A generalization of the Weibull distribution
Four parameter generalization of Weibull distribution for more versatile life testing model
Cohen, A. C.↗
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Reliability analysis of structural ceramic components using a three-parameter Weibull distribution
Described here are nonlinear regression estimators for the three-Weibull distribution. Issues relating to the bias and invariance associated with these estimators are examined numerically using Monte Carlo simulation methods. The estimators were used to extract parameters from sintered silicon nitride failure data. A reliability analysis was performed on a turbopump blade utilizing the three-parameter Weibull distribution and the estimates from the sintered silicon nitride data.
Duffy, Stephen F.↗
Software for Statistical Analysis of Weibull Distributions with Application to Gear Fatigue Data: User Manual with Verification
The Weibull distribution has been widely adopted for the statistical description and inference of fatigue data. This document provides user instructions, examples, and verification for software to analyze gear fatigue test data. The software was developed presuming the data are adequately modeled using a two-parameter Weibull distribution. The calculations are based on likelihood methods, and the approach taken is valid for data that include type 1 censoring. The software was verified by reproducing results published by others.
Krantz, Timothy L.↗
Software for Statistical Analysis of Weibull Distributions with Application to Gear Fatigue Data: User Manual with Verification
The Weibull distribution has been widely adopted for the statistical description and inference of fatigue data. This document provides user instructions, examples, and verification for software to analyze gear fatigue test data. The software was developed presuming the data are adequately modeled using a two-parameter Weibull distribution. The calculations are based on likelihood methods, and the approach taken is valid for data that include type I censoring. The software was verified by reproducing results published by others.
Kranz, Timothy L.↗
Reliability analysis of structural ceramic components using a three-parameter Weibull distribution
Described here are nonlinear regression estimators for the three-parameter Weibull distribution. Issues relating to the bias and invariance associated with these estimators are examined numerically using Monte Carlo simulation methods. The estimators were used to extract parameters from sintered silicon nitride failure data. A reliability analysis was performed on a turbopump blade utilizing the three-parameter Weibull distribution and the estimates from the sintered silicon nitride data.
Duffy, Stephen F.↗
Statistical analysis of censored motion sickness latency data using the two-parameter Weibull distribution
The suitability of the two-parameter Weibull distribution for describing highly censored cat motion sickness latency data was evaluated by estimating the parameters with the maximum likelihood method and testing for goodness of fit with the Kolmogorov-Smirnov statistic. A procedure for determining confidence levels and testing for significance of the difference between Weibull parameters is described. Computer programs for these procedures may be obtained from an archival source.
Park, Won J.↗
Estimation of parameters in compound Weibull distributions
Estimating procedure using electronic digital computers applicable to experiments in which mixed Weibull distribution is statistical model
DIGITAL COMPUTER↗
Smooth empirical Bayes estimation with application to the Weibull distribution
Smooth empirical Bayes estimation with application to Weibull distribution
Bennett, G. K.↗
Lower bound on reliability for Weibull distribution when shape parameter is not estimated accurately
The mathematical relationships between the shape parameter Beta and estimates of reliability and a life limit lower bound for the two parameter Weibull distribution are investigated. It is shown that under rather general conditions, both the reliability lower bound and the allowable life limit lower bound (often called a tolerance limit) have unique global minimums over a range of Beta. Hence lower bound solutions can be obtained without assuming or estimating Beta. The existence and uniqueness of these lower bounds are proven. Some real data examples are given to show how these lower bounds can be easily established and to demonstrate their practicality. The method developed here has proven to be extremely useful when using the Weibull distribution in analysis of no-failure or few-failures data. The results are applicable not only in the aerospace industry but anywhere that system reliabilities are high.
Huang, Zhaofeng↗
Lower bound on reliability for Weibull distribution when shape parameter is not estimated accurately
The mathematical relationships between the shape parameter Beta and estimates of reliability and a life limit lower bound for the two parameter Weibull distribution are investigated. It is shown that under rather general conditions, both the reliability lower bound and the allowable life limit lower bound (often called a tolerance limit) have unique global minimums over a range of Beta. Hence lower bound solutions can be obtained without assuming or estimating Beta. The existence and uniqueness of these lower bounds are proven. Some real data examples are given to show how these lower bounds can be easily established and to demonstrate their practicality. The method developed here has proven to be extremely useful when using the Weibull distribution in analysis of no-failure or few-failures data. The results are applicable not only in the aerospace industry but anywhere that system reliabilities are high.
Huang, Zhaofeng↗
Statistical analysis of S—N type environmental fatigue data of Ni-base alloy welds using weibull distribution
In this study, the probabilistic fatigue life model for Ni-base alloys was developed based on the Weibull distribution using statistical analysis of fatigue data reported in NUREG/CR-6909 and the new fatigue data of Alloy 52M/152 and 82/182. The developed Weibull model can consider right-censored data (i.e., non-failed data) and quantify the improved safety (or reliability) based on the level of failure probability. The overall margin in the current fatigue design limit model (ASME design curve + NUREG/CR-6909 F en model) is similar to that of the Weibull model with a cumulative failure probability of approximately 2.5%. The margin in the current fatigue design limit model demonstrated inconsistencies for the Ni-base alloy weld data, whereas the Weibull model showed a consistent margin. Therefore, the Weibull model can systematically mitigate the excessive safety margin.
