. Furthermore, we incorporate the generalized logistic testing-effort function into software reliability modeling, and evaluate its fault-prediction capability through several numerical experiments based on real data. Secondly, we address the effects of new testing techniques or tools for increasing the efficiency of software testing. Based on the proposed software reliability model, we present a software cost model to reflect the effectiveness of introducing new technologies. Numerical examples & related data analyzes are presented in detail. From the experimental results, we obtain a software economic policy which provides a comprehensive analysis of software based on cost & test efficiency. Moreover, the policy can also help project managers determine when to stop testing for market release at the right time.     

Availability of a periodically inspected system, maintained under an imperfect-repair policy

A periodically inspected system is maintained through a fixed number of imperfect-repairs before being replaced or perfectly repaired. The lifetime distribution of the system in its new and imperfectly repaired states is arbitrary. The times required for imperfect repairs and for perfect repair or replacement are random. The repaired system is restored to operation at the next scheduled inspection time. The system availability function is expressed as the weighted average of the survival functions and their shifts, and gives the limiting average availability.     

An Extended Periodic Imperfect Preventive Maintenance Model With Age-Dependent Failure Type

This paper presents a generalized periodic imperfect preventive maintenance (PM) model for a system with age-dependent failure type. The imperfect PM model proposed in this study incorporates improvement factors vis-À-vis the hazard-rate function, and effective age. As failures occur, the system experiences one of the two types of failure: type-I failure (minor), and type-II failure (catastrophic). Type-I failures are rectified with minimal repair. In a PM period, the system is preventively maintained following the occurrence of a type-II failure, or at age $T$ , whichever takes place first. At the $N$th PM, the system is replaced. An approach that generalizes the existing studies on the periodic PM policy is proposed. Taking age-dependent failure type into consideration, the objective consists of determining the optimal PM & replacement schedule that minimize the expected cost per unit of time, over an infinite horizon.      

An optimal replacement policy for a three-state repairable system with a monotone process model

In this paper, a deteriorating simple repairable system with three states, including two failure states and one working state, is studied. Assume that the system after repair cannot be "as good as new", and the deterioration of the system is stochastic. Under these assumptions, we use a replacement policy N based on the failure number of the system. Then our aim is to determine an optimal replacement policy N/sup */ such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. An explicit expression of the average cost rate is derived. Then, an optimal replacement policy is determined analytically or numerically. Furthermore, we can find that a repair model for the three-state repairable system in this paper forms a general monotone process model. Finally, we put forward a numerical example, and carry through some discussions and sensitivity analysis of the model in this paper.     

Maintenance strategy optimization using a continuous-state partially observable semi-Markov decision process

Due to the limitation of current condition monitoring technologies, the estimates of asset health states may contain some uncertainties. A maintenance strategy ignoring this uncertainty of asset health state can cause additional costs or downtime. The partially observable Markov decision process (POMDP) is a commonly used approach to derive optimal maintenance strategies when asset health inspections are imperfect. However, existing applications of the POMDP to maintenance decision-making largely adopt the discrete time and state assumptions. The discrete-time assumption requires the health state transitions and maintenance activities only happen at discrete epochs, which cannot model the failure time accurately and is not cost-effective. The discrete health state assumption, on the other hand, may not be elaborate enough to improve the effectiveness of maintenance. To address these limitations, this paper proposes a continuous state partially observable semi-Markov decision process (POSMDP). An algorithm that combines the Monte Carlo-based density projection method and the policy iteration is developed to solve the POSMDP. Different types of maintenance activities (i.e., inspections, replacement, and imperfect maintenance) are considered in this paper. The next maintenance action and the corresponding waiting durations are optimized jointly to minimize the long-run expected cost per unit time and availability. The result of simulation studies shows that the proposed maintenance optimization approach is more cost-effective than maintenance strategies derived by another two approximate methods, when regular inspection intervals are adopted. The simulation study also shows that the maintenance cost can be further reduced by developing maintenance strategies with state-dependent maintenance intervals using the POSMDP. In addition, during the simulation studies the proposed POSMDP shows the ability to adopt a cost-effective strategy structure when multiple types of maintenance activities are involved.     

A geometric-process repair-model with good-as-new preventive repair

This paper studies a deteriorating simple repairable system. In order to improve the availability or economize the operating costs of the system, the preventive repair is adopted before the system fails. Assume that the preventive repair of the system is as good as new, while the failure repair of the system is not, so that the successive working times form a stochastic decreasing geometric process while the consecutive failure repair times form a stochastic increasing geometric process. Under this assumption and others, by using geometric process we consider a replacement policy N based on the failure number of the system. Our problem is to determine an optimal replacement policy N such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. And the fixed-length interval time of the preventive repair in the system is also discussed. Finally, an appropriate numerical example is given. It is seen from that both the optimal policies N** and N* are unique. However, the optimal policy N** with preventive repair is better than the optimal policy N* without preventive repair     

