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

2. Project instruction Step 1 : Linearity check and R comparison Step 2 : Goodness of fit test (Kolomogorov- Smirnov test) Step 3 : Conclusion

3. Zino’s samples 632 457 216 308 196 406 570 397 641 476 599 411 574 491 139 466

4. Symmetric simple cumulative distribution

5. Mean rank

6. Median rank

7. The rest Method

8. Check linearity through our eyes Symm.S.CMeanMedianThe rest Normal0000 LogNormalxxxx Weibull0000 Biexponenti al 0000

9. R value comparison Symm.S.CMean RR bie0.98035bie0.98705 log0.92914log0.92854 nor0.97216nor0.97552 wei0.97561wei0.97128 MedianThe rest Method RR bie0.98424bie0.98307 log0.92912log0.92918 nor0.97409nor0.9735 wei0.97414wei0.97478

10. Getting theoretical equation using linear fitting

11. K-S test Normal distribution D 0.150.184 0.250.169

12. K-S test Weibull distribution D 0.150.188

13. K-S test Bi-exponential distribution D 0.150.188 0.250.172

14. Conclusion Linearity test through eyes Normal, Weibull, Biexponential distribution are suitable R value comparaison Bi-exp > Weibull > Normal K-S test : BI-exponential and Normal pass the test Data follows Bi-exponential distribution function

15. 송민호 samples 425 265 376 384 510 58 679 125 88

16. Symmetric sample cumulative Weibull Log-normal Bi-exponential Normal

17. Mean rank Weibull Log-normal Bi-exponential Normal

18. Median rank Weibull Log-normal Bi-exponential Normal

19. The rest method Weibull Log-normal Bi-exponential Normal

20. Linearity with eyes Symmetric.S.CMean RankMedian RankThe rest method NormalOOOO Log NormalXXXX WeibullOOOO Bi-exponentialXXXX

21. R value comparison Symmetric.S.C R Normal 0.97776 Log normal 0.95424 Weibull 0.97391 Bi-exponential 0.94494 Mean Rank R Normal 0.98012 Log normal 0.95699 Weibull 0.97716 Bi-exponential 0.95909 Median Rank R Normal 0.97915 Log normal 0.95583 Weibull 0.97613 Bi-exponential 0.95243 The Rest Method R Normal 0.97873 Log normal 0.95535 Weibull 0.97552 Bi-exponential 0.95003

22. Slope & Intercept values SSCNormalLognormalWeibullBi-exponential Slope0.004641.102321.38460.00552 Intercept-1.49987-6.07909-8.18318-2.33133 Mean rankNormalLognormalWeibullBi-exponential Slope0.003860.917941.126020.00454 Intercept-1.24842-5.06226-6.69991-1.95776 Median rankNormalLognormalWeibullBi-exponential Slope0.004271.015991.261270.00505 Intercept-1.38208-5.603-7.47463-2.15319 Rest methodNormalLognormalWeibullBi-exponential Slope0.00441.045761.303310.00521 Intercept-1.42268-5.76718-7.71596-2.21394

23. NormalSSCMean rankMedian rankRest method 323.25323.42323.67323.34 215.52259.07234.19227.27 LognormalSSCMean rankMedian rankRest method 5.515 0.90711.08940.98430.9562 WeibullSSCMean rankMedian rankRest method 1.38461.126021.261271.30331 368.76383.78374.76372.52 Bi-exponentialSSCMean rankMedian rankRest method 181.16220.26198.02191.94 422.34431.22426.37424.94

24. Normal distribution(Symmetric S.C) D 0.250.218 0.200.227 SSCMean rank Median rankRest method

25. Lognormal distribution D 0.250.218 0.200.227 SSC Rest method Mean rank Median rank

26. Weibull distribution D 0.250.220 0.200.229 SSC Rest methodMedian rank Mean rank

27. Bi-exponential distribution D 0.250.220 0.200.229 SSC Median rankRest method Mean rank

28. Conclusion R values show normal and Weibull as the most appropriate cumulative probability distribution function for the data given K-S test All distribution functions passed the test. However normal and bi-exponential cumulative distribution functions fit better to the formulated function line As normal distribution satisfy both tests and have the highest R value we concluded that the data given follow normal distribution

29. Total samples 425 265 376 384 510 58 679 125 88 632 457 216 308 196 406 570 397 641 476 599 411 574 491 139 466

30. Symmetric simple cumulative distribution

31. Mean rank

32. Median rank

33. The rest Method

34. Check linearity through ours eyes Symm.S.CMeanMedianThe rest Normal0000 LogNormalxxxx Weibull0000 Biexponenti al 0000

35. R value comparison Symmetric.S.C R Normal 0.98141 Log normal 0.92252 Weibull 0.97712 Bi-exponential 0.97510 Mean Rank R Normal 0.98533 Log normal 0.92130 Weibull 0.97274 Bi-exponential 0.98547 Median Rank R Normal 0.98355 Log normal 0.92217 Weibull 0.97561 Bi-exponential 0.98066 The Rest Method R Normal 0.98288 Log normal 0.92234 Weibull 0.97625 Bi-exponential 0.97890

36. Slope & Intercept values SSCNormalLognormalWeibullBi-exponential Slope0.00541.406131.870310.00674 Intercept-2.1378-8.1891-11.45834-3.2333 Mean rankNormalLognormalWeibullBi-exponential Slope0.004941.279081.659820.00608 Intercept-1.95497-7.44905-10.19739-2.93397 Median rankNormalLognormalWeibullBi-exponential Slope0.00521.348641.772750.00644 Intercept-2.05565-7.85427-10.87374-3.09808 Rest methodNormalLognormalWeibullBi-exponential Slope0.005271.368831.806540.00654 Intercept-2.08462-7.97188-11.07616-3.14391

37. NormalSSCMean rankMedian rankRest method 395.90395.74395.32395.56 185.19202.43192.31189.75 LognormalSSCMean rankMedian rankRest method 5.824 0.71120.78180.74150.7306 WeibullSSCMean rankMedian rankRest method 1.870311.659821.772751.80654 457.80465.76461.20459.96 Bi-exponentialSSCMean rankMedian rankRest method 148.37164.47155.28152.91 479.72482.55481.07480.74

38. K-S test Normal distribution D 0.150.150 0.250.135

39. K-S test Weibull distribution D 0.100.163 0.250.141

40. K-S test Bi-exponential distribution D 0.150.154 0.250.141

41. Conclusion Linearity test through eyes Normal,Weibull,Biexponential distribution are suitable R value comparaison Normal>Bi-exp>Weibull K-S test - Normal & Bi-exp passed the test The emerged data set follows normal distribution

42. Q & A