3,322 research outputs found
Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics
The calculation of shape and scale parameters of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by uing the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded. The techniques described were verified with several example problems from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program
Modeling Reliability Growth in Accelerated Stress Testing
Qualitative accelerated test methods improve system reliability by identifying and removing initial design flaws. However, schedule and cost constraints often preclude sufficient testing to generate a meaningful reliability estimate from the data obtained in these tests. In this dissertation a modified accelerated life test is proposed to assess the likelihood of attaining a reliability requirement based on tests of early system prototypes. Assuming each prototype contains an unknown number of independent competing failure modes whose respective times to occurrence are governed by a distinct Weibull law, the observed failure data from this qualitative test are shown to follow a poly-Weibull distribution. However, using an agent-based Monte Carlo simulation, it is shown that for typical products subjected to qualitative testing, the failure observations result from a homogenous subset of the total number of latent failure modes and the failure data can be adequately modeled with a Weibull distribution. Thus, the projected system reliability after implementing corrective action to remove one or more failure modes can be estimated using established quantitative accelerated test data analysis methods. Our results suggest that a significant cost and time savings may be realized using the proposed method to signal the need to reassess a product’s design or reallocate test resources to avoid unnecessary maintenance or redesigns. Further, the proposed approach allows a significant reduction in the test time and sample size required to estimate the risk of meeting a reliability requirement over current quantitative accelerated life test techniques. Additional contributions include a numerical and analytical procedure for obtaining the maximum likelihood parameter estimates and observed Fisher information matrix components for the generalized poly-Weibull distribution. Using this procedure, we show that the poly-Weibull distribution outperforms the best-fit modified Weibull alternatives in the literature with respect to their fit of reference data sets for which the hazard rate functions are non-monotone
Prediction of remaining life of power transformers based on left truncated and right censored lifetime data
Prediction of the remaining life of high-voltage power transformers is an
important issue for energy companies because of the need for planning
maintenance and capital expenditures. Lifetime data for such transformers are
complicated because transformer lifetimes can extend over many decades and
transformer designs and manufacturing practices have evolved. We were asked to
develop statistically-based predictions for the lifetimes of an energy
company's fleet of high-voltage transmission and distribution transformers. The
company's data records begin in 1980, providing information on installation and
failure dates of transformers. Although the dataset contains many units that
were installed before 1980, there is no information about units that were
installed and failed before 1980. Thus, the data are left truncated and right
censored. We use a parametric lifetime model to describe the lifetime
distribution of individual transformers. We develop a statistical procedure,
based on age-adjusted life distributions, for computing a prediction interval
for remaining life for individual transformers now in service. We then extend
these ideas to provide predictions and prediction intervals for the cumulative
number of failures, over a range of time, for the overall fleet of
transformers.Comment: Published in at http://dx.doi.org/10.1214/00-AOAS231 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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