TABLE OF CONTENTS The S-shaped reliability growth curve, such as shown in Figs. 16.3 and 16.4 (Type 2), is used to describe the reliability growth trend with a lower rate of debugging and growth at the early stage and a higher rate later on as good fixes are found and implemented. In some situations, it is unreasonable to set a high growth rate of improvement during the early stages of development for Complex systems because of the difficulty of identifying the sources and Causes of the failures, hence requiring the use of S-shaped reliability growth curves. In this section, models having S-shaped reliability growth curves are given and their use is illustrated by examples.
The Gompertz curve given by Eq. (16.1) may be S-shaped if it has a point of inflection, 
. which is positive. This can be determined by setting the second derivative of Eq. (16.1) to zero; i.e.
| (16.15) |  |
Solving for T a yields, 
, or
| (16.16) |  |
where
Also, the growth rate
| (16.17) |  |
is positive for all values of T a because 0 < b < 1 and 0 < c < 1. When 
, then d 2 R / 
< 0; hence reliability increases at an increasing rate. When 
, then d 2 R / 
> 0; hence reliability increases at a decreasing rate. This means that the Gompertz curve may be S-shaped.
Since the domain...
