A comparison of Weibull parameter estimation techniques in small sample inspection

Small sample inspection in manufacturing has traditionally relied on conventional statistical analysis to predict the parent population characteristics [1]. The theory of t-distributions and the central limit theorem assumes samples will have near normal distributions, which cannot be guaranteed. What the conventional approach has failed to address is the implications of the small sample inspection and predicting function parameters with acceptable accuracy. Weibull analysis applied to sample inspection can be shown to allow predicting the critical parameters values. Nevertheless, small samples implementation in Weibull analysis shows a clear lack of predicting such parameter in reasonable accuracy, which does not correspond with the theory behind Weibull distribution. Small samples will be used to achieve a clear understanding of the estimation of Weibull shape parameter and calculate accurate confidence intervals constraining the estimation range.