1. HardwareSoftware Success Failure Input Output

2. N-Version Programming Fault-Tolerant Programming Version 1 Version 2 Version N … Voter M Identical Outputs Correct Result Failure Recovery Blocks Scheme Version 1 AT Correct Result + - Version 2 AT Correct Result + - … Version N AT Correct Result + - Failure

3. t1t1 t1t1 t2t2 t3t3 t4t4 t5t5 t2t2 t3t3 t4t4 t5t5 TT failure success voting N-Version Programming M=3 Parallel Execution of Versions Consecutive Execution of Versions

4. Fault-Tolerant System Structure … … … Software Running on Different Hardware Blocks Software Running on Single Hardware Block

5. t 1 +t 4 t 1 +t 3 13 245 t 1 +t 2 +t 3 +t 4 1 2 3 4 5 3 14 25 t3t3 1 2 3 4 5 t3t3 1 2 3 4 5 L=1L=2 L=3L=4L=5 Effect of Parallel Versions Execution

6. Characteristics of Version Execution Time Computational Resources Reliability Characteristics of System Expected Execution Time E(T) Reliability Pr{ T < T* } Conditional Expected Execution Time E(T) | T < T* Reliability/Performance Analysis Problem

7. Distribution of System Execution Time Q(k/n)=Pr{ k out of n first versions succeed } i 1 : {1…n-k+1} i 2 : { i 1 +1 …n-k+2} Pj=Pr{ system succeeds after execution of version j } = r j Q(M-1/j-1)

8. UGF Approach Single version i: j first versions: For j = M: PMPM P j-1 PjPj

9. UGF Approach For each component c: P cM, P cM+1,…, P cn T cM, T cM+1,…, T cn For the entire system:

10. t1+t3t1+t3 13 245 1 2 3 4 5 3 215 4 3 1 2 5 4 Effect of Versions Sequencing t2+t4+t5t2+t4+t5 t3+t4t3+t4 t1+t2+t5t1+t2+t5 3-out-of-5 system

11. versions McMc ncnc No of component 54321 75322017t141 -0.980.890.850.71r --585528t232 --0.930.85 r 6341382017t353 0.98 0.860.80 r --322017t234 --0.970.930.75r --705430t135 --0.890.800.70r Parameters of Software System

12. R(300(E(T)E(T)T max T min Sequence of versionsProblem formulation No 0.914211.914291832134|132|54321|213|132 Min E(T) 1 0.915220.224291982314|312|43521|321|123 Max R(300) 2 0.909213.844491771234|123|12345|123|123 increasing t 3 0.776277.674322474312|213|52134|132|231 Max E(T) 4 Optimal Version Sequences

13. T* Software Structure Optimization R(T*) MAX |C < C* R(T*) MAX | C < C*

14. R(250)(T)E(T)ET max T min CSequence of versionsC* 0.913188.34307166159231|541|37162|324|214160 0.868194.4330117314034|241|64231|234|123140 0.752217.072492051195|431|31562|43|21120 0.598220.522702051003|241|4562|43|41100 Optimal Fault-Tolerant System Structures