Law of Rare Events ◾ 201
Review Questions
1. Relate the Poisson distribution to the exponential distribution.
2. How does the nonhomogeneous Poisson process (NHPP) differ from homo-
geneous Poisson process (HPP)?
3. Why is the exponential distribution considered as a fundamental engineering
curve?
4. How does carbon dating illustrate a fundamental application of the exponen-
tial distribution followed by nature?
5. How did the Prussian cavalrymen death data prove that the Poisson distribu-
tion works?
Exercises
1. Applying the Goel–Okumoto NHPP model defined in Equation 12.8, given
that b = 0.04, estimate time t to reach a reliability level of 0.95. Let us denote
this time as t
95
.
2. Apply Equation 12.9 and find out the probability of finding two defects at
a point of time = t
95
. Clue: substitute x = 2 in Equation 12.9. Also consult
Figure 12.13 for understanding the problem.
3. If the average defects per module = 0.4, find the right first-time index of the
application.
Clue 1: RFT is the probability of getting zero defects in a module during
testing.
Clue 2: Use Excel function POISSON.DIST to calculate this number.
4. Let us take the example of testing 100 components in an application. e
average defect per module is 0.2. What is the upper control limit on a quality
control chart for the components?
5. Assume the Power Law for NHPP. e constant b = 0.5. e failure rate of
an application is 5 defects per week immediately after release. What would be
the failure rate in the fifth week?
Using the mean values, intertribal times have been fitted to exponential
distributions. e researchers find a good fit between the actual data and
exponential fit, except in the case of triples.
Overall, this is a very good illustration of building Poisson and exponen-
tial models for rare events.
202 ◾ Simple Statistical Methods for Software Engineering
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