Manuals/calci/WEIBULL

WEIBULL(x,alpha,beta,lv)

• $x$ is the value of the function.
• $alpha$ and $beta$ are the parameter of the distribution.
• $lv$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 WEIBULL(x,alpha,beta,lv),x is the value to evaluate the function.
• alpha is the shape parameter of the distribution.beta is the scale parameter of the distribution.
• lv is the logical value which determines the form of the distribution.
• When lv is TRUE, this function gives the value of the cumulative distribution. When lv is FALSE, then this function gives the value of the probability density function.
• When we are not omitting the value of lv, 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 (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: Double exponent: use braces to clarify"): {\displaystyle F(x,\alpha ,\beta )=1-e^{-({\frac {x}{\beta }})}^{\alpha }} .
• The equation for probability density function is:

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: Double exponent: use braces to clarify"): {\displaystyle f(x,\alpha ,\beta )={\frac {\alpha }{\beta ^{\alpha }}}.x^{\alpha -1}.e^{-({\frac {x}{\beta }})}^{\alpha }.}

• When alpha =1, then this function gives the exponentail with λ=1/β.
• This function gives the result as error when

   1. Any one of the argument is non-numeric.
   2. x is negative.
   3.alpha$\leq 0$ or beta <math>\le 0.

WEIBULL(x,alpha,beta,lv), where , and , and .

WEIBULL(x ,a, b, cum)

Where 'x' Is the value at which to estimate the function, 'a'(Alpha) and 'b'(Beta) are the parameters to the distribution, and 'cum' determines the form of the function.

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  This function returns the Weibull distribution.

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• WEIBULL returns the error value, when x, a, b is nonnumeric or x < 0
• WEIBULL returns the error value, when a ≤ 0 or b ≤ 0.
• The equation for the Weibull cumulative distribution function is:

• The equation for the Weibull probability density function is:

• When alpha = 1, WEIBULL returns the exponential distribution with:

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WEIBULL

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Lets see an example,

B

100

25

110

?UNIQ686c29c343f4309c-nowiki-00000004-QINU?

?UNIQ686c29c343f4309c-nowiki-00000005-QINU?

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Syntax

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Remarks

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Examples

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Description

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	Column1	Column2	Column3	Column4
Row1	100	0.088165
Row2	25	0.02104
Row3	110
Row4
Row5
Row6

File:Calci1.gif

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http://store.zcubes.com/33975CA25A304262905E768B19753F5D/Uploaded/25.JPG

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http://store.zcubes.com/33975CA25A304262905E768B19753F5D/Uploaded/26.JPG

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http://store.zcubes.com/33975CA25A304262905E768B19753F5D/Uploaded/27.JPG

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