基于软交换的集群媒体服务器高可用性系统建模与分析

在研究基于软交换的集群媒体服务器的系统结构基础上,提出了一个高可用性系统方案。利用广义随机Petri网理论对高可用性方案进行了建模和仿真实验。实验结果表明,该方案可以显著提高系统的可用性,是一个有效方案。基于可用性模型分析了系统修复速率、请求处理机数量、以及请求处理机故障特征对集群可用性的影响,分析结论对基于软交换的集群媒体服务器的可用性设计具有重要参考价值。     

Reliability analysis of interconnection networks using hierarchicalcomposition

Based on the nature of the upper- and lower-bound block diagram models of multistage interconnection networks (MINs), a series system consisting of independent subsystems is considered. To model the reliability of such a system with online repair and imperfect coverage, the usual approach is to construct and solve a large, overall Markov model. A two-level hierarchical model is instead proposed in which each subsystem is modeled as a Markov chain and the system reliability is then modeled as a series system of independent Markov components. This technique is extended to compute the instantaneous availability of the system with imperfect coverage and online repair. Extensions to allow for transient faults and phase-type repair time distributions are straightforward. It should be possible to apply this approach to other fault-tolerant MINs and to any system that can be modeled as a series system where each subsystem has a parallel-redundant structure     

Availability analysis under multiple link failures in WDM networks with shared-link connections

In optical Wavelength Division Multiplexing (WDM) networks, different protection schemes have been proposed in the literature, namely, dedicated protection and shared protection. Shared protection techniques significantly reduce the required spare capacity by providing the same level of availability as dedicated protection. However, current mission critical applications (which heavily depend on the availability of communication resources) require connection availability in the order of 99.999% or higher, which corresponds to a downtime of almost 5 min a year on the average. Therefore, in order to satisfy a connection serviceavailability requirement defined by the users Service Level Agreement in a cost-effective and resource-efficient way, network operators need a systematic mechanism to evaluate the network availability under multiple failure scenario to ensure that current network configuration can meet the required availability degree; otherwise, a network upgrade is required. Unfortunately, under multiple failure scenario, traditional availability analysis techniques based on reliability block diagrams are not suitable for survivable networks with shared spare capacity. Therefore, a new concept is proposed to facilitate the calculations of network availability. In this paper, we propose an analytical model for evaluating the availability of a WDM network with shared-link connections under multiple link failures. The analytical model is also verified using Monte Carlo simulation. The proposed model significantly contributes to the related areas by providing network operators with a quantitative tool to evaluate the system availability and, thus, the expected survivability degree of WDM optical networks with shared connections under multiple link failures.     

Optimal replacement policy for a warrantied system with imperfect preventive maintenance operations

This paper determines the optimal replacement time for a system with imperfect preventive maintenance operations under the modified warranty policy. The hazard rate after preventive maintenance lies between the states as good as new and as bad as old. After minimal repair, the hazard rate remains unchanged. Modified warranty policy is a mixed type of free and pro-rata warranty policy. Numerical examples using the Weibull case are presented.     

MDP-based lightpath establishment for service differentiation in all-optical WDM networks with wavelength conversion capability

In this paper, we propose a service differentiation method for lightpath establishment in all-optical WDM networks. The proposed method derives the optimal lightpath establishment policy for each serve class based on a Markov Decision Process (MDP). The optimal policy considered here is to provide service differentiation for lightpath establishment and to utilize wavelengths effectively. Here, we focus on two cases for wavelength conversion capability; full-range wavelength conversion and limited-range wavelength conversion. For full-range wavelength conversion, the number of lightpaths for each class is considered as a state of MDP. On the other hand, for limited-range wavelength conversion, the service class of lightpath that has been established with each output wavelength is considered as the state. Based on these states, we derive the optimal policy for lightpath establishment. In both cases, we evaluate the performance of the proposed method with simulation. In numerical examples, we show that our proposed method can provide service differentiation and use wavelengths effectively regardless of wavelength conversion capability.     

A general isodegrading model for predicting mechanical equipment reliability and performance degradation

This paper develops an efficient reliability degrading model, referred to as a general isodegrading model, for mechanical equipment reliability and performance prediction under the PM (preventive maintenance) policy that the number of failures in each PM cycle should be kept as near as possible the same, the operational time in each PM cycle is maximized availability, and the equipment should be overhauled or scrapped on time when the economical benefit in a PM cycle is less than the demanded level. The core of the model is that there are isodegrading rates between neighbouring PM cycles for the equipment reliability and the performance parameters optimal operational time, MTBF, output and operational cyclic number, and there is an isodegrading speed between the parameters. This model, introducing an integrated measurement-general isodegrading rate γ and an idea of demanded PM, has broken through the restriction that equipment has the same maintenance time intervals and steady-state availability as in traditional models. It combines natural reliability degradation with performance degradation, and provides a scientific basis for the reliability and performance prediction of equipment both in operation and in development. The model is effectively applied in the determination of recommended PM criteria in the first overhaul cycle of the gantry cranes used at railway terminals in China. The field inspection of the recommend criteria has proved that the general isodegrading model is practical and effective.     

