Software Reliability Models

1
Software Reliability Models

• Ph.D Student Seminar
• Monday September 18, 2006

2
Why Software Reliability?

• Increased control by software
• Increase of size and complexity of software
• Critical software failures
• Ariane 5 1996
• Phone network outage 1991
• Therac 25 1985-1986
• Software reliability - one of the attributes of
  software quality
• Software reliability - one of the system
  dependability
• Software reliability - an essential ingredient in
  customer satisfaction

3
Hardware Reliability Vs. SR
4
What is Software Reliability?

• The probability of failure-free software
  operation for a specified period of time in a
  specified environment.
• ANSI 1991

5
SR Measures

• Cumulative failure function
• The probability of failure by time t
• Mean-value function
• The expected number of failures experienced
  by time t according to the model
• Reliability Function
• The probability that the time to failure is
  larger than t

6
SR Measures

• Hazard rate function
• The conditional probability that a failure
  per unit time occurs in the intervals given that
  a failure has not occurred before t.
• Mean Time To Failure (MTTF)
• The expected time during which the system
  will function successfully without maintenance or
  repair
• Failure intensity function
• the instantaneous rate of change of the
  expected number of failures with respect to time.

7
Why Software Reliability Modeling?

• Predict probability of failure of a component or
  system
• Estimate the mean time to the next failure
• Predict number of (remaining) failures

8
Model Classification

• Musa and okumoto 83
• Time domain wall clock vs. execution time
• Category total number of failures (finite or
  infinite)
• Type Distribution of number of failures
  (Poisson, binomial)
• Class (finite) functional form of the failure
  intensity expressed in terms of time
• Family (infinite) functional form of the failure
  intensity function expressed in terms of the
  expected number of failure

9
Model Classification
10
Model Classification
11
Standard (basic) Assumptions for Exponential
Models

• The software is operated in a similar manner as
  that in which reliability predictions are to be
  made.
• Every fault has the same chance to of being
  encountered
• The failures are independent.

0
t
12
Perfect Fix (Debugging)

• Perfect Debugging
• Defects are removed certainly and instantaneously
• No new defects are introduced during debugging.

13
Jelinski-Moranda Model (1972)

• Assumptions
• Initial defects N, an unknown but fixed constant
• The failure rate during a failure interval is
  constant and is proportional ( ) to the
  number of remaining defect
• Perfect debugging
• Data Requirements
• Actual failure times t1, t2, , tn
• Elapsed time between failures xi ti ti-1

14
Jelinski-Moranda Model (1972)

• Estimation

Z(t)
n Number of faults observed Xi fault observed
in I interval N total number of faults
Cumulative time
15
SR Tools (SMERFS3)
16
Musas Model (1975)

• Times between failures are expressed in CPU time
  (1st component)
• The ability to convert the execution time results
  to calendar time (2nd component)

17
Musas Basic Execution Model (1975)

• Assumptions
• Cumulative number of failures by time t follows a
  Poisson process.
• Mean value function
• where total number of detected faults
• failure rate
• Failure intensity function
• Hazard rate for a single fault is constant

18
Musas Model (1975)

• Estimate

Failure Intensity
n Number of faults observed x elapsed time
without failure failure at time t failure
rate Total number of failures
Execution Time
19
SR Tools (SMERFS3)
20
Goel-Okumoto Model (1979)

• Non-Homogenous Poisson Process (NHPP)
• Assumes that the cumulative number of failures
  detected at any time follows a Poisson
  distribution.
• Time intervals can be unequal

21
Goel-Okumoto Model (1979)

• Assumptions
• The mean value function ( )has the boundary
  conditions
• and
• The number of failures that occur in
  with
• Is proportional to the expected number of
  undetected faults
• The constant proportionality is b
• Data Requirements
• Fault counts on each testing interval f1, f2, ,
  fn
• Cumulative completion time of each period t1,
  t2, , tn

22
Goel-Okumoto Model (1979)

• Estimation

n Number of faults observed b Failure rate
failure at time t
23
Generalized exponential model (AIAA 1993)

• Simplify the modeling process
• Single set of equations to represent number of
  models

Z(.) Hazard rate t time or resource
variable measuring the progress of the project K
constant of proportionality initial
number of faults in SW number of faults
thats been found and corrected after t