<title>Comparison of the distribution of estimated Weibull parameters from optical fiber strength measurements and Monte Carlo simulations</title>

Abstract

In this paper we present results obtained from computational studies on a set of experimental data concerning the strength of commercially available silica optical fibres. We report on the distribution of estimated values of the Weibull modulus using a variety of Weibull estimators and sample sizes. We compare the distribution of the estimated Weibull parameters from experimental data to analogous distributions obtained using Monte Carlo methods. We show that for small sample sizes <40 the maximum likelihood method produces a skewed distribution of estimated Weibull parameters. There is a small but finite probability that the Weibull modulus will be overestimated by a factor of 2. We also show that the experimental data are in reasonable agreement with our Monte Carlo simulation for linear regression methods. However, for maximum likelihood methods the peak of the distribution of estimated Weibull modulus can be seen to shift for the strength data but the peak is more stable for the Monte Carlo data The increased bias of the distribution of estimated Weibull modulus from experimental data must be considered when inferring the reliability of optical fibers from strength data.