Bootstrap confidence intervals for percentiles of reliability data for wood-plastic composites

Improving product reliability is an important goal that may be achieved from a better understanding of the product’s lower percentiles. These lower percentiles provide practitioners with an evaluation of the product’s early failures along with providing information for specification limits, warranty, and cost analysis. Estimation of lower percentiles is sometimes difficult, since substantive data are often sparse in the lower tails. Bootstrap techniques provide important solutions for confidence interval evaluations of these percentiles. This paper applies three bootstrapping methods to appraise the modulus of elasticity (MOE) and modulus of rupture (MOR) test results on sampled wood plastic composites (WPC). The fully nonparametric, the fully parametric, and the nonparametric bootstrap for parametric inference (NBSP) bootstrapping methods for the MOE and MOR of WPC were assessed. For each of the three methods, three different types of confidence intervals, including the standard, percentile, and bias-corrected intervals were evaluated. For smaller sample sizes, the fully nonparametric bootstrapping method was less desirable than the fully parametric or NBSP methods for smaller percentiles. The fully parametric method cannot be used when the censoring technique is unknown. These bootstrapping methods may benefit WPC manufacturers with a better understanding of material properties by providing warning signs of poor reliability. Meeker and Escobar (1998) remarked that traditional parameters of a statistical model (e.g., mean and SD) are not of primary interest. Instead, design engineers, reliability engineers, managers, and customers are interested in specific measures of product reliability or particular characteristics of a failure-time (or failure-pressure) distribution (e.g., failure probabilities, quantiles of the life distribution, failure rates, etc.). This paper focuses on estimating percentiles of material properties with an emphasis on the lower percentiles that relate to product failure. These estimation procedures may also be applied more generally with many other parameters of interest in wood science. The objective of the research was to estimate the lower percentiles of the material properties using nonparametric bootstrapping methods. Wood-plastic composites data are used as an example even though bootstrapping methods can be applied to any data set. The bootstrapping methods outlined in this paper can be applied to generating tolerance limits for product design and may also be helpful to the practitioner in ensuring product quality in the lower percentiles of material properties. Reliability measurements using any parameters (e.g., percentiles), must acknowledge statistical variation so that product improvements may be realized. Thus, wood scientists, supervisors, and line workers need realistic and robust