General Examples Using the Gompertz Models
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General Examples Using the Gompertz Models |
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The Gompertz reliability growth model is often used when analyzing reliability data. It is most applicable when the data set follows a smooth curve, as shown in Figure 7.1. The Gompertz model is mathematically given by [1]:
(1)
where:
the system's reliability at development time, launch number or stage number, 
.
the upper limit that the reliability approaches asymptotically as 
, or the maximum reliability that can be attained.
initial reliability at 
the growth pattern indicator (small values of 
indicate rapid early reliability growth and large values of 
indicate slow reliability growth).
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Figure 7.1: Reliability growth data following a smooth curve |
As it can be seen from the mathematical definition, the Gompertz model is a 3-parameter model with the parameters 
, 
and 
. The solution for the parameters, given 
and 
, is accomplished by fitting the best possible line through the data points. Many methods are available; all of which tend to be numerically intensive. When analyzing reliability data in RGA, you have the option to enter the reliability values in percent or in decimal format. However, 
will always be returned in decimal format and not in percent. The estimated parameters in RGA are unitless. The next section presents an overview and background on some of the most commonly used algorithms/methods for obtaining these parameters.
Note that this discussion describes the application of the model for the Reliability data type but the Standard Gompertz model also can be applied for discrete (success/failure) data. For more information, refer to Using the Gompertz Model for Discrete Data.
