Difference between revisions of "Manuals/calci/WEIBULL"
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| − | <div style="font-size:30px">'''WEIBULL( | + | <div style="font-size:30px">'''WEIBULL (Number,Alpha,Beta,Cumulative) '''</div><br/> |
| − | *<math> | + | *<math>Number </math> is the value of the function. |
| − | *<math> | + | *<math>Alpha </math> and <math> Beta </math> are the parameter of the distribution. |
| − | *<math> | + | *<math>Cumulative</math> is the logical value. |
| + | **WEIBULL(),returns the Weibull distribution. | ||
==Description== | ==Description== | ||
| Line 10: | Line 11: | ||
*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( | + | *In <math>WEIBULL(Number,Alpha,Beta,Cumulative)</math>,<math> Number </math> is the value to evaluate the function. |
| − | *<math> | + | *<math> Alpha </math> is the shape parameter of the distribution.<math> Beta </math> is the scale parameter of the distribution. |
| − | *<math> | + | *<math>Cumulative</math> is the logical value which determines the form of the distribution. |
| − | *When <math> | + | *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> | + | *When we are not omitting the value of <math>Cumulative</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. | ||
*This function gives the value of 2-parameter weibull distribution by setting the third parameter (location parameter) is zero. | *This function gives the value of 2-parameter weibull distribution by setting the third parameter (location parameter) is zero. | ||
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*If alpha=1, then the failure rate of the device is constant 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. | *If alpha>1, then the failure rate of the device increases over time. | ||
| − | *The equation for cumulative distribution function is: <math>F(x,\alpha,\beta) = 1-e^-{(\frac{x}{ | + | *The equation for cumulative distribution function is: <math>F(x,\alpha,\beta)</math> =<math>1-e^-{(\frac{x}{\beta})}^\alpha</math>. |
*The equation for probability density function is: | *The equation for probability density function is: | ||
<math>f(x,\alpha,\beta) = \frac{\alpha}{\beta^\alpha}.x^{\alpha-1}.e^-{(\frac{x}{\beta})}^\alpha.</math> | <math>f(x,\alpha,\beta) = \frac{\alpha}{\beta^\alpha}.x^{\alpha-1}.e^-{(\frac{x}{\beta})}^\alpha.</math> | ||
| Line 26: | Line 27: | ||
*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. | + | 2. Number is negative. |
| − | 3. | + | 3. Alpha<math>\le 0</math> or Beta <math>\le 0</math> |
==Examples== | ==Examples== | ||
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#= WEIBULL(10.5,2.1,5.3,TRUE) = 0.9850433821261 | #= WEIBULL(10.5,2.1,5.3,TRUE) = 0.9850433821261 | ||
#=WEIBULL(10.5,2.1,5.3,FALSE) = 0.0125713406729 | #=WEIBULL(10.5,2.1,5.3,FALSE) = 0.0125713406729 | ||
| + | |||
| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|mMo0Nvqq3qA|280|center|Weibull Probability}} | ||
==See Also== | ==See Also== | ||
*[[Manuals/calci/EXPONDIST | EXPONDIST ]] | *[[Manuals/calci/EXPONDIST | EXPONDIST ]] | ||
| − | *[[Manuals/calci/ | + | *[[Manuals/calci/LOGNORMDIST | LOGNORMDIST ]] |
==References== | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Weibull_distribution Weibull distribution] | ||
| + | |||
| + | |||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | |||
| + | *[[ Z3 | Z3 home ]] | ||
Latest revision as of 16:32, 10 August 2018
WEIBULL (Number,Alpha,Beta,Cumulative)
- is the value of the function.
- and are the parameter of the distribution.
- is the logical value.
- WEIBULL(),returns the Weibull distribution.
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
or Beta Examples
- =WEIBULL(202,60,81,TRUE) = 1
- =WEIBULL(202,60,81,FALSE) = 0
- =WEIBULL(160,80,170,TRUE) = 0.00779805060
- =WEIBULL(160,80,170,FALSE) = 0.0038837823333
- = WEIBULL(10.5,2.1,5.3,TRUE) = 0.9850433821261
- =WEIBULL(10.5,2.1,5.3,FALSE) = 0.0125713406729
Related Videos
See Also
References