Harmonic mean estimates for recapture debugging
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In this thesis we examine the problem of estimating the number of errors (bugs) in a reliability system using the recapture debugging model suggested by Nayak (1988). The reliability system contains a certain number N of errors. Each causes system failures independently of the others. The times between failures for any bug are assumed to be independent exponential random variables with a parameter X common to all bugs. We assume the system is observed for a fixed length of time. The maximum likelihood estimate of N was considered by Nayak. We derive the profile likelihood interval for N, and consider as a point estimate the harmonic mean of the endpoints. This estimate was used for the Jelinski-Moranda model by Joe and Reid (1985). The exact probability distribution of the harmonic mean estimator is computed. A generalization of the harmonic mean estimate, called the weighted harmonic mean estimate is proposed as a further improvement. A comparison is drawn between this estimator and the maximum likelihood estimator, using their computed distributions for various values of N.
Thesis, MSc Master of Science
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