12May 2019

AN APPLICATION OF ESTIMATING CAPABILITY INDICES FOR FATIGUE LIFE DISTRIBUTION.

  • Assistant Professor, Department of Statistics, University of Karachi.
  • Dean, Computer Science, College of Computer Science & Information Systems, Karachi Institute of Business Management Korangi Creek.
  • Abstract
  • Keywords
  • References
  • Cite This Article as
  • Corresponding Author

There are variety of statistical distributions which cover most of the problem in reliability and time to event analysis. Birnbaum Saunders?s distribution popularly named as Fatigue Life model is commonly and extensively applied for those quality characteristics of measurements which are associated with high occurrences. In this paper an applicative example is illustrated for earlier presented data sets that exhibiting Fatigue measurements constituted by Fatigue failure time of 3034 aluminum coupons oscillated at 18 cycles per second under 3 different stress levels with the fact that varying stress level producing number of failures which make the process out of control. So an algorithm is defined to first transform fatigue measurements to standard normal, make the process statistically controlled and estimate capability indices for measurements exhibit Fatigue distribution. An algorithm is made in R-console.


  1. Birnbaum, Z. W. and Saunders, S. C. (1969) Estimation for a Family of Life Distributions with Applications to Fatigue. Journal of Applied Probability, 6, 328?347.
  2. Pan, J. N, Wu S. L. (1997) Process Capability Analysis for Non-normal Relay Test Data. Microelectronics and Reliability, 37:421
  3. Juran, J.M. (1974) Juran?s Quality Control 3rd Edition. McGraw-Hill, New York.
  4. Kane, V.E. (1986) Process Capability Indices. Journal of Quality Technology, 18, 41-52.
  5. Chan, L.K., Cheng, S.W. and Spiring, F.A. (1988). A New Measure of Process Capability: Cpm. Journal of Quality Technology, 20, 162-175.
  6. Boyles, R. A. (1991). The Taguchi Capability Index. Journal of Quality Technology, 23, 107-126.
  7. Pearn, W.L., Kotz, S. and Johnson, N.L. (1992) Distributional and Inferential Properties of Process Capability Indices. Journal of Quality Technology, 24, 216 -231.
  8. Gunter, B.H. (1989). The Use and Abuse of Cpk. Quality Progress, 22, 108-109.
  9. Boyles, R.A. (1994) Process Capability with Asymmetric Tolerance. Communications in Statistics: Simulations and Computation, 23, 615-643. http://dx.doi.org/10.1080/0361091940881319
  10. Zwick, D. (1995) A Hybrid Method for Fitting Distributions to Data and It Use in Computing Process Capability Indices. Quality Engineering, 7, 601-613. http://dx.doi.org/10.1080/08982119508918806
  11. E and Safdar. S, (2010) Process Capability Indices for on-Normal Data, Pakistan Business Review July 234-243
  12. Safdar, S. and Ahmed, E. (2014) Process Capability Indices for Shape Parameter of Weibull Distribution, Open Journal of Statistics, 4, 207-219. http://dx.doi.org/10.4236/ojs.2014.43020
  13. SuboohiSafdar, Ejaz Ahmed, Tehseen Ahmed and ArfaMaqsood International Journal of Advance Computer Science and Applications Vol 10, 3 , 2019
  14. SuboohiSafdar, Ejaz Ahmed and ArfaMaqsood (2019) Advanced and Applications in statistics (Accepted)
  15. Baumel, Jr. and T. Seeger (1990) Materials data for cyclic loading, supplement 1. Elsevier ISBN?978-0-444-88603-3.
  16. A. Fleck, C.S. Shin, and R.A. Smith, (1985) Fatigue Crack Growth under Compressive Loading. Engineering Fracture Mechanics, 21(1) 173-185
  17. Stephens, Ralph I.; Fuchs, Henry O. (2001) Metal Fatigue in Engineering (Second edition John Wiley & Sons, Inc. p.?69
  18. VannVilca-Labra and V. Leiva (2006) A New Fatigue Life Model based on the Family of Skew-Elliptical Distributions. Communications in Statistics: Theory and Methods, 35(2):1-16.
  19. Vannman K. (1995) A Unified Approach to Capability Indices. StatisticaSinica, 5, 805-820.
  20. Pearn, W. L, Kotz, S and Johnson, N. L. (1992) Distributional and Inferential Properties of Process Capability Indices. Journal of Quality Technology, 24, 216?231.
  21. Nagata, Y. and Nagahata, H. (1992) Approximate Formulas for the Confidence Intervals of Process Capability Indices. Reports of Statistical Application Research 39:15-29
  22. Nagata Y, Nagahata H. (1993) Approximation Formulas for the Confidence Intervals of Process Capability Indices. Technical Report Okayama University, Japan
  23. Boyles, R. A. (1991). The Taguchi Capability Index. Journal of Quality Technology, 23, 107-126.
  24. Subbaiah, P. and Taam, W. (1991) Inference on the Capability Index Cpm, MS, Dept. Math. Sci., Oakland University, Rochester, Minnesota
  25. Patnaik, P. B. (19490 The Non-Central - and F Distributions and their Applications, Biometrika, 36, 202-332
  26. Chen, S. M. and Hsu, N. F. (1995). The Asymptotic Distribution of the Process Capability Index Cpmk. Communications in Statistics: Theory and Methods, 24(5), 1279-1291.

[Suboohi Safdar, Ejaz Ahmed and Arfa Maqsood. (2019); AN APPLICATION OF ESTIMATING CAPABILITY INDICES FOR FATIGUE LIFE DISTRIBUTION. Int. J. of Adv. Res. 7 (May). 399-404] (ISSN 2320-5407). www.journalijar.com


Suboohi Safdar
Assistant Professor, Department of Statistics, University of Karachi.

DOI:


Article DOI: 10.21474/IJAR01/9051      
DOI URL: https://dx.doi.org/10.21474/IJAR01/9051