Participating 
     Organizations 
  Research   
     Topics 
  People 
   

formalWARE 
    results  

  Overview 
  Publications 
  Presentations 
  Tools   
  Methods 
  Examples   
  Training 

formalWARE  
  information  

  Events 
  Index  
  Links   
  Contacts

Abstract:   
This talk will provide an intuitive tutorial of the principles and concepts which are the basis of probability and statistics, especially as needed for software testing.  We will characterize the difference between a population and samples of that population in terms of appropriate statistics (or measures).  Several example probability distributions will be related to the testing problem.  Examples will be given to show why the Normal and Poisson distributions can be used to approximate probability distributions that arise in testing or other practical situations.  The role of adding random variables in this process will be explained.  In conclusion, it will be emphasized that probability and statistics should be considered as just tools, and as such do not dictate the correct answer to any practical problem.  There are different models for many practical problems, and then probability and statistics will give different answers depending upon the model selected for the problem. 
 
Part 2:  Probabilistic Analysis of Software Testing for a Rare Condition   
    
Abstract:   
An industrial problem is discussed and analyzed:  given a rare condition "C", we are interested in statistically modeling the occurrence of the rate of "false positives", i.e., the rate at which the system incorrectly reports that condition C has occurred.  (Of course, we are also interested in the "misclassification" rate, i.e., the rate at which the system misses the detection of condition C when it in fact has occurred).   

The talk will address the following issues:      

•How many tests are required to estimate a probability parameter of 0.01 to within a specified interval with high confidence?  Of 0.001?  Of 0.0001?  
•Two models will be presented for the solution of this problem, illustrating the fact that more than one solution approach may make sense.  
•In the first model, it turns out that the analysis of the false positive rate is essentially the same as that for the misclassification rate.  
•How to quantify the level of confidence that we have in the test results?  
•What assumptions are needed to make the tests representative of normal operations of the system?

.