Template:Modified gompertz model: Difference between revisions

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==Modified Gompertz Model==
#REDIRECT [[Gompertz_Models#Modified_Gompertz_Model]]
Sometimes reliability growth data with an S-shaped trend cannot be described accurately by the Gompertz or Logistic (Chapter 8) curves. Since these two models have fixed values of reliability at the inflection points, only a few reliability growth data sets following an S-shaped reliability growth curve can be fitted to them. A modification of the Gompertz curve, which overcomes this shortcoming, is given next [5].
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If we apply a shift in the vertical coordinate, then the Gompertz model is defined by:
 
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::<math>R=d+a{{b}^{{{c}^{T}}}}</math>
 
:where:
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:::::<math>0<a+d\le 1</math>
::::<math>0<b<1,0<c<1,\text{and}T\ge 0</math>
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::<math>R</math> = system's reliability at development time <math>T</math> or at launch number <math>T</math>, or stage number <math>T</math>.
::<math>d</math> = shift parameter.
:<math>d+a</math> = upper limit that the reliability approaches asymptotically as <math>T\to\infty</math>
:<math>d+ab</math> = initial reliability at <math>T=0</math>
::<math>c</math> = growth pattern indicator(small values of <math>c</math> indicate rapid early reliability growth and large values of <math>c</math> indicate slow reliability growth).
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The Modified Gompertz model is more flexible than the original, especially when fitting growth data with S-shaped trends.
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{{parameter estimation gumpz}}
 
{{confidence bounds gompz}}

Latest revision as of 02:14, 27 August 2012

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