Law of Rare Events ◾ 195
e HPP can be described only by exponential law, an oversimplification though.
Constant failure rate, a key assumption in HPP, is too ideal to be true even in the
case of mechanical systems. A bulb, under HPP, will have the same reliability after
burning through 400 hours or any time fixed by the analyst. Physically this is mean-
ingless. Similarly, the physical meaning of a failure rate in a situation shown in Figure
12.2 begs explanation. No software ever operates at a constant failure rate, although
the exponential representation produces such a parameter. It must be borne in mind
that Figure 12.2 has been obtained by numerical curve fitting rather than by using
physically reasonable reliability parameters such as failure rates or MTBF or MTTF.
e bath tub curve, in its entirety, is true for mechanical systems. In the case
of software, failures are constrained to Region 1, which records reliability growth.
Hence, software failure models are called reliability growth models. For both the
cases, we now need the help of NHPP modeling for a more accurate representation
of real world failure patterns.
Nonhomogeneous Poisson Process (NHPP)
Real-life software defect arrival is more complex than simple exponential curves, an
example available in Figure 12.12. It presents a typical defect arrival pattern during
system testing. Approximately 140 defects are discovered over a time span of about
three months. It is not a smooth exponential cumulative distribution. e curve is
0
20
40
60
80
100
120
140
0 20 40 60 80 100
Day of failure
Figure 12.12 Defect arrival pattern—empirical model.