Manuals/calci/WEIBULL

WEIBULL (Number,Alpha,Beta,Cumulative)

• $Number$ is the value of the function.
• $Alpha$ and $Beta$ are the parameter of the distribution.
• $Cumulative$ is the logical value.
  • WEIBULL(),returns the Weibull distribution.

Description

• This function gives the value of the weibull distribution with 2-parameters.
• It is a continuous probability distribution.
• Weibull distribution also called Rosin Rammler distribution.
• It is used to model the lifetime of technical devices and is used to describe the particle size distribution of particles generated by grinding, milling and crushing operations.
• This distribution is closely related to the lognormal distribution.
• In $WEIBULL(Number,Alpha,Beta,Cumulative)$,$Number$ is the value to evaluate the function.
• $Alpha$ is the shape parameter of the distribution.$Beta$ is the scale parameter of the distribution.
• $Cumulative$ is the logical value which determines the form of the distribution.
• When $Cumulative$ is TRUE, this function gives the value of the cumulative distribution. When $Cumulative$ is FALSE, then this function gives the value of the probability density function.
• When we are not omitting the value of $Cumulative$, then it consider as FALSE.
• Weibull distribution is of two type :3-parameter weibull distribution and 2-parameter weibull distribution.
• This function gives the value of 2-parameter weibull distribution by setting the third parameter (location parameter) is zero.
• Also if alpha<1,then the failure rate of the device decreases over time.
• If alpha=1, then the failure rate of the device is constant over time.
• If alpha>1, then the failure rate of the device increases over time.
• The equation for cumulative distribution function is: $F(x,\alpha ,\beta )$ =$1-e^{-}{({\frac {x}{\beta }})}^{\alpha }$.
• The equation for probability density function is:

$f(x,\alpha ,\beta )={\frac {\alpha }{\beta ^{\alpha }}}.x^{\alpha -1}.e^{-}{({\frac {x}{\beta }})}^{\alpha }.$

• When alpha =1, then this function gives the exponential with $\lambda ={\frac {1}{\beta }}$.
• This function gives the result as error when

   1. Any one of the argument is non-numeric.
   2. Number is negative.
   3. Alpha$\leq 0$ or Beta $\leq 0$

Examples

1. =WEIBULL(202,60,81,TRUE) = 1
2. =WEIBULL(202,60,81,FALSE) = 0
3. =WEIBULL(160,80,170,TRUE) = 0.00779805060
4. =WEIBULL(160,80,170,FALSE) = 0.0038837823333
5. = WEIBULL(10.5,2.1,5.3,TRUE) = 0.9850433821261
6. =WEIBULL(10.5,2.1,5.3,FALSE) = 0.0125713406729

Related Videos

Weibull Probability

See Also

• EXPONDIST
• LOGNORMDIST

References

• Weibull distribution

• List of Main Z Functions

• Z3 home