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Submitted by sde on 12 August, 2018 - 15:51

Date/Time:

Monday, August 13, 2018 - 16:30 to 17:30

Venue:

SMS seminar room

Speaker:

Prof. Subrata Kundu

Affiliation:

Dept. of Statistics, George Washington University

Title:

Some Aspects of Modeling Software Reliability

Generalized Order Statistics(GOS) models and Non-homogeneous PoissonProcess (NHPP) models form a significant subclass of the many softwarereliability models proposed in the literature. First, we discuss themodels followed by some logical implications of NHPP models andestimability of the underlying parameters. We prove an importantlimitation of NHPP models for which the limit of the expected numberof failures $m(t)$ as the testing time $t\to\infty$ is finite.Specifically, the parameters of those models cannot be estimatedconsistently as the testing time approaches infinity. Then, we presenta nonparametric method for estimating $\nu$, the number of bugs present in acode, and investigate its properties. Our results show that theproposed estimator performs well in terms of bias and asymptoticnormality, while the MLE of $\nu$ derived assuming that the commonrenewal distribution is exponential may be seriously biased if thatassumption does not hold. We present a new parametric approach aswell.

**School of Mathematical Sciences**

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