Manuals/calci/WEIBULL

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WEIBULL(x,alpha,beta,lv)


  • is the value of the function.
  • and are the parameter of the distribution.
  • is the logical value.

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 , is the value to evaluate the function.
  • is the shape parameter of the distribution. is the scale parameter of the distribution.
  • is the logical value which determines the form of the distribution.
  • When is TRUE, this function gives the value of the cumulative distribution. When is FALSE, then this function gives the value of the probability density function.
  • When we are not omitting the value of , 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: Failed to parse (syntax error): {\displaystyle F(x,\alpha,\beta) = 1-e^-{(\frac{x}{β})}^α}
  • The equation for probability density function is:

  • When alpha =1, then this function gives the exponential with .
  • This function gives the result as error when
   1. Any one of the argument is non-numeric.
   2. x is negative.
   3. alpha or beta <math>\le 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

See Also

References