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The purpose of this paper is to present a novel method to estimate the optimal software testing time which minimizes the relevant expected software cost via a refined neural network approach with the grouped data, where the multi-stage look ahead prediction is carried out with a simple three-layer perceptron neural network with multiple outputs.

To analyze the software fault count data which follows a Poisson process with unknown mean value function, the authors transform the underlying Poisson count data to the Gaussian data by means of one of three data transformation methods, and predict the cost-optimal software testing time via a neural network.

In numerical examples with two actual software fault count data, the authors compare the neural network approach with the common non-homogeneous Poisson process-based software reliability growth models. It is shown that the proposed method could provide a more accurate and more flexible decision making than the common stochastic modeling approach.

It is shown that the neural network approach can be used to predict the optimal software testing time more accurately.

In this paper, we consider a repair‐time limit replacement problem with imperfect repair and develop a graphical method to determine the optimal repair‐time limit which minimizes the expected total discounted cost over an infinite time horizon. The method proposed can be applied to an estimation problem of the optimal repair‐time limit from the empirical repair‐time data. Then, the modified scaled total time on test transform of the underlying repair‐time distribution function is used. Numerical examples are devoted to examine asymptotic properties of the nonparametric estimator for the optimal repair‐time limit.

This paper deals with economic manufacturing quantity (EMQ) models with stochastic machine breakdown and repairs. Under two minimal repair policies to maintain a production machine, the expected cost functions per unit time in the steady state, incurred in the manufacturing operation, are formulated and the optimal policies which minimize them are calculated. As a special case, we consider the case where the machine breakdown time follows the homogeneous Poisson process and calculate the optimal EMQ policies numerically. Also, an approximation method is used to represent the expected cost.

To determine the optimal spare part order‐replacement policy for any high cost single unit complex system in a discrete‐time circumstance.

The expected total discounted cost over an infinite planning horizon is taken as a criterion of optimality as it allows us to put emphasis on the present behavior of the system.

The problem under consideration is a two‐dimensional discrete optimization problem (regular ordering time and inventory time limit for the spare are decision variables) which is difficult to handle, in general. However, it is explored that the problem can be reduced to a simple one‐dimensional one and the optimal ordering time is to be determined under the two extreme situations: no replacement of the spare until the original unit fails and replacement of the spare as soon as it is delivered.

For modeling simplicity, deterministic lead time is considered for both regular and expedited orders. A more appropriate assumption would be to consider randomized lead time for both the orders.

The research provides a useful order‐replacement strategy for a single‐unit system where the failure of the unit is better measured by the number of cycles completed before failure rather than the instant of failure.

The work done in this paper carries certain values as any continuous time model for the problem under consideration can be regarded as only an approximate model.

A Legacy Community is a living and learning community supported by broader institutional departments (e.g., student affairs, academic affairs, foundation, and alumni affairs) that dedicate resources, opportunities, and supports intended to: (a) undo legacies of educational disparities that Black/African American males have historically witnessed and (b) build capacity for students engaged in these communities (i.e., Black/African American males) to create and leave positive legacies on their terms. In this qualitative study of Black and African American undergraduate male living and learning community (LLC) participants at a primarily white institution (Legacy House), we investigate the LLC program elements that impact participants' educational and social experiences, and foster pathways for student legacy building. Legacy house participants describe brotherhood, sense of belonging, and leaving a legacy as elements that enable positive student academic and social outcomes, campus involvement, and career readiness.

In this paper, the authors propose two construction methods to estimate confidence intervals of the time-based optimal software rejuvenation policy and its associated maximum system availability via a parametric bootstrap method. Through simulation experiments the authors investigate their asymptotic behaviors and statistical properties.

The present paper is the first challenge to derive the confidence intervals of the optimal software rejuvenation schedule, which maximizes the system availability in the sense of long run. In other words, the authors concern the statistical software fault management by employing an idea of process control in quality engineering and a parametric bootstrap.

As a remarkably different point from the existing work, the authors carefully take account of a special case where the two-sided confidence interval of the optimal software rejuvenation time does not exist due to that fact that the estimator distribution of the optimal software rejuvenation time is defective. Here the authors propose two useful construction methods of the two-sided confidence interval: conditional confidence interval and heuristic confidence interval.

