Block-Bootstrap-based Estimation of the Distribution of Cumulative Degradation due to Outdoor Weathering

• Activity Number: 44
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics*
• Author(s): Victor Chan*+
• Affiliation(s): Western Washington University
• Keywords: Reliability ; resampling ; periodic dependent time series

Abstract

One of the primary reliability quantities of interest involving degradation of materials exposed to the outdoor environment is the distribution of future possible cumulative degradation at a given amount of exposure time. The distribution arises from the long-term inherent unpredictability/uncertainty of the state of the outdoor environment (i.e., the weather). The problem of estimating this distribution is equivalent to the estimation of the distribution of the sum of periodic-dependent time series. In this paper, we propose a nonparametric method based on block bootstrap to estimate this distribution. Unlike typical block bootstrap techniques, specification of a block length and resampling of bootstrap data are not required, partly because of the resulting normality of the distribution of the sum. The key parameters to be estimated are the mean and the variance of the distribution. By means of simulated data from a model used to describe the daily degradation of a solar reflector material, we show that, for typical moderate-sized data sets, our block-bootstrap-based estimator of the variance is more efficient than the sample variance based on yearly data.