A Misperception in Reliability Growth Modelling

The Duane reliability growth model is
n(t)/t = k t^-alpha (1)
The reliability growth rate is alpha, the downward slope of n(t)/t versus t. It usually varies from 0.2 to 0.6. k is a constant. Crow used a 56-failure data set to illustrate reliability growth.1
A graphical Duane model fit to this data gives
n(t)/t = 0.640 t^-0.283 (2)
A problem in using the Duane-Crow reliability growth model is that it assumes that reliability growth continues and the failure rate decreases throughout the test period. It is more usual that reliability growth stops when the failure rated is low enough. Growth testing is often followed by testing with a low constant failure rate due to rare or uncorrectable failure modes. As more and more low constant rate acceptable failures accumulate after the period of reliability growth, the reliability growth time exponent alpha decreases toward zero. This occurs if constant rate failures are treated as occurring during the reliability growth period. It is more accurate to model a period of initial reliability growth followed by testing without repair to more accurately determine the final constant failure rate. This is done in the abcd model.
n(t)/t = a t^-b + c from t = 0 to td (3)
= c + d after td, where d = a td^-b (4)

The term a t^-b describes the continuous reliability growth that continues out to time td and c is the constant uncorrected failure rate. The parameter d represents an additional constant failure rate due to correctable but uncorrected failure modes. After the reliability growth process is terminated, the failure rate n(t)/t = c + d.