The Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent the usual states of a system after a repair: as new, as old, or in a condition between new and old. It is often coupled with the Weibull distribution, widely used in the reliability context. In this paper, we develop novel GRP models based on probability distributions that stem from the Tsal...

Two important wood properties are the modulus of elasticity (MOE) and the modulus of rupture (MOR). In the past, the statistical distribution of the MOE has often been modeled as Gaussian, and that of the MOR as lognormal or as a twoor three-parameter Weibull distribution. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior of MOE and MOR for the purp...

The typical experimental procedure for testing stress corrosion cracking initiation involves an interval-censored reliability test. Based on these test results, the parameters of a Weibull distribution, which is a widely accepted crack initiation model, can be estimated using maximum likelihood estimation or median rank regression. However, it is difficult to determine the appropriate number of...

It is known that the single-modal Weibull model describes well the size effect of brittle fiber tensile strength. However, some ceramic fibers have been reported that single-modal Weibull model provided biased estimation on the gauge length dependence. A hypothesis on the bias is that the density of critical defects is very small, thus, fracture probability of small gauge length samples distrib...

Recently, several attempts have been made to define new models that extend well-known distributions and at the same time provide great flexibility in modelling real data. We propose a new four-parameter model named the Weibull-power function (WPF) distribution which exhibits bathtub-shaped hazard rate. Some of its statistical properties are obtained including ordinary and incomplete moments, qu...

The authors will demonstrate how a major Chemical Process company has successfully utilized this new technique to answer questions such as: 1. Do I have a reliability problem or a production problem? 2. What is the demonstrated capacity of my plant? 3. What are efficiency/utilization losses costing me? 4. What is the reliability of my process plant? The Weibull technique described has helped th...

Minnesord över Jörgen Weibull.

In this paper we propose a mixture of two different distributions such as Exponential-Gamma, Exponential-Weibull and Gamma-Weibull to model heterogeneous survival data. Various properties of the proposed mixture of two different distributions are discussed. Maximum likelihood estimations of the parameters are obtained by using the EM algorithm. Illustrative example based on real data are also g...

The statistics of texture operators on natural images are empirically determined to conform to a Weibull process. We explain these findings from the physical principles of fragmentation processes. The Weibull parameters are known to indicate the fractal dimension of the underlying system. Hence, we show the Weibull process to have a physical foundation for describing natural image statistics. K...

Weibull distribution was used to fit tree diameter data collected from 86 sample plots located in Chinese pine stand in Beijing. To estimate the Weibull distribution parameters, three methods [namely maximum likelihood estimation method (MLE), method of moment (MOM) and least-squares regression method (LSM)] were compared and evaluated on the basis of the mean square error (MSE) and sample size...