1. 1 NASA OSMA SAS02 Software Reliability Modeling: Traditional and Non-Parametric Dolores R. Wallace Victor Laing SRS Information Services Software Assurance Technology Center http://satc.gsfc.nasa.gov/ dwallac, vlaing@pop300.gsfc.nasa.gov http://satc.gsfc.nasa.gov/ NASA OSMA SAS '02

2. 2 NASA OSMA SAS02 The Problem Critical NASA systems must execute successfully for a specified time under specified conditions -- Reliability Most systems rely on software Hence, a means to measure software reliability is essential to determining readiness for operation Software reliability modeling provides one data point for reliability measurement

3. 3 NASA OSMA SAS02 Software Reliability Modeling (SRM) – Traditional Captures hardware reliability engineering concepts Mathematically models behavior of a software system from failure data to predict reliability growth Invokes curve-fitting techniques to determine values of parameters used in the models Validates models with data with statistical analysis Using parametric values, predicts future measurements, e.g., –Mean time to failure –Total number faults remaining –Number faults at time t

4. 4 NASA OSMA SAS02 Synopsis FY01 –Identify mathematics of hardware reliability not used in software –Identify differences between hardware, software affecting reliability measurement –Identify possible improvements FY02 –Demonstrate practicality of SRM at GSFC –Fault correction improvement – Schneidewind –Non-parametric model - Laing

5. 5 NASA OSMA SAS02 SRM: Data Collection Resistance to data collection Data content –Accuracy of content –Dates of failure, correction –Calendar time not execution time –Activities/ phase when failures occur Data manipulation –Frequency counts –Interval size and length –Time between failure

6. 6 NASA OSMA SAS02 IntervalCounter Sample had 35 weeks – simplified fault count

7. 7 NASA OSMA SAS02 SMERFS^3 3-D OUTPUT

8. 8 NASA OSMA SAS02 Practical Method SATC Services –SATC executes models and prepares analysis –SATC provides training and public domain tool Improvements –Recommendations to projects for data collection –IntervalCounter to simplify data manipulation

9. 9 NASA OSMA SAS02 Fault Correction Adjustments Reliability growth occurs from fault correction Failure correction proportional to rate of failure detection Adjusted model with delay dT (based on queuing service) but same general form as faults detected at time T Process: use SMERFS Schneidewind model to get parameters; apply to revised model via spreadsheet Results –Show reliability growth due to fault correction –Predict stopping rules for testing

10. 10 NASA OSMA SAS02 SMERFS^3 – Excel Approach* Best approach: combine SMERFS^3 with Excel. SRT provides model parameter estimation. Copy and paste parameters from SRT into spreadsheet. Excel extends capabilities of SRT by allowing user to provide equations, statistical analysis, and plots. * CASRE or other software reliability modeling tool may be used with EXCEL Recommended approach until the SRM tools incorporate this new model.

11. 11 NASA OSMA SAS02 Non-parametric Reliability Modeling Hardware - Wears out over time - Increasing failure rate Software - Do not wear over time - Decreasing failure rate

12. 12 NASA OSMA SAS02 Continued Hardware Reliability Modeling - “Large” independent random sampling - Model reliability - Make predictions Software Reliability Modeling - “Small” observed dependent sample (of size one?) - Not based on independent random sampling - Model reliability - Make predictions? Do we search for the silver bullet of SWR models?

13. 13 NASA OSMA SAS02 Reliability Trending Hardware Reliability 100% Maximum 0% Minimum 0 1 2 3 4 …  Time Software Reliability 100% Maximum 0% Minimum 0 1 2 3 4 …  Time

14. 14 NASA OSMA SAS02 Software Reliability Bounds 100% Maximum Estimated Bound Estimated Model 0% Minimum 0 1 2 3 4 …  Time

15. 15 NASA OSMA SAS02 Calculation of Estimated Models and Bounds Dynamic Metrics - Failure rate data - Problem reports Static Code Metrics - Traditional - Source Lines of Code (SLOC) - Cyclomatic Complexity (CC) - Comment Percentage (CP) - Object-Oriented - Coupling Between Objects (CBO) - Depth of Inheritance Tree (DIT) - Weighted Methods per Class (WMC)

16. 16 NASA OSMA SAS02 Combining Dynamic and Static Metrics The Proportional Hazards Model (PHM) PHM Non-Parametric Component (Static) R(t|z) = {R 0 (t)} g(z) Parametric Component (Dynamic) - Where zβ = z 1 β 1 + z 2 β 2 + … + z p β p, β i ’s are unknown regression coefficients and z i ’s are static code metrics data

17. 17 NASA OSMA SAS02 Tool Schema Input Data z = (z 1, z 2, … z p ) Database Observed Data Data Processing R(t|z) = {R 0 (t)} g(z) Weighted Average Raw Data Output Data Estimated Model Estimated Bound - Process Below Bounds Action - Corrective Action - Process Above Bounds - No Corrective Action

18. 18 NASA OSMA SAS02 SUMMARY Software reliability modeling –Provides useful measurements for decisions –Does not require expert knowledge of the math! –Is relatively easy with use of software tools Fault correction improvement –Adapts model to be more like software –Demonstrates combined use of traditional SRM tools with spreadsheet technology Non-parametric modeling –New approach shows promise –Prototype to be expanded

19. 19 NASA OSMA SAS02 AIAA Recommended Steps (specific to SRM) Characterizing the environment Determining test approach Selecting models Collecting data Estimating parameters Validating the models Performing analysis

20. 20 NASA OSMA SAS02 Fault Correction Modeling Software reliability models focus on modeling and predicting failure occurrence –There has not been equal priority on modeling the fault correction process. Fault correction modeling and prediction support to –predict whether reliability goals have been achieved –develop stopping rules for testing –formulate test strategies –rationally allocate test resources.

21. 21 NASA OSMA SAS02 Equations: Prediction and Comparison Worksheets Remaining Failures Predicted at Time t: r(t) = (  /  ) – X s,t Cumulative Number of Failures Detected at Time T: D(T) = (α/β)[1 – exp (-β ((T –s + 1)))] + X s-1 Cumulative Number of Failures Detected Over Life of Software T L : D(T L ) =  /  + X s-1 Equations developed by Dr. Norman Schneidewind, Naval Postgraduate School, Monterey, CA Time to Next Failure(s) Predicted at Time t