This article deals with the Bayesian inference of the unknown parameters of the Weibull distribution based on the left truncated and right censored data. It is assumed that the scale parameter of the Weibull distribution has a gamma prior. The shape parameter may be known or unknown. If the shape parameter is unknown, it is assumed that it has a very general log-concave prior distribution. When...

The design of a new adaptive version the multiple dependent state (AMDS) sampling plan is presented based on time truncated life test under Weibull distribution. We achieved proposed by applying concept double and existing plans. A warning sign for acceptance number was to increase probability current lot acceptance. optimal parameters were determined simultaneously with nonlinear optimization ...

The Weibull distribution is a very popular distribution for modeling lifetime data. Left truncation and right censoring are often observed in lifetime data. Here, the EM algorithm is applied to estimate the model parameters of the Weibull distribution fitted to data containing left truncation and right censoring. The maximization part of the EM algorithm is carried out using the EM gradient alg...

We report a statistical analysis of some highly infected countries by the novel coronavirus (COVID-19). The cumulative data were fitted with various growth models (e.g. Logistic equation, Weibull equation and Hill equation) obtained power index top ten countries. newly Gaussian distribution peak at ~40 days for whose infection curves are seem to be saturated. similarity in kinetics people diffe...

We exhibit a new stability property of Weibull tail-distributions. It is shown that the power of a random variable with a Weibull tail-distribution still has a Weibull tail-distribution and the associated Weibull tail-coefficient is exhibited. Weibull tail-distributions are defined through their distribution function by:

This report explains Weibull plotting and its rationale. It shows how the two Weibull parameter estimates are easily read off from the Weibull plot. The use of Weibull plotting is introduced first in the context of complete samples and then extended to two common forms of censoring: type I or multiple censoring and type II censoring. Two blank Weibull plotting templates are provided, one for a ...

Modeling of microbial inactivation by high hydrostatic pressure (HHP) requires a plot of the log microbial count or survival ratio versus time data under a constant pressure and temperature. However, at low pressure and temperature values, very long holding times are needed to obtain measurable inactivation. Since the time has a significant effect on the cost of HHP processing it may be reasona...

This paper addresses the void fraction of polydisperse particles with a Weibull (or Rosin-Rammler) size distribution. It is demonstrated that the governing parameters of this distribution can be uniquely related to those of the lognormal distribution. Hence, an existing closed-form expression that predicts the void fraction of particles with a lognormal size distribution can be transformed into...

One method of calculating the parameters of the Weibull distribution is by using probability plotting. To better illustrate this procedure, consider the following example from Kececioglu [18]. Example 1 Assume that six identical units are being reliability tested at the same application and operation stress levels. All of these units fail during the test after operating the following number of ...