Lower Quantile Estimation of Wood Strength Data

In wood engineering, lower quantile estimation is vital to the safety of the construction with wood materials. In this thesis, we will first study the censored Weibull maximum likelihood estimate (MLE) of the lower quantile as in the current industrial standard D5457 (ASTM, 2004a) from a statistical point of view. According to our simulations, the lower quantile estimated by the censored Weibull MLE with the 10th empirical percentile as the threshold has a smaller mean squared error (MSE) than the intuitive parametric or non-parametric quantile estimate. This advantage can be shown to be achieved by a good balance between the variance and bias with the help of subjective censorship. However, the standard D5457 (ASTM, 2004a) only utilizes a small (10%) and ad-hoc proportion of the data in the lower quantile estimation, which stimulates us to further improve it. First, we can consider fitting a more complex model, such as the Weibull mixture, to a larger, (e.g., 70%) proportion of the data set with the subjective censorship, which leads to the censored Weibull mixture estimate of the lower quantile. Also, the bootstrap can be used to select a better censoring threshold for the censored Weibull MLE, which leads to the bootstrap censored Weibull MLE. According to our simulations, both proposals can yield a better lower quantile estimates than the standard D5457 and the bootstrap censored Weibull MLE is better than the censored Weibull mixture.