Template:Mixed weibull distribution: Difference between revisions

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{{introduction of weibull distribution}}
#REDIRECT [[The_Mixed_Weibull_Distribution]]
 
{{background of weibull distribution}}
 
{{mixed weibull parameter estimation}}
 
===Using the Mixed Weibull Distribution in Weibull++===
 
[[Image:2subpopmixedweibull.png|thumb|center|400px]]  
 
To use the mixed Weibull distribution, simply select the Mixed option under Parameters/Type, and click the Calculate icon. A window will appear asking you which form of the mixed Weibull you would like to use, i.e. S = 2, 3 or 4. In other words, How many subpopulations would you like to consider? 
 
Simply select the number of subpopulations you would like to consider and click OK. The application will automatically calculate the parameters of each subpopulation for you.
 
'''Viewing the Calculated Parameters'''
 
When using the Mixed Weibull option, the parameters given in the result area apply to different subpopulations. To view the results for a particular subpopulation, select the subpopulation, as shown next.
 
[[Image:subpop1.png|thumb|center|400px| ]]
 
[[Image:subpop2.png|thumb|center|400px| ]]
 
 
'''About the Calculated Parameters'''
 
Weibull++ uses the numbers 1, 2, 3 and 4 (or first, second, third and fourth subpopulation) to identify each subpopulation. These are just designations for each subpopulation, and they are ordered based on the value of the scale parameter,  <math>\eta </math> . Since the equation used is additive or:
 
::<math>{{R}_{1,..,S}}(T)=\underset{i=1}{\overset{S}{\mathop \sum }}\,\frac{{{N}_{i}}}{N}{{e}^{-{{\left( \tfrac{T}{{{\eta }_{i}}} \right)}^{{{\beta }_{i}}}}}}</math>
 
the order of the subpopulations which are given the designation 1, 2, 3, or 4 is of no consequence. For consistency, the application will always return the order of the results based on the magnitude of the scale parameter.
 
===Mixed Weibull, Other Uses===
====Reliability Bathtub Curves====
A reliability bathtub curve is nothing more than the graph of the failure rate versus time, over the life of the product. In general, the life stages of the product consist of early, chance and wear-out. Weibull++ allows you to plot this by simply selecting the failure rate plot, as shown next.
 
[[Image:ldachp10fig5.gif|thumb|center|500px| ]]
 
====Determination of the Burn-in Period====
If the failure rate goal is known, then the burn-in period can be found from the failure rate plot by drawing a horizontal line at the failure rate goal level and then finding the intersection with the failure rate curve. Next, drop vertically at the intersection, and read off the burn-in time from the time axis. This burn-in time helps insure that the population will have a failure rate that is at least equal to or lower than the goal after the burn-in period. The same could also be obtained using the Function Wizard and generating different failure rates based on time increments. Using these generated times and the corresponding failure rates, one can decide on the optimum burn-in time versus the corresponding desired failure rate.
 
{{Example:2Subpop Mixed Weibull}}

Latest revision as of 00:28, 15 August 2012

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