Using Excel to Implement Software Reliability Models

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Using Excel to Implement Software Reliability
Models

• Norman F. Schneidewind
• Naval Postgraduate School
• 2822 Racoon Trail,
• Pebble Beach, California, 93953, USA
• Voice [phone]
• Fax [phone]
• nschneid_at_nps.navy.mil

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Outline

• Introduction
• Characteristics of Excel Implementation
• Combined Software Reliability Tools Excel
  Approach
• Structure of Combined Approach
• Notation for Prediction Worksheet
• Equations for Prediction and Comparison
  Worksheets
• Example Prediction Worksheet
• Analysis of Prediction Worksheet
• Notation for Actual Prediction Comparisons
  Worksheet
• Example Actual Prediction Comparisons Worksheet
• Analysis of Comparison Worksheet
• Cumulative Failure Prediction Plots
• Validation of Failure Count Predictions
• Time to Failure Plot
• Validation of Time to Failure Predictions
• Conclusions
• Excel Demo

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Introduction

• CASRE and SMERFS, hereafter referred to as SRT
  (software reliability tools), were developed
  prior to the availability of mature spreadsheet
  programs.
• Programs like Excel were not an option, but
  things have changed.
• In Excel, the user can create equations, do data
  and statistical analysis, make plots, an do
  programming, using Visual Basic.
• In SRT, the programming of the models has been
  done for the user, but the functionality is fixed
  until the next revision.

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Characteristics of Excel Implementation 1

• Advantages
• Almost all practitioners have Excel. A minority
  of practitioners have SRT.
• Easier for practitioners to use than SRT.
• Typically, failure data is provided by
  practitioners in Excel.
• Improve technology transfer
• Predictions can be made by the researcher in the
  spreadsheet and returned to the practitioner in
  the same spreadsheet.
• Formatted Excel data can be imported into Word
  and PowerPoint for creating reports and
  presentations.

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Characteristics of Excel Implementation 2

• Advantages
• User has more control over formatting of data,
  prediction results, and plots.
• A large set of built-in mathematical and
  statistical functions are available for
  reliability analysis.
• SRT limited to functions like Chi-square.
• User can construct his own reliability equations.
• SRT equations are fixed, based on the models
  implemented.
• More flexibility in changing term in equations.
• Change cell values copy and paste equations.

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Characteristics of Excel Implementation 3

• Disadvantages
• Column and cell orientation of spreadsheets is
  cumbersome.
• It is not a natural mathematical format.
• Need to repeat parameter entries for iterations
  of equations.
• Variable names are not case sensitive.
• Variable names cannot be the same as column or
  cell names.
• Thus, some variables must renamed to avoid naming
  conflicts.

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Characteristics of Excel Implementation 4

• Disadvantages
• Mathematical library is not as extensive as
  Fortran and C libraries used in SRT.
• Does not have sophisticated model evaluation
  criteria of SRT.
• However, error analysis between actuals and
  predictions (i.e., validation) can be done in
  Excel.

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Combined Software Reliability Tools Excel
Approach

• Best approach may be to combine SRT with Excel.
• SRT provides model parameter estimation.
• Beyond the capabilities of Excel unless
  programmed in Visual Basic.
• Copy and paste parameters from SRT into
  spreadsheet.
• Excel extends capabilities of SRT by allowing
  user provided equations, statistical analysis,
  and plots.

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Structure of Combined Approach

• Worksheets
• Definitions
• Notation
• Equations
• Predictions
• Analysis
• Actual Prediction Comparisons
• Analysis
• Plots
• Validation
• Examples of this approach follow.

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Notation for Prediction Worksheet
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Equations for Prediction and Comparison
WorksheetsTime to Next Failure(s) Predicted at
Time t
Remaining Failures Predicted at Time t
r(t) (?/?) Xs,t Cumulative Number
of Failures Detected at Time T D(T) (a/ß)1
exp (-ß ((T s 1))) Xs-1
Cumulative Number of Failures Detected Over Life
of Software TL D(TL) ?/? Xs-1
References 1, 2, 3.
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Example Prediction Worksheet
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Analysis of Prediction Worksheet 1

• s, ?, and ? obtained from SMERFS.
• One interval one week of calendar time.
• Project 1
• Optimal s 1 for both failure count and time to
  failure predictions.
• t26 interval when time to next failure
  prediction made This is also the last interval of
  observed failure data.
• X26 130 observed failure count in the range
  1,26.
• F1 1 given number of failures to occur after
  interval 26.
• TF(26) 3.96 intervals time to next failure
  predicted at time 26 intervals.

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Analysis of Prediction Worksheet 2

• Project 1
• r(26) 2.14 remaining failures predicted at
  time 26 intervals.
• T 27 intervals test time.
• D(27) 130.32 cumulative number of failures
  detected at time 27 intervals.
• D(?) 132.14 cumulative number of failures
  detected over life of software (conservatively,
  infinity).
• r(26) D(?) - X26 132.14 130 2.14
  remaining failures, as in the above.

