• Title, Summary, Keyword: Non-Homogeneous Poisson Process

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The Likelihood for a Two-Dimensional Poisson Exceedance Point Process Model

  • Yun, Seok-Hoon
    • Communications for Statistical Applications and Methods
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    • v.15 no.5
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    • pp.793-798
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    • 2008
  • Extreme value inference deals with fitting the generalized extreme value distribution model and the generalized Pareto distribution model, which are recently combined to give a single model, namely a two-dimensional non-homogeneous Poisson exceedance point process model. In this paper, we extend the two-dimensional non-homogeneous Poisson process model to include non-stationary effect or dependence on covariates and then derive the likelihood for the extended model.

Reliability Analysis Procedures for Repairable Systems and Related Case Studies (수리 가능 시스템의 신뢰성 분석 절차 및 사례 연구)

  • Lee, Sung-Hwan;Yum, Bong-Jin
    • Journal of the Korea Institute of Military Science and Technology
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    • v.9 no.2
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    • pp.51-59
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    • 2006
  • The purpose of this paper is to present reliability analysis procedures for repairable systems and apply the procedures for assessing the reliabilities of two subsystems of a specific group of military equipment based on field failure data. The mean cumulative function, M(t), the average repair rate, ARR(t), and analytic test methods are used to determine whether a failure process follows a renewal or non-renewal process. For subsystem A, the failure process turns out to follow a homogeneous Poisson process, and subsequently, its mean time between failures, availability, and the necessary number of spares are estimated. For subsystem B, the corresponding M(t) plot shows an increasing trend, indicating that its failure process follows a non-renewal process. Therefore, its M(t) is modeled as a power function of t, and a preventive maintenance policy is proposed based on the annual mean repair cost.

Human Machine Serial Systems Reliability and Parameters Estimation Considering Human Learning Effect (학습효과를 고려한 인간 기계 직렬체계 신뢰도와 모수추정)

  • KIM, Kuk
    • Journal of the Korea Management Engineers Society
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    • v.23 no.4
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    • pp.159-164
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    • 2018
  • Human-machine serial systems must be normal in both systems. Though the failure of machine is irreducible by itself, the human errors are of recurring type. When the human performance is described quantitatively, non-homogeneous Poisson Process model of human errors can be developed. And the model parameters can be estimated by maximum likelihood estimation and numerical analysis method. System reliability is obtained by multiplying machine reliability by human reliability.

A General Coverage-Based NHPP SRGM Framework

  • Park, Joong-Yang;Lee, Gye-Min;Park, Jae-Heung
    • Communications for Statistical Applications and Methods
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    • v.15 no.6
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    • pp.875-881
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    • 2008
  • This paper first discusses the existing non-homogeneous Poisson process(NHPP) software reliability growth model(SRGM) frameworks with respect to capability of representing software reliability growth phenomenon. As an enhancement of representational capability a new general coverage-based NHPP SRGM framework is developed. Issues associated with application of the new framework are then considered.

Two model comparisons of software reliability analysis for Burr type XII distribution

  • An, Jeong-Hyang
    • Journal of the Korean Data and Information Science Society
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    • v.23 no.4
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    • pp.815-823
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    • 2012
  • In this paper reliability growth model in which the operating time between successive failure is a continuous random variable is proposed. This model is for Burr type XII distribution with two parameters which is discussed in two versions: the order statistics and non-homogeneous Poisson process. The two software reliability measures are obtained. The performance for two versions of the suggested model is tested on real data set by U-plot and Y-plot using Kolmogorov distance.

A Queueing System with Work-Modulated Arrival and Service Rates

  • Lee, Jiyeon
    • Journal of the Korean Statistical Society
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    • v.28 no.1
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    • pp.125-133
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    • 1999
  • We consider a FIFO single-server queueing model in which both the arrival and service processes are modulated by the amount of work in the system. The arrival process is a non-homogeneous Poisson process(NHPP) modulated by work, that is, with an intensity that depends on the work in the system. Each customer brings a job consisting of an exponentially distributed amount of work to be processed. The server processes the work at various service rates which also depend on the work in the system. Under the stability conditions obtained by Browne and Sigman(1992) we derive the exact stationary distribution of the work W(t) and the first exit probability that the work level b is exceeded before the work level a is reached, starting from x$\in$[a, b].

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A Study of Software Optimal Release Time for Based on Superposition NHPP Model (중첩 NHPP 모형에 근거한 소프트웨어 최적방출시기에 관한 연구)

  • Kim, Hee Cheul
    • Journal of the Korea Society of Digital Industry and Information Management
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    • v.6 no.3
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    • pp.9-17
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    • 2010
  • Decision problem called an optimal release policies, after testing a software system in development phase and transfer it to the user, is studied. The applied model of release time exploited infinite non-homogeneous Poisson process. This infinite non-homogeneous Poisson process is a model which reflects the possibility of introducing new faults when correcting or modifying the software. The failure life-cycle distribution used superposition which has various intensity, if the system is complicated. Thus, software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement becomes an optimal release policies. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, estimated software optimal release time. Through this study, in terms of superposition model and simply model, the optimal time to using superposition model release the software developer to determine how much could count will help.

A Study on Optimal Release Time for Software Systems based on Generalized Gamma Distribution (일반화 감마분포에 근거한 소프트웨어 최적방출시기에 관한 비교 연구)

  • Kim, Jae-Wook;Kim, Hee-Cheul
    • Journal of the Korea Society of Digital Industry and Information Management
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    • v.6 no.1
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    • pp.55-67
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    • 2010
  • Decision problem called an optimal release policies, after testing a software system in development phase and transfer it to the user, is studied. The applied model of release time exploited infinite non-homogeneous Poisson process. This infinite non-homogeneous Poisson process is a model which reflects the possibility of introducing new faults when correcting or modifying the software. The failure life-cycle distribution used generalized gamma type distribution which has the efficient various property because of various shape and scale parameter. Thus, software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement becomes an optimal release policies. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, estimated software optimal release time.

A Study on Optimal Release Time for Software Systems based on Mixture Weibull NHPP Model (혼합 와이블 NHPP 모형에 근거한 소프트웨어 최적방출시기에 관한 연구)

  • Lee, Sang Sik;Kim, Hee Cheul
    • Journal of the Korea Society of Digital Industry and Information Management
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    • v.6 no.2
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    • pp.183-191
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    • 2010
  • Decision problem called an optimal release policies, after testing a software system in development phase and transfer it to the user, is studied. The applied model of release time exploited infinite non-homogeneous Poisson process. This infinite non-homogeneous Poisson process is a model which reflects the possibility of introducing new faults when correcting or modifying the software. The failure life-cycle distribution used mixture which has various intensity, if the system is complicated. Thus, software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement becomes an optimal release policies. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, estimated software optimal release time.

Optimization of Software Cost Model with Warranty and Delivery Delay Costs

  • Lee, Chong-Hyung;Jang, Kyu-Beom;Park, Dong-Ho
    • Communications for Statistical Applications and Methods
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    • v.12 no.3
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    • pp.697-704
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    • 2005
  • Computer software has gradually become an indispensable elements in many aspects of our daily lives and an important factor in numerous systems. In recent years, it is not unusual that the software cost is more than the hardware cost in many situations. In addition to the costs of developing software, the repair cost resulting from the software failures are even more significant. In this paper, a cost model with warranty cost, time to remove each fault detected in the software system, and delivery delay cost is developed. We use a software reliability model based on non-homogeneous Poisson process (NHPP). We discuss the optimal release policies to minimize the expected total software cost. Numerical examples are provided to illustrate the results.