A cost model for N-version programming with imperfect debugging

One of the challenging problems for software companies is to find the optimal time of release of the software so as to minimize the total cost expended on testing and potential penalty cost due to unresolved faults. If the software is for a safety critical system, then the software release time becomes more important. The criticality of a failure caused by a fault also becomes an important issue for safety critical software. In this paper we develop a total cost model based on criticality of the fault and cost of its occurrence during different phases of development for N-version programming scheme, a popular fault-tolerant architecture. The mathematical model is developed using the reliability growth model based on the non-homogeneous Poisson process. The models for optimal release time under different constraints are developed under the assumption that the debugging is imperfect and there is a penalty for late release of the software. The concept of Failure Mode Effects and Criticality Analysis is used for measuring criticality.     

Effect of change point and imperfect debugging in software reliability and its optimal release policy

This article presents a software reliability growth model based on non-homogeneous Poisson process. The main focus of this article is to deliver a method for software reliability modelling incorporating the concept of time-dependent fault introduction and fault removal rate with change point. Also in this article, a cost model with change point has been developed. Based on the cost model optimal release policy with change point has been discussed. Maximum likelihood technique has been applied to estimate the parameters of the model. The proposed model has been validated using some real software failure data. Comparison has been made with models incorporating change point and without change point. The application of the proposed cost model has been shown using some numerical examples.     

Short-term booking of air cargo space

This paper proposes a stochastic dynamic programming model for a short-term capacity planning model for air cargo space. Long-term cargo space is usually acquired by freight forwarders or shippers many months ahead on a contract basis, and usually the forecasted demand is unreliable. A re-planning of cargo space is needed when the date draws nearer to the flight departure time. Hence, for a given amount of long-term contract space, the decision for each stage is the quantity of additional space required for the next stage and the decision planning model evaluates the optimal cost policy based on the economic trade-off between the cost of backlogged shipment and the cost of acquiring additional cargo space. Under certain conditions, we show that the return function is convex with respect to the additional space acquired for a given state and the optimal expected cost for the remaining stages is an increasing convex function with respect to the state variables. These two properties can be carried backward recursively and therefore the optimal cost policy can be determined efficiently.     

股票指数的时间序列模型分析

借助于SA S软件将工程中的K a lm an滤波方法与时间序列的状态空间模型结合对上海A股指数进行了拟合与预测分析,通过对拟合与预测误差的计算可以发现这种模型是可行的;然后还把与滤波结合的状态空间模型的分析结果和常见的时间序列模型如:AR IM A模型、逐步自回归模型以及指数平滑模型的分析结果进行比较,比较的结果说明结合滤波的状态空间模型分析的结果比后三种的结果更加精确.结果为时间序列数据分析提供了一个较好的分析工具.     

Stackelberg strategy solution for optimal software release policies

We present a software release policy which is based on the Stackelberg strategy solution concept. The model formulated assumes the existence of two type of producers in the market, the leader and follower. The resulting release policy combines both cost factors and a loss of opportunity factor which is the result of competition between the rival producers. We define a Stackelberg strategy pair in the context of our model and, through a series of preliminary results, show that an optimal strategy pair exists. We also present a numerical example which utilizes a software reliability growth model based on the nonhomogeneous Poisson process. Finally, we explore the relative leadership property of the optimal strategies.This work was supported in part by a FOAS Research Grant provided by RMIT. The author would like to thank the referees for constructive suggestions which helped to improve a previous version of this paper.     

Sensitivity analysis of release time of software reliability models incorporating testing effort with multiple change-points

To accurately model software failure process with software reliability growth models, incorporating testing effort has shown to be important. In fact, testing effort allocation is also a difficult issue, and it directly affects the software release time when a reliability criteria has to be met. However, with an increasing number of parameters involved in these models, the uncertainty of parameters estimated from the failure data could greatly affect the decision. Hence, it is of importance to study the impact of these model parameters. In this paper, sensitivity of the software release time is investigated through various methods, including one-factor-at-a-time approach, design of experiments and global sensitivity analysis. It is shown that the results from the first two methods may not be accurate enough for the case of complex nonlinear model. Global sensitivity analysis performs better due to the consideration of the global parameter space. The limitations of different approaches are also discussed. Finally, to avoid further excessive adjustment of software release time, interval estimation is recommended for use and it can be obtained based on the results from global sensitivity analysis.     

A generalized JM model with applications to imperfect debugging in software reliability

For their nice mathematical properties, state space models have been widely used, especially for forecasting. Over the last decades, the study of tracking software reliability by statistical models has attracted scientists’ attention. However, most of models focus on perfect debugging although practically imperfect debugging arises everywhere. In this paper, a non-Gaussian state space model is modified to predict software failure time with imperfect debugging. In fact, this model is very flexible so that we can modify the system equation in this model to satisfy the various situations. Besides, this model is suitable for tracking software reliability, and applied to two well known datasets on software failures.     

