• Convergence Security Journal
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• v.6 no.3
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• pp.145-153
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• 2006

Infinite failure NHPP models for a record value satisfies mode proposed in the literature exhibit either monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, propose comparative study of software reliability model using Erlang distribution, Rayleigh and Gumbel distribution. Equations to estimate the parameters using maximum likelihood estimation of infinite failure NHPP model based on failure data collected in the form of interfailure times are developed. For the sake of proposing distribution, we used to the special pattern. Analysis of failure data set using arithmetic and Laplace trend tests, goodness-of-fit test, bias tests is presented.

• The KIPS Transactions:PartD
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• v.9D no.3
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• pp.389-398
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• 2002

Software reliability growth models are used in testing stages of software development to model the error content and time intervals between software failures. This paper presents a stochastic model for the software failure phenomenon based on a nonhomogeneous Poisson process(NHPP) and performs Bayesian inference using prior information. The failure process is analyzed to develop a suitable mean value function for the NHPP ; expressions are given for several performance measure. Actual software failure data are compared with several model on the constant reflecting the quality of testing. The performance measures and parametric inferences of the suggested models using Rayleigh distribution and Laplace distribution are discussed. The results of the suggested models are applied to real software failure data and compared with Goel model. Tools of parameter point inference and 95% credible intereval was used method of Gibbs sampling. In this paper, model selection using the sum of the squared errors was employed. The numerical example by NTDS data was illustrated.

• The Korean Journal of Applied Statistics
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• v.23 no.3
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• pp.573-584
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• 2010

This paper considers the differences in the software execution environments in the testing phase and the operational phase to determine the optimal release time and warranty period of software systems. We formulate equations for the total expected software cost until the end of the software life cycle based on the NHPP. In addition, we derive the optimal release time that minimizes the total expected software cost for an imperfect debugging software reliability model. Finally, we analyze the sensitivity of the optimal testing and maintenance design related to variation of the cost model parameters based on the fault data observed in the actual testing process, and discuss the quantitative properties of the proposed model.

• Journal of Korean Society for Quality Management
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• v.34 no.3
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• pp.73-78
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• 2006

In this paper, we propose a software reliability growth model based on the testing domain in the software system, which is isolated by the executed test cases in software testing. In particular, our model assumes an imperfect debugging environment in which new faults are introduced in the fault-correction process, and is formulated as a nonhomogeneous Poisson process(NHPP). Further, it is applied to fault-detection data, the results of software reliability assessment are shown, and comparison of goodness-of-fit with the existing software reliability growth model is performed.

• Journal of Korean Society for Quality Management
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• v.30 no.4
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• pp.94-105
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• 2002

In this paper, replacement problems for a deteriorating system are considered. In the system under consideration, the successive lifetimes after repair become shorter and shorter, while the consecutive repair times become longer and longer. More specifically, the lifetimes of the system form a nonhomogeneous Poisson process, whereas the consecutive repair times constitute a stochastically increasing geometric process. Optimal replacement policies for the long-run average cost rate and the steady state availability are considered. Also taking the cost and the availability into consideration at the same time, the properties of optimal policies under the Cost Priority Policy and the Availability Priority Policy are obtained.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.1
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• pp.7-14
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• 2006

The finite failure NHPP models proposed in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, we propose the Erlang reliability model, which can capture the increasing nature of the failure occurrence rate per fault. Equations to estimate the parameters of the Erlang finite failure NHPP model based on failure data collected in the form of inter-failure times are developed. For the sake of proposing shape parameter of the Erlang distribution, we used to the goodness-of-fit test of distribution. Data set, where the underlying failure process could not be adequately described by the existing models, which motivated the development of the Erlang model. Analysis of the failure data set which led us to the Erlang model, using arithmetic and Laplace trend tests, goodness-of-fit test, bias tests is presented.

• Journal of the Korea Society of Computer and Information
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• v.10 no.6 s.38
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• pp.27-36
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• 2005

Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates Per fault. This Paper Proposes reliability model using the generalized gamma distribution, which can capture the monotonic increasing(or monotonic decreasing) nature of the failure occurrence rate per fault. Equations to estimate the parameters of the generalized gamma finite failure NHPP model based on failure data collected in the form of interfailure times are developed. For the sake of proposing shape parameter of the generalized gamma distribution, used to the special pattern. Data set, where the underlying failure process could not be adequately described by the knowing models, which motivated the development of the gamma or Weibull model. Analysis of failure data set for the generalized gamma modell, using arithmetic and Laplace trend tests . goodness-of-fit test, bias tests is presented.

• The KIPS Transactions:PartD
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• v.11D no.6
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• pp.1269-1276
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• 2004

The Parameter Estimation for software existing reliability models, Goel-Okumoto, Yamada-Ohba-Osaki model was reviewed and Rayleigh model based on Rayleigh distribution was studied. In this paper, we discusses comparison of parameter estimation using maximum likelihood estimator and Bayesian estimation based on Gibbs sampling to analysis of the estimator' pattern. Model selection based on sum of the squared errors and Braun statistic, for the sake of efficient model, was employed. A numerical example was illustrated using real data. The current areas and models of Superposition, mixture for future development are also employed.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.4
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• pp.368-378
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• 2002

As more companies are equipped with data aquisition systems for their products, huge amount of field warranty data has been accumulated. We focus on the case when the field data for a given product comprise with the number of sales and the number of the first failures for each period. The number of censored items and their ages are assumed to be given. This type of data are incomplete in the sense that the age of a failed item is unknown. We construct a model for this type of data and propose an algorithm for nonparametric maximum likelihood estimation of the product reliability. Unlike the nonhomogeneous Poisson process(NHPP) model, our method can handle the data with censored items as well as those with small population. A few examples are investigated to characterize our model, and a real field warranty data set is analyzed by the method.

• International Journal of Reliability and Applications
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• v.4 no.1
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• pp.1-12
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• 2003

Many software reliability growth models (SRGM's) based on a nonhomogeneous Poisson process (NHPP) have been proposed by many researchers. Most of the SRGM's which have been proposed up to the present treat the event of software fault-detection in the testing and operational phases as a counting process. However, if the size of the software system is large, the number of software faults detected during the testing phase becomes large, and the change of the number of faults which are detected and removed through debugging activities becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. Therefore, in such a situation, we can model the software fault-detection process as a stochastic process with a continuous state space. In this paper, we propose a new software reliability growth model describing the fault-detection process by applying a mathematical technique of stochastic differential equations of an Ito type. We also compare our model with the existing SRGM's in terms of goodness-of-fit for actual data sets.