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Analysis of Prediction Worksheet 3

• Project 2
• Total range of 35 weeks divided into Parameter
  Estimation Range 1, 23 weeks and Prediction
  Range 24, 35 weeks for the purpose of model
  validation.
• Model fit using historical data does not
  demonstrate validity!
• Estimate model parameters in range 1, 23 weeks.
• Accuracy of future predictions demonstrates
  validity.
• Predict in range 24, 35 weeks and compare with
  actuals.
• Optimal s 12 for both failure count and time to
  failure predictions.

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Analysis of Prediction Worksheet 4

• Project 2
• t23 interval when time to next failure
  prediction made
• X11 39 observed failure count in the range
  1,11.
• X12,23 32 observed failure count in the
  range 12,23.
• X23 71 observed failure count in the range
  1,23.
• F1 5, , 20 given number of failures to occur
  after interval 23.
• TF(23) 2.63, , 13.14 intervals time to next
  failures predicted at time 23 intervals.

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Analysis of Prediction Worksheet 5

• Project 2
• r(23) 44.96 remaining failures predicted at
  time 23 intervals.
• T 23, , 35 intervals test time.
• D(23, , 35) 71.00, , 89.69 cumulative number
  of failures detected at time 23, , 35 intervals.
• D(?) 115.96 cumulative number of failures
  detected over life of software (conservatively,
  infinity).
• r(23) D(?) - X23 115.96 71 44.96 remaining
  failures, as in the above.

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Notation for Actual Prediction Comparisons
Worksheet

• Parameter Estimation Range 1, 23 weeks
  Prediction Range 24, 35 weeks s 12 weeks.
• D(T) Actual Actual Cumulative Count, from
  Interval 1, in Prediction Range
• D(T) Pred Predicted Cumulative Count, from
  Interval1, in Prediction Range
• Interval Actual Difference in D(T) Actual
• Interval Pred Difference in D(T) Pred
• Int Act Cum Interval Actual Cumulative Count,
  from Interval 24, in Prediction Range
• Int Pred Cum Interval Predicted Cumulative
  Count, from Interval 24, in Prediction Range
• TF(t) Actual Actual Time to Next Given Number
  of Failures in the Int Act Cum column
• TF(t) Pred Predicted Time to Next Given Number
  of Failures in the Int Act Cum
  column

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Example Actual Prediction Comparisons Worksheet
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Analysis of Comparison Worksheet 1

• Project 2
• D(T) Actual is compared with D(T) Prediction.
• Failure counts are accumulated from Interval1in
  the parameter estimation range, but are compared
  in the prediction range.
• Interval Actual is compared with Interval
  Prediction.
• Interval failure counts are compared in the
  prediction range.
• Int Act Cum is compared with Int Pred Cum.
• Interval failure counts are accumulated from
  Interval 24 in the prediction range and compared
  in the prediction range.

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Analysis of Comparison Worksheet 2

• Project 2
• Make plots in prediction range
• Actual and Predicted Cumulative Failures in Range
  1, 35 Weeks.
• Actual and Predicted Cumulative Failures in Range
  24,35 Weeks.
• Validation of Failure Count Predictions.
• Residuals (Predicted Actual) versus week.
• Residuals do not show bias (i.e., trend in either
  positive or negative direction).
• Average Residual -0.55 failures indicates
  optimistic prediction on average.

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Cumulative Failures in Range 1, 35
WeeksParameter Estimation Range plus Prediction
Range
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Cumulative Failures in Range 24,35
WeeksPrediction Range
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Validation of Failure Count Predictions
Average Residual -0.55 failures
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Analysis of Comparison Worksheet 3

• Project 2
• Make plot in prediction range
• Actual and Predicted Time to Next Failures versus
  given number of failures.
• Validation of Time to Failure Predictions.
• Residuals (Predicted Actual) versus given
  number of failures.
• Residuals show bias starting at 15 failures (week
  32) as it becomes difficult to predict further
  out into the future.
• Average Residual 0.87 weeks indicates
  optimistic prediction on average.

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Time to Given Number of Failures
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Validation of Time to Failure Predictions
Average Residual 0.87 weeks
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Conclusions

• Spreadsheet technology can effectively support
  software reliability modeling and prediction.
• Advantages relative to SRT are
• Easier transfer of technology to practitioners.
• More user control of programs operation.
• Many built-in mathematical and statistical
  functions.
• Disadvantages relative to SRT are
• Cell format is not conducive to mathematical
  modeling.
• No built-in model evaluation criteria.
• SRT and Excel can be combined to advantage
• SRT for reliability model parameter estimation.
• Excel for reliability prediction.

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References

• 1 Norman F. Schneidewind, "Reliability Modeling
  for Safety Critical Software", IEEE Transactions
  on Reliability, Vol. 46, No.1, March 1997,
  pp.88-98.
• 2 Norman F. Schneidewind, "Software Reliability
  Model with Optimal Selection of Failure Data",
  IEEE Transactions on Software Engineering, Vol.
  19, No. 11, November 1993, pp. 1095-1104.
• 3 Norman F. Schneidewind and T. W. Keller,
  "Application of Reliability Models to the Space
  Shuttle", IEEE Software, Vol. 9, No. 4, July 1992
  pp. 28-33.