NHPP software reliability model considering the uncertainty of operating environments with imperfect debugging and testing coverage

In this paper, we propose a testing-coverage software reliability model that considers not only the imperfect debugging (ID) but also the uncertainty of operating environments based on a non-homogeneous Poisson process (NHPP). Software is usually tested in a given control environment, but it may be used in different operating environments by different users, which are unknown to the developers. Many NHPP software reliability growth models (SRGMs) have been developed to estimate the software reliability measures, but most of the underlying common assumptions of these models are that the operating environment is the same as the developing environment. But in fact, due to the unpredictability of the uncertainty in the operating environments for the software, environments may considerably influence the reliability and software's performance in an unpredictable way. So when a software system works in a field environment, its reliability is usually different from the theory reliability, and also from all its similar applications in other fields. In this paper, a new model is proposed with the consideration of the fault detection rate based on the testing coverage and examined to cover ID subject to the uncertainty of operating environments. We compare the performance of the proposed model with several existing NHPP SRGMs using three sets of real software failure data based on seven criteria. Improved normalized criteria distance (NCD) method is also used to rank and select the best model in the context of a set of goodness-of-fit criteria taken all together. All results demonstrate that the new model can give a significant improved goodness-of-fit and predictive performance. Finally, the optimal software release time based on cost and reliability requirement and its sensitivity analysis are discussed.     

Enhancing software reliability modeling and prediction through the introduction of time-variable fault reduction factor

Over the past three decades, many software reliability models with different parameters, reflecting various testing characteristics, have been proposed for estimating the reliability growth of software products. We have noticed that one of the most important parameters controlling software reliability growth is the fault reduction factor (FRF) proposed by Musa. FRF is generally defined as the ratio of net fault reduction to failures experienced. During the software testing process, FRF could be influenced by many environmental factors, such as imperfect debugging, debugging time lag, etc. Thus, in this paper, we first analyze some real data to observe the trends of FRF, and consider FRF to be a time-variable function. We further study how to integrate time-variable FRF into software reliability growth modeling. Some experimental results show that the proposed models can improve the accuracy of software reliability estimation. Finally, sensitivity analyses of various optimal release times based on cost and reliability requirements are discussed. The analytic results indicate that adjusting the value of FRF may affect the release time as well as the development cost.     

Analytically measurable selection of epsilon optimal transition kernals

The problem of existence of ah ε-optimal transition kernel for a canonical continuous time stochastic process with a general cost variable is considered. An analytically measurable, ε-optimal kernel exists if the state space is a compact Banach space, the cost variable is lower-semi-analytic, and the graph of the admissibility function is an analytic set. The result is applied to a problem in which the controller is to optimally select transition probabilities for a non-Markovian step process based on statistical estimates of holding time distributions.     

Optimal Infinite-Horizon Multicriteria Feedback Control of Stationary Systems with Minimax Objectives and Bounded Disturbances

This article presents a methodology for exploring the solution surface in a class of multicriteria infinite-horizon closed-loop optimal control problems with bounded disturbances and minimax objectives. The maximum is taken with respect to both time and all sequences of disturbances; that is, the value of a criterion is the maximal stage cost for the worst possible sequence of disturbances. It is assumed that the system and the cost functions are stationary. The proposed solution method is based on reference point approach and inverse mapping from the space of objectives into the space of control policies and their domains in state space.     

Optimal software release policies with simultaneous cost and reliability requirements

A cost-reliability optimal software release problem is investigated for three existing software reliability growth models. The decision policies on the optimum software release times are discussed by evaluating both software cost and software reliability criteria simultaneously.     

A state space condition monitoring model for furnace erosion prediction and replacement

The paper develops a replacement action decision aid for a key furnace component subject to condition monitoring. A state space model is used to predict the erosion condition of the inductors in an induction furnace in which a measure of the conductance ratio (CR) is used to indirectly assess the relative condition of the inductors, and to guide replacement decisions. This study seeks to improve on this decision process by establishing the relationship between CR and the erosion condition of the inductors. To establish such a relationship, a state space model has been established and the system parameters estimated from CR data. A replacement cost model to balance at any time costly replacements with possible catastrophic failure is also proposed based upon the predicted probability of inductor erosion conditional upon all available information. The well known Kalman filter is employed to derive the predicted and updated probability of inductor erosion level conditional upon CR data to date. This is the first time the condition monitoring decision process has been modelled for real plant based upon filtering theory. The model fits the data well, gives a sensible answer to the actual problem, and is transferable to other condition monitoring contexts. Possible extensions are discussed in the paper.     

