1. ECE 355: Software Engineering
CHAPTER 11
Part I

2. Course outline Unit 1: Software Engineering Basics
Unit 2: Process Models and Software Life Cycles
Unit 3: Software Requirements
Unit 4: Unified Modeling Language (UML)
Unit 5: Design Basics and Software Architecture
Unit 6: OO Analysis and Design
Unit 7: Design Patterns
 Unit 8: Testing and Reliability
Unit 9: Software Engineering Management and Economics

3. Overview Software Reliability What Is Software Reliability?
Basic concepts
Models

4. Software Reliability What Is Software Reliability? Uses
Defn.: Probability(failure-free op, specified time, given environment)  P(t)
Affected by development process—not ageing/ manufacturing
Uses
Criterion for technology evaluation: expensive
Project management: ready to release? More test?
Size of change: change decreases reliability

5. Basic Concepts Failure and fault Time
Failure: departure of external results of program operation
Fault: cause of failure that is a defect in the code (localized or not)
Time
Execution time (t)
Calendar time (t): meaningful to managers
Characterizing failure occurrence in time
Time of failure: instant
Time interval between failures
Cumulative failures up to a given time
Failures in a time interval

6. Basic Concepts Software System Random process Failure behavior:
- # of faults in the SW
- Exec environment (run types)
Failures
Average Total Number of Failures: μ(τ),
Failure Intensity – Number of Failures per time unit : λ(τ)
Mean Time to Failure 1/λ(τ)

7. Reliability Models (of Musa)
Assumptions
Two models
Basic
Logarithmic
Diff: Change in failure intensity per failure seen
Basic: decrement is constant
Logarithmic: decrement reduces

8. Assumptions for the Basic Reliability Model
Faults are independent and distributed with constant rate of encounter
Well mixed types of instructions execution time between failures is large compared to instruction execution time
Test space covers use space
Tests selected from a complete set of use input sets
Set of inputs for each run selected randomly
All failures are observed implied by our definition of failure
Fault causing failure is corrected immediately otherwise reoccurrence of that failure is not counted

9. Basic (Linear) Model
Assumption: decrement in failure intensity function derivative w.r.t. number of expected failures) is constant
Consequence: failure intensity is function of average number of failures experienced at any given point in time failure probability

10. Logarithmic Model Decrement per encountered failure decreases
Θ is a failure intensity decay parameter
Comparison of models:
Basic model assumes that there is a failure intensity - logarithmic model assumes convergence to 0 failure intensity
Basic model assumes a finite number of failures in the system - logarithmic model assumes infinite number

11. Reliability Models Basic model Logarithmic model l(m) = l0[1 - m/v0]
l(m) = l0exp(-qm)
q: failure intensity decay
λ: Failure intensity
λ0: Initial failure intensity
at start of execution
μ: Average total number of
failures at a given point
in time
v0: Total number of failures
over infinite time
Initial failure intensity, l0
l: failure intensity
Basic
Log. v0
m: Mean failures exp.

12. Reliability Models Basic model Logarithmic model
m(t) = v0[1 – exp(-l0t/v0)]
m(t) = (1/q).ln(l0qt + 1)
l(t) = l0/(l0qt + 1)
l(t) = l0exp(-l0t/v0) l m
Log.
Log. v0
Basic
Basic t t

13. Reliability Models
Example: Assume that a program will experience 100 failures in infinite time.
The initial failure intensity was 10 failures/CPU-hr, the
present failure intensity is 3.68 failures/CPU-hour and our
objective intensity is failure/CPU-hr.
Predict the additional testing time to achieve the stated objective.
Ans.: We know that l(t) = l0exp(-l0t/v0)
At time t1, l(t1) = l0exp(-l0t1/v0) = lp
At time t2, l(t2) = l0exp(-l0t2/v0) = lf
t2 - t1 = (v0/ l0).ln(lp/ lf)
v0 = 100 faults, l0 = 10 failures/CPU-hr
lp = 3.68 failures/CPU-hr, lf = failure/CPU-hr
Testing time = (t2 - t1 ) = 90 CPU-hr