Process capability indices (PCIs) are used to measure process potential and performance. This study constructs an uniformly minimum variance unbiased estimator (UMVUE) of the lifetime performance index based on the upper record values for Weibull lifetime model. Then the UMVUE of the lifetime...

The method of probability-weighted moments is used to derive estimators of parameters and quantiles of the three-parameter Weibull distribution. The properties of these estimators are studied. The results obtained are compared with those obtained by using the method of maximum likelihood. The...

The Weibull family is widely used to model failure data, or lifetime data, although the classical two-parameter Weibull distribution is limited to positive data and monotone failure rate. The parameters of the Weibull model are commonly obtained by maximum likelihood estimation; however, it is...

We compare the small sample performance (in terms of bias and root mean squared error) of L-moment estimator of 3-parameter Weibull distribution with Maximum likelihood Estimation (MLE), Moment Estimation (MoE), Least squared estimation (LSE), the Modified MLE (MMLE), Modified MoE (MMoE), and...

In this paper, we present a Bayesian analysis for the Weibull proportional hazard (PH) model used in step-stress accelerated life testings. The key mathematical and graphical difference between the Weibull cumulative exposure (CE) model and the PH model is illustrated. Compared with the CE...

Estimating equation approaches have been widely used in statistics inference. Important examples of estimating equations are the likelihood equations. Since its introduction by Sir R. A. Fisher almost a century ago, maximum likelihood estimation (MLE) is still the most popular estimation method...

Maximum likelihood parameter estimation becomes easy by augmenting the parameter space of the probability distribution. A newly proposed extended model of the four-parameter generalized gamma distribution includes the three-parameter generalized extreme-value distribution which includes the...

This paper proposes, implements, and evaluates an original discretization method for estimating the reliability of systems for which stress and strength are defined as complex functions of continuous random variables, when reliability is not derivable through common analytic techniques. This...

The two parameters of a Weibull density distribution function were calculated for three different locations; a city area, an extremely exposed area in a city centre and an open sea area in Hong Kong. A long-term data source, consisting of thirty years (1968–1997) of hourly mean wind data, was...

A wind energy system converts the kinetic energy of the wind into mechanical or electrical energy that can be harnessed for practical uses and transform the economy of rural areas where access to water and electricity is very restricted and industry is almost nonexistent in most of the...