Accelerated life test plan under modified ramp-stress loading with two stress factors

  • Srivastava, P.W. (University of Delhi) ;
  • Gupta, T. (University of Delhi)
  • Received : 2017.07.31
  • Accepted : 2017.12.27
  • Published : 2017.12.31

Abstract

Accelerated life tests (ALTs) are frequently used in manufacturing industries to evaluate the reliability of products within a reasonable amount of time and cost. Test units are subjected to elevated stresses which yield quick failures. Most of the previous works on designing ALT plans are focused on tests that involve a single stress. Many times more than one stress factor influence the product's functioning. This paper deals with the design of optimum modified ramp-stress ALT plan for Burr type XII distribution with Type-I censoring under two stress factors, viz., voltage and switching rate each at two levels- low and high. It is assumed that usage time to failure is power law function of switching rate, and voltage increases linearly with time according to modified ramp-stress scheme. The cumulative exposure model is used to incorporate the effect of changing stresses. The optimum plan is devised using D-optimality criterion wherein the ${\log}_{10}$ of the determinant of Fisher information matrix is maximized. The method developed has been explained using a numerical example and sensitivity carried out.

Keywords

References

  1. Bai D. S. and Chun Y. R. (1993). Non-parametric inferences for ramp-stress test under random censoring, Reliability Engineering and System Safety, 41, 217 - 223. https://doi.org/10.1016/0951-8320(93)90072-7
  2. Bai D. S. and Chung S. W. (1992). Optimal design of partially accelerated life tests for the exponential distribution under type-I censoring, IEEE Transactions on Reliability, 41, 400-406. https://doi.org/10.1109/24.159807
  3. Bai D. S. Chun Y. R. and Cha M. S. (1997). Time-censored ramp tests with stress bound for the Weibull life distribution, IEEE Transactions on Reliability, 46, 99 - 107. https://doi.org/10.1109/24.589934
  4. Bai D. S., Chun Y. R. and Chung S. W. (1993). Optimal design of partially accelerated life tests for lognormal distribution under type-I censoring, Reliability Engineering and System Safety, 40, 85-92. https://doi.org/10.1016/0951-8320(93)90122-F
  5. Bessler S., Chernoff H. and Marshall A. W. (1962). An Optimal Sequential Accelerated Life Test, Technometrics, 4, 367-379. https://doi.org/10.1080/00401706.1962.10490019
  6. Bhattacharyya G. K. and Soejoeti Z. (1989). A tampered failure rate model for step-stress accelerated life test, Communications in Statistics - Theory and Methods, 18, 1627-1643. https://doi.org/10.1080/03610928908829990
  7. Chernoff H. (1962). Optimal accelerated life designs for estimation, Technometrics, 4, 381-408. https://doi.org/10.1080/00401706.1962.10490020
  8. DeGroot M. H.and Goel P. K. (1979). Bayesian estimation and optimal designs in partially accelerated life testing, Naval research logistics, 26, 223-235. https://doi.org/10.1002/nav.3800260204
  9. Elsayed E. A. (1996). Reliability Engineering, Massachusetts, Addison-Wesley.
  10. Fei H. (2000). The statistical analysis of combined data from the progressively and constantly life tests under power-Weibull model, Journal of Mathematical Applications, 13, 102-106.
  11. Gao N., Hu J. M., Shi Y. M. and Qin X. Q. (2008). Statistical analysis of the mixed accelerated life test for the type-II progressively censored sample, Journal of Physical Sciences, 12, 23-32.
  12. Gouno E. and Balakrishnan N. (2001). Step-stress accelerated life test, Handbook of Statistics-20: Advances in Reliability, Amsterdam: North-Holland, 623-639.
  13. Meeker W. Q. and Escobar L. A. (1995). Planning accelerated life tests with two or more experimental factors, Technometrics, 37, 411-427. https://doi.org/10.1080/00401706.1995.10484374
  14. Meeker W. Q. and Escobar L. A. (1998). Statistical Methods for Reliability, and Data, John Wiley & Sons, New York.
  15. Nelson W. (1982). Applied Life Data Analysis, John Wiley & Sons.
  16. Nelson W. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analysis, John Wiley & Sons, New York.
  17. Nelson W. (2005a). A bibliography of accelerated test plans, IEEE Transactions on Reliability, 54, 194-197. https://doi.org/10.1109/TR.2005.847247
  18. Nelson W. (2005b). A bibliography of accelerated test plans part II - reference, IEEE Transactions on Reliability, 54, 370-373. https://doi.org/10.1109/TR.2005.853289
  19. Park J. W. and Yum B. J. (1996). Optimum design of accelerated life tests with two stresses, Naval research logistics, 43, 863-884. https://doi.org/10.1002/(SICI)1520-6750(199609)43:6<863::AID-NAV5>3.0.CO;2-2
  20. Park J. W. and Yum B. J. (1998). Optimal design of accelerated life tests under modified stress loading methods, Journal of Applied Statistics, 25, 41-62. https://doi.org/10.1080/02664769823296
  21. Soliman A. A. (2005). 'Estimation of parameters of life from progressively censored data using Burr type XII model', IEEE Transactions on Reliability. 54, 34 - 42. https://doi.org/10.1109/TR.2004.842528
  22. Srivastava P. W. and Mittal N. (2013). Optimum multi-objective modified constant-stress ALT plan for the Burr type XII distribution with type-I censoring, Journal of Risk and Reliability, 227, 132-143.
  23. Tadikamalla P. R. (1980). A Look at the Burr and Related Distributions, International Statistical Review, 48, 337-344. https://doi.org/10.2307/1402945
  24. Tamai T., Miyagawa K. and Furukawa M. (1997). Effect of switching rate on contact failure from contact resistance of micro relay under environment containing silicone vapour, Proc. 43rd IEEE Holm Conference on Electrical Contacts, 333-339.
  25. Wang B. (2001). Models and Statistical analysis for the mixed accelerated life test, Applied Mathematics-A Journal of Chinese Universities Ser. A, 16, 101 - 106.
  26. Yang G. (2005). Accelerated Life Tests at Higher Usage Rates, IEEE Transactions On Reliability, 54, 53-57. https://doi.org/10.1109/TR.2004.841730
  27. Yang G. (2007). Life cycle reliability engineering, John Wiley & Sons.
  28. Zhu Y. and Elsayed E. A. (2001). Design of Equivalent Accelerated Life Testing Plans under Different Stress Applications, Quality Technology and Quality Management, 8, 463-478.
  29. Zimmer W. J., Keats J. B. and Wang F. K. (1998). The Burr XII Distribution in Reliability Analysis, Journal of Quality Technology, 30, 337-344.