Template:Lambda-beta parameter relationship - Revision history

Richard House: Redirected page to Reliability Growth Planning#Lambda - Beta Parameter Relationship

2012-08-27T01:48:46Z

Redirected page to Reliability Growth Planning#Lambda - Beta Parameter Relationship

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	~~====Lambda~~ - ~~Beta Parameter Relationship====~~		#REDIRECT [[Reliability_Growth_Planning#Lambda_-_Beta_Parameter_Relationship]]
	~~<br>~~
	Under the Crow-AMSAA (NHPP) model, the time to first failure is a Weibull random variable. The MTTF of a Weibull distributed random variable with parameters <math>\beta </math> and <math>\eta </math> is:


	~~::<math>MTTF=\eta \cdot \Gamma \left( 1+\frac{1}{\beta } \right)</math>~~


	~~The parameter lambda is defined as:~~


	~~::<math>\lambda =\frac{1}{{{\eta }^{\beta }}}</math>~~


	~~Using Eqn. (lambda eta relationship), the MTTF relationship shown in Eqn. (Weibull MTTF) becomes:~~


	~~::<math>MTB{{F}_{B}}=\frac{\Gamma \left( 1+\tfrac{1}{\beta } \right)}{{{\lambda }^{\left( \tfrac{1}{\beta } \right)}}}</math>~~


	~~Or, in terms of failure intensity:~~


	~~::<math>{{\lambda }_{B}}=\frac{{{\lambda }^{\left( \tfrac{1}{\beta } \right)}}}{\Gamma \left( 1+\tfrac{1}{\beta } \right)}</math>~~

Nicolette Young: Created page with '====Lambda - Beta Parameter Relationship====
Under the Crow-AMSAA (NHPP) model, the time to first failure is a Weibull random variable. The MTTF of a Weibull distributed ran…'

2012-01-10T21:49:36Z

Created page with '====Lambda - Beta Parameter Relationship==== <br> Under the Crow-AMSAA (NHPP) model, the time to first failure is a Weibull random variable. The MTTF of a Weibull distributed ran…'

New page

====Lambda - Beta Parameter Relationship====
<br>
Under the Crow-AMSAA (NHPP) model, the time to first failure is a Weibull random variable. The MTTF of a Weibull distributed random variable with parameters <math>\beta </math> and <math>\eta </math> is:

::<math>MTTF=\eta \cdot \Gamma \left( 1+\frac{1}{\beta } \right)</math>

The parameter lambda is defined as:

::<math>\lambda =\frac{1}{{{\eta }^{\beta }}}</math>

Using Eqn. (lambda eta relationship), the MTTF relationship shown in Eqn. (Weibull MTTF) becomes:

::<math>MTB{{F}_{B}}=\frac{\Gamma \left( 1+\tfrac{1}{\beta } \right)}{{{\lambda }^{\left( \tfrac{1}{\beta } \right)}}}</math>

Or, in terms of failure intensity:

::<math>{{\lambda }_{B}}=\frac{{{\lambda }^{\left( \tfrac{1}{\beta } \right)}}}{\Gamma \left( 1+\tfrac{1}{\beta } \right)}</math>

Template:Lambda-beta parameter relationship - Revision history

Richard House: Redirected page to Reliability Growth Planning#Lambda - Beta Parameter Relationship

Nicolette Young: Created page with '====Lambda - Beta Parameter Relationship==== Under the Crow-AMSAA (NHPP) model, the time to first failure is a Weibull random variable. The MTTF of a Weibull distributed ran…'

Nicolette Young: Created page with '====Lambda - Beta Parameter Relationship====
Under the Crow-AMSAA (NHPP) model, the time to first failure is a Weibull random variable. The MTTF of a Weibull distributed ran…'