Difference between revisions of "Manuals/calci/WEIBULL"

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<div style="font-size:30px">'''WEIBULL(x,alpha,beta,lv)'''</div><br/>
 
<div style="font-size:30px">'''WEIBULL(x,alpha,beta,lv)'''</div><br/>
*<math>x </math>  is the value of the function.
+
(Number,Alpha,Beta,Cumulative)
*<math>alpha </math> and <math> beta </math> are the parameter of the distribution.
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*<math>Number </math>  is the value of the function.
*<math>lv</math> is the logical value.
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*<math>Alpha </math> and <math> Beta </math> are the parameter of the distribution.
 +
*<math>Cumulative</math> is the logical value.
  
 
==Description==
 
==Description==
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*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.  
 
*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.  
 
*This distribution is closely related to the lognormal distribution.  
*In <math>WEIBULL(x,alpha,beta,lv)</math>,<math> x </math> is the  value to evaluate the function.
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*In <math>WEIBULL(Number,Alpha,Beta,Cumulative)</math>,<math> Number </math> is the  value to evaluate the function.
*<math> alpha </math> is the shape parameter of the distribution.<math> beta </math> is the scale parameter of the distribution.
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*<math> Alpha </math> is the shape parameter of the distribution.<math> Beta </math> is the scale parameter of the distribution.
*<math>lv</math> is the logical value which determines the form of the distribution.  
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*<math>Cumulative</math> is the logical value which determines the form of the distribution.  
*When <math>lv</math> is TRUE, this function gives the value of the cumulative distribution. When <math>lv</math> is FALSE, then this function gives the value of the probability density function.  
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*When <math>Cumulative</math> is TRUE, this function gives the value of the cumulative distribution. When <math>Cumulative</math> is FALSE, then this function gives the value of the probability density function.  
 
*When we are not omitting the value of <math>lv</math>, then it consider as FALSE.  
 
*When we are not omitting the value of <math>lv</math>, then it consider as FALSE.  
 
*Weibull distribution is of two type :3-parameter weibull distribution and 2-parameter weibull distribution.  
 
*Weibull distribution is of two type :3-parameter weibull distribution and 2-parameter weibull distribution.  
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*This function gives the result as error when
 
*This function gives the result as error when
 
     1. Any one of the argument is non-numeric.
 
     1. Any one of the argument is non-numeric.
     2. x is negative.
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     2. Number is negative.
     3. alpha<math>\le 0</math> or beta <math>\le 0</math>
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     3. Alpha<math>\le 0</math> or Beta <math>\le 0</math>
  
 
==Examples==
 
==Examples==

Revision as of 16:00, 18 June 2018

WEIBULL(x,alpha,beta,lv)


(Number,Alpha,Beta,Cumulative)

  • 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: =.
  • 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. Number is negative.
   3. Alpha or Beta 

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

References