Modeling a shared-load k-out-of-n:G system

A Markov model for analyzing the reliability and availability of an n-unit shared-load repairable k-out-of-n:G system with imperfect switching is presented. The equations for both time-dependent and steady-state system availability are given. An inverse Laplace transform is used to solve the simultaneous differential equations for the nonrepairable case. A generalized analytic function for system reliability is obtained. Examples are provided to demonstrate the model and the impact of a load-sharing strategy on the reliability. The load-sharing strategy can improve system reliability and availability, if the controller and switching parameters are adequate. The proposed approach and solution are helpful to system engineers and reliability analysts     

The branching nonhomogeneous Poisson process and its application to a replacement model

In studying and analysing the failure patterns of complex system, plausible stochastic models are needed to represent the sequence of events. A simple and frequently used model is derived by the assumption that the times-between-failures of a system are exponentially distributed and independent. Experience has shown, however, that successive times-between-failures are not exponentially distributed and not independent.These deviations are due to imperfect search of failed components. We constitute a plausible stochastic process which describes the sequence of events, and obtain the interval reliability and the expected number of failures.As an application of these results, we deal with the replacement model where a system undergoes minimal repair before time T and is replaced at time T. We discuss an optimum policy minimizing the total expected cost per unit time.     

Performance analysis of maximum ratio transmission with imperfect channel estimation

Maximal ratio transmission (MRT) is designed assuming the availability of perfect channel state information (CSI) at both the transmitter and the receiver. However, perfect CSI is not available in practice. This paper investigates the impact of Gaussian estimation errors on the MRT performance in independently and identically distributed (i.i.d.) Rayleigh fading channels. We derive the cumulative distribution function (cdf), the probability density function (pdf) and the moment generating function (mgf) of the MRT output signal-to-noise ratio (SNR) with imperfect CSI, enabling the evaluation of some useful performance metrics such as the average error rate and the outage performance. Numerical and simulation results are provided to show the impact of imperfect CSI on the MRT performance.     

两维转镜的等效动态控制误差模型辨识

两维转镜的动态控制误差是影响激光制导武器对抗闭环半实物仿真试验精度的重要误差源,建立准确的控制误差模型是系统精度分析的基础。对于转镜的动态控制误差分析建模问题,常采用经典的频域设计法建立控制系统的传递函数来分析其控制误差,建模过程复杂且难以建立准确的模型,提出了一种过程辨识的方法,分析了辨识原理、辨识输入信号设计、模型阶次及模型参数的辨识方法等,在使用行列式比定阶法确定模型阶次的基础上,采用递推最小二乘法建立了转镜的等效动态控制误差模型。然后,根据转镜控制系统指标设计等效正弦信号对该模型进行了验证,结果表明:动态控制误差模型估计输出与实际仿真输出基本相同,估计误差均值为0,最大值仅为13,说明了建模的准确性,同时也为激光制导武器对抗闭环半实物仿真试验系统中其他仿真设备的建模提供了方法支持。     

Optimal periodic preventive repair and replacement policy assuming geometric process repair

In this paper, a simple deteriorating system with repair is studied. When failure occurs, the system is replaced at high cost. To extend the operating life, the system can be repaired preventively. However, preventive repair does not return the system to a "good as new" condition. Rather, the successive operating times of the system after preventive repair form a stochastically decreasing geometric process, while the consecutive preventive repair times of the system form a stochastically increasing geometric process. We consider a bivariate preventive repair policy to solve the efficiency for a deteriorating & valuable system. Thus, the objective of this paper is to determine an optimal bivariate replacement policy such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived, and the corresponding optimal replacement policy can be determined numerically. An example is given where the operating time of the system is given by a Weibull distribution.     

基于BayesBootStrap的特种设备可靠性模型参数确定方法

为了进行有效的预先维修保障,合理的可靠性模型十分必要。针对某型特种设备数量少,先验信息不足的特点．将BayesBootStrap方法应用于某型航海特种设备的可靠性模型参数的确定,给出了该方法的基本原理以及实现步骤。并结合某型航海特种设备小样本试验数据,计算了维修时间概率密度函数、修复率函数、平均修复时间、最大修复时间等,验证了本方法的可行性。     

Optimal Number of Minimal Repairs before Replacement

This paper presents a model for determining the optimal number of minimal repairs before replacement. The basic concept paralles the periodic replacement model with minimal repair at failure introduced by Barlow & Hunter, the only difference being the replacement is signaled by the number of previous minimal repairs performed on the unit. In the case of Weibull distribution, which is widely used for failures, the optimal solution is simple and more cost effective compared to Barlow & Hunter's Policy II.     

Availability-based life cycle cost model: A simulation approach

Life Cycle Costing (LCC) has become a popular technique for studying operating facility designs prior to their construction. However, many such designs have operating characteristics that are marked by uncertainty. In particular, component failure rates and repair/replacement rates are uncertain. Thus, downtimes and maintenance costs are similarly uncertain. These various costs and uncertainties must be balanced if intelligent cost-based design decisions are to be made. This paper developes a model of Life Cycle Cost which integrates various availability parameters of reliability and maintainability. A simulation algorithm is presented as the appropriate tool for studying life cycle cost of a plant design.