36 MATERIALS SCIENCE↗
Bayesian estimation of life parameters in the Weibull distribution.
Development of a Bayesian analysis of the scale and shape parameters in the Weibull distribution and the corresponding reliability function with respect to the usual life-testing procedures. For the scale parameter theta, Bayesian estimates of theta and reliability are obtained for the uniform, exponential, and inverted gamma prior probability densities. Bhattacharya's results (1967) for the one-parameter exponential life-testing distribution are reduced to a special case of these results. A fully Bayesian analysis of both the scale and shape parameters is developed by assuming independent prior distributions; since in the latter case, analytical tractability is not possible, Bayesian estimates are obtained through a conjunction of Monte Carlo simulation and numerical-integration techniques. In both cases, a computer simulation is carried out, and a comparison is made between the Bayesian and the corresponding minimum-variance unbiased, or maximum likelihood, estimates. As expected, the Bayesian estimates are superior.
Canavos, G. C.↗
Weibull Distribution From Interval Inspection Data
Most likely failure sequence assumed. Memorandum discusses application of Weibull distribution to statistics of failures of turbopump blades. Is generalization of well known exponential random probability distribution and useful in describing component-failure modes including aging effects. Parameters found from experimental data by method of maximum likelihood.
Rheinfurth, Mario H.↗
Effects of the addition of boron nitride nanoplate on the fracture toughness, flexural strength, and Weibull Distribution of hydroxyapatite composites prepared by spark plasma sintering
Hydroxyapatite (HA) has inherently low fracture toughness and low flexural strength, thus limiting it from wide scale application as an implant material in the biomedical field. To increase the fracture toughness and flexural strength, HA composites were fabricated by adding boron nitride nanoplatelets (BNNP) as reinforcement. Spark plasma sintering was utilized to achieve fine grain structure. The addition of BNNP facilitated grain size refinement. The BNNP reinforced HA composites exhibited increased fracture toughness (2.3 MPa m 1/2 ) and flexural strength (79.79 MPa) of HA over previous published values (1.0 MPa m 1/2 ). Despite that the Weibull Distribution indicated a sacrifice in mechanical reliability, all the composites fabricated in this study showed a low probability of failure and a factor of safety (~ 5.6) that is consistent with that of human bones (~ 6). In addition, the current study provides an approach to statistically design sintering parameters and mechanical loading for fabrication of ceramics.
36 MATERIALS SCIENCE↗
Integrating GLL-Weibull Distribution Within a Bayesian Framework for Life Prediction of Shape Memory Alloy Spring Undergoing Thermo-mechanical Fatigue
The present paper tackles an important but unmapped problem of the reliability estimations of smart materials. First, an experimental setup is developed for accelerated life testing of the shape memory alloy (SMA) springs. Generalized log-linear Weibull (GLL-Weibull) distribution-based novel approach is then developed for SMA spring life estimation. Applied stimulus (voltage), elongation and cycles of operation are used as inputs for the life prediction model. The values of the parameter coefficients of the model provide better interpretability compared to artificial intelligence based life prediction approaches. In addition, the model also considers the effect of operating conditions, making it generic for a range of the operating conditions. Moreover, a Bayesian framework is used to continuously update the prediction with the actual degradation value of the springs, thereby reducing the uncertainty in the data and improving the prediction accuracy. In addition, the deterioration of material with number of cycles is also investigated using thermogravimetric analysis and scanning electron microscopy.
36 MATERIALS SCIENCE↗
Weibull distribution based on maximum likelihood with interval inspection data
The two Weibull parameters based upon the method of maximum likelihood are determined. The test data used were failures observed at inspection intervals. The application was the reliability analysis of the SSME oxidizer turbine blades.
Rheinfurth, M. H.↗
Least Squares Best Fit Method for the Three Parameter Weibull Distribution: Analysis of Tensile and Bend Specimens with Volume or Surface Flaw Failure
Material characterization parameters obtained from naturally flawed specimens are necessary for reliability evaluation of non-deterministic advanced ceramic structural components. The least squares best fit method is applied to the three parameter uniaxial Weibull model to obtain the material parameters from experimental tests on volume or surface flawed specimens subjected to pure tension, pure bending, four point or three point loading. Several illustrative example problems are provided.
Gross, Bernard↗
Table for estimating parameters of Weibull distribution
Table yields best linear invariant /BLI/ estimates for log of reliable life under censored life tests, permitting reliability estimations in failure analysis of items with multiple flaws. These BLI estimates have uniformly smaller expected loss than Gauss-Markov best linear unbiased estimates.
Mann, N. R.↗