Although the authors applied a simulation-based bootstrap confidence method in this paper, another re-sampling-based approach can be also applied to the same problem. In addition, the authors just focused on a parametric bootstrap, but a non-parametric bootstrap method can be also applied to the confidence interval estimation of the optimal software rejuvenation time interval, when the complete knowledge on the distribution form is not available.

The statistical software fault management techniques proposed in this paper are useful to control the system availability of operational software systems, by means of the control chart.

Through the online monitoring in operational software systems, it would be possible to estimate the optimal software rejuvenation time and its associated system availability, without applying any approximation. By implementing this function on application programming interface (API), it is possible to realize the low-cost fault-tolerance for software systems with aging.

In the past literature, almost all authors employed parametric and non-parametric inference techniques to estimate the optimal software rejuvenation time but just focused on the point estimation. This may often lead to the miss-judgment based on over-estimation or under-estimation under uncertainty. The authors overcome the problem by introducing the two-sided confidence interval approach.

To determine the optimal software warranty period in continuous and discrete circumstances where the difference between the software testing environment and the operational environment can be characterised by an environment factor.

Software reliability models based on continuous and discrete time non‐homogeneous Poisson processes are assumed to describe the failure occurrence phenomena under both environments. Based on the idea of accelerated life testing for hardware products, the operational profile of the software is modeled, and the total expected software cost incurred in both testing and operational phases is formulated.

Under a milder condition, the optimal warranty period which minimizes the total software cost is derived analytically.

This paper introduces the operational profile of software to model the difference between the testing environment and the operational environment.

The determination of the release schedule for a new software product is the most important issue for designing and controlling a software development process. In fact, the optimal software release problem based on some software reliability growth models has been studied by many authors. In this paper, we propose a new method to estimate the optimal software release time under an alternative cost criterion. More precisely, two kinds of artificial neural networks are used to estimate the fault‐detection time observed in both testing and operation phases. As a cost criterion, we adopt the expected cost rate (the expected total software cost per unit testing time). Then, it is shown that the optimization problem to obtain the optimal release time can be reduced to a graphical one to minimize the tangent slope from a point to an (estimated) empirical curve in two‐dimensional space. Through numerical examples using actual fault‐detection time data, it is illustrated that the method proposed is a very useful device to estimate the optimal software release time precisely.

The software reliability models to describe the reliability growth phenomenon are formulated by any stochastic point process with state‐dependent or time‐dependent intensity function. On the other hand, to deal with the environmental data, which consists of covariates influencing times to software failure, it may be useful to apply the Cox’s proportional hazards model for assessing the software reliability. In this paper, we review the proportional hazards software reliability models and discuss the problem to determine the optimal software release time under the expected total software cost criterion. Numerical examples are devoted to examine the dependence of the covariate structure in both the software reliability prediction and the optimal software release decision.

To provide a brief survey of the literature directed towards the analysis of warranty claim data.

For convenience, this survey of the analysis of warranty claims data is somewhat arbitrarily be classified by topics as follows: age‐based claims analysis, aggregated warranty claims analysis, marginal counts of claims analysis, warranty claims analysis by using covariates, estimation of lifetime distribution using supplementary data, two‐dimensional warranty, warranty costs analysis, sales lag and reporting lag analysis, and forecasts of warranty claims.

Emphasis is placed on a discussion of different kinds of warranty claims data selected from reviews and on a comparison of the statistical models and methods used to analyze such data.

Since the literature on product warranty data is vast, more work on this problem is needed.

This review points out why warranty claims data is important and gives a survey of the literature pertaining to the analysis of such data. The emphasis is on the analysis of minimal databases of real warranty data, constructed by combining information from different sources, which can be collected economically and efficiently through service networks. The research is applicable for those responsible for product reliability, product design decisions and warranty management in manufacturing industries.

The paper reviews different statistical models and methods used to analyze warranty claims data. The statistical models and methods presented are be valuable and meaningful tools for product reliability and warranty management and analysis.