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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>
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| :where:
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| <br>
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| <br>
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| :::::<math>0<a+d\le 1</math>
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| ::::<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>.
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| ::<math>d</math> = shift parameter.
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| :<math>d+a</math> = upper limit that the reliability approaches asymptotically as <math>T\to\infty</math>
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| :<math>d+ab</math> = initial reliability at <math>T=0</math>
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| ::<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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| <br>
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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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| <br>
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| {{parameter estimation gumpz}}
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| {{confidence bounds gompz}}
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