A continuous time,deterministic, nonstationary model of economic ordering

The paper considers the problem of economic ordering for a deterministic, nonstationary environment in continuous time. Previous work on the topic is reviewed. The specification of the cost criterion common in inventory theory is called in question for nonstationary situations as far as interest cost is concerned. It is proposed to account for interest by discounting rather than in a holding cost expression. The main interest of the paper is in three versions of the problem: First an unconstrained version, for which inventory is allowed to become negative (backlogging model), second a model in which inventory is constrained to be nonnegative (non-backlogging model), and third a nonbacklogging model with a storage space constraint. For the first two problems necessary optimality conditions are derived which are based on control theory for continuous time systems with jumps in the state trajectories, especially on Blaquière's impulsive maximum principle. These conditions reduce the problem of finding an optimal ordering plan, i.e. an unknown number of optimal ordering times and for each of them an optimal order size to a one parameter search problem. Due to the possibility of multiple solutions of the optimality conditions for each ordering time, one cannot in general identify a unique candidate ordering plan for each value of the search parameter, but only a tree-structured set of such plans. The optimality conditions for the first two problem versions and for a fourth one with a storage space constraint but without a non-backlogging constraint are eventually combined to yield a solution of the storage space constrained non-backlogging version.     

Asymptotic properties of constrained Markov Decision Processes

We present in this paper several asymptotic properties of constrained Markov Decision Processes (MDPs) with a countable state space. We treat both the discounted and the expected average cost, with unbounded cost. We are interested in (1) the convergence of finite horizon MDPs to the infinite horizon MDP, (2) convergence of MDPs with a truncated state space to the problem with infinite state space, (3) convergence of MDPs as the discount factor goes to a limit. In all these cases we establish the convergence of optimal values and policies. Moreover, based on the optimal policy for the limiting problem, we construct policies which are almost optimal for the other (approximating) problems. Based on the convergence of MDPs with a truncated state space to the problem with infinite state space, we show that an optimal stationary policy exists such that the number of randomisations it uses is less or equal to the number of constraints plus one. We finally apply the results to a dynamic scheduling problem.This work was partially supported by the Chateaubriand fellowship from the French embassy in Israel and by the European Grant BRA-QMIPS of CEC DG XIII     

The nisio semigroup for controlled diffusions with partial observations

A one parameter semigroup of nonlinear operators on an appropriate Banach space is constructed in the spirit of Nisio for controlled diffusions with partial observations. The method is based upon considering an equivalent problem of controlling a measure-valued process representing the conditional law of the state given past observations. The latter evolves according to the usual equations of nonlinear filtering. By considering an appropriate augmentation of the class of controls, it is shown that the “minimum cost” operators associated with this control problem indeed form a semigroup of nonlinear contractions on the space of bounded continuous real-valued functions on the state space of the above measure-valued process.     

A State Space Model for Software Reliability

In this paper, we propose a non-Gaussion state space model to apply in software reliability. This model assumes an exponential distribution for the failure time in every test-debugging stage, conditionally on the state parameter — the number of faults in the program. It is a generalized JM model which can be applied to the imperfect debugging situation as well as in evolving programs. By examining a set of data on evolving program failures, the effect of evolving program model is amply proved.     

Application of fuzzy time series in prediction of time between failures &; faults in software reliability assessment

Since last seventies, various software reliability growth models (SRGMs) have been developed to estimate different measures related to quality of software like: number of remaining faults, software failure rate, reliability, cost, release time, etc. Most of the exiting SRGMs are probabilistic. These models have been developed based on various assumptions. The entire software development process is performed by human being. Also, a software can be executed in different environments. As human behavior is fuzzy and the environment is changing, the concept of fuzzy set theory is applicable in developing software reliability models. In this paper, two fuzzy time series based software reliability models have been proposed. The first one predicts the time between failures (TBFs) of software and the second one predicts the number of errors present in software. Both the models have been developed considering the software failure data as linguistic variable. Usefulness of the models has been demonstrated using real failure data.     

A branch and bound algorithm for class based storage location assignment

Class-based storage implementation decisions have significant impact on the required storage space and the material handling cost in a warehouse. In this paper, a nonlinear integer programming model is proposed to capture the above. Effects of storage area reduction on order picking and storage space cost are incorporated. A branch and bound algorithm is developed to solve the model. Computational experience with randomly generated data sets and an industrial case shows that branch and bound algorithm is computationally more efficient than a baseline dynamic programming algorithm. It is further observed that the class based policy results in lower total cost of order picking and storage space than the dedicated policy.     

Parameter estimation for time varying nonlinear circuit from state analysis and simulation

This paper develops a parameter estimation technique for a nonlinear circuit. The nonlinear circuit is represented by a state space model and perturbation theory is applied to obtain the approximate analytical solution for the state vector. The state model is assumed to be slowly time varying so that the parameter vector is constant over different time slots. The expressions obtained for the state vector are matched with the noisy data using the gradient algorithm and hence the parameter vector is estimated. Simulations are based on discretization of the state space model using MATLAB.