1. Introduction to Reliability in Mechanical Engineering Project II Introduction to Reliability in Mechanical Engineering Project II 송민호 Morkache Zinelabidine

2. Presentation Outline Project 1 Results Reliability calculation by using graphical method Reliability calculation by using PDF from project 1 values Results and Conclusion

3. Project 1 Results

4. Zino Data 1 (N= 16) 632 457 216 308 196 406 570 397 641 476 599 411 574 491 139 466 D 0.150.188 0.250.172 512.4 148.14 Bi-exponential distribution Mean rank method

5. 송민호 Data 2 (N=9) Normal distribution Mean rank method 425 265 376 384 510 58 679 125 88 323.42 259.07 D 0.250.218 0.200.227

6. Project 2 Analysis

7. Determining Strength/Stress for Data 1&2 DataNo of DataMean Set116436 Set29323.42

8. Calculation with only the data sets

9. CDF value graph of the data Since the data value does not match one to one, interpolation is done to have CDF values for every natural number data values within the overlapping range

10. Calculation : Lower limit case Re = 0.645Pf = 0.329

11. Calculation : Upper limit case Re = 0.6706Pf = 0.354

12. Calculation : Triangle method Re = 0.6579Pf = 0.342

13. Reliability calculation from equation

14. Probality Density Function Stress : Normal distribution Fsig(x) = 0.5+0.5*erf((1/2)*sqrt(2)*(x-323.42)/(259.07)) Strength : Bi-exponential distribution Fs(x) = 1-exp(-exp((x-512.4)/(148.14)))

15. Using equation from project 1 CDF value is not 0 when the data value is 0 : integrate from -1000 to 1000

16. Probability distribution function From -1000 to 1000 Graph from Origin by using Derivative() function f(stress) = Derivative(F(stress)) f(strength) = Derivative(F(strength))

17. Using Origin Re = 0.64034 Pf =0.35966

18. Results & Conclusion Lower RUpper RTriangle REquation R 0.6450.67060.65790.64034 Upper PfLower PfTriangle PfEquation Pf 0.3450.3290.3420.35966 Sum0.9990.99960.99991.00000 Sum of reliability and probability of failure is almost unity for every calculation method used Calculation is correct As the reliability is lowest when using the equation from project 1, this method is the most strict method.