Gompertz Models (Standard and Modified)Gompertz Models (Standard and Modified)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:
R
= the system's reliability at development time, launch number or stage
number, T.
a
= the upper limit that the reliability approaches
asymptotically as 
, or the maximum reliability
that can be attained.
ab
= initial reliability at T
= 0.
c
= the growth pattern indicator (small values of c
indicate rapid early reliability growth and large values of c
indicate slow reliability growth).
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 a, b and c. The solution for the parameters, given Ti and Ri, 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, a will always be returned in decimal format and not in percent. The estimated parameters in RGA are unitless. The Parameter Estimation for the Gompertz Models Using Least Squares in Nonlinear Regression section of this on-line reference presents an overview and background on some of the most commonly used algorithms/methods for obtaining these parameters.
This chapter includes the following sections:
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