Confidence Intervals for Predicting Lumber Strength Properties Based on Ratios of Percentiles from Two Weibull Populations

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Ratios of strength properties of lumber are commonly used to calculate property values for standards. Although originally proposed in terms of means, ratios are being applied without regard to position in the distribution. It is now known that lumber strength properties are generally not normally distributed. Therefore, nonparametric methods are often used to derive property values. In some situations, estimating properties based on a parametric estimate is required. For these situations, the three-parameter Weibull distribution looks promising. To use this approach, procedures for estimating confidence intervals for ratios of percentiles from two Weibull populations are needed. In this study, we employed the large sample properties of maximum likelihood estimators to obtain a confidence interval for the ratio of 100Sa-th percentiles from two different three-parameter Weibull distributions. The coverage probabilities were investigated by a computer simulation study. We concluded that the procedure has considerable promise, but many questions remain to be answered.

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