Research Article

Testing of UBAC(2) Class of Life Distributions based on TTT - Transform

by  S.E. Abu-Youssef, A.A. El-Toony
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 175 - Issue 29
Published: Nov 2020
Authors: S.E. Abu-Youssef, A.A. El-Toony
10.5120/ijca2020920820
PDF

S.E. Abu-Youssef, A.A. El-Toony . Testing of UBAC(2) Class of Life Distributions based on TTT - Transform. International Journal of Computer Applications. 175, 29 (Nov 2020), 9-12. DOI=10.5120/ijca2020920820

                        @article{ 10.5120/ijca2020920820,
                        author  = { S.E. Abu-Youssef,A.A. El-Toony },
                        title   = { Testing of UBAC(2) Class of Life Distributions based on TTT - Transform },
                        journal = { International Journal of Computer Applications },
                        year    = { 2020 },
                        volume  = { 175 },
                        number  = { 29 },
                        pages   = { 9-12 },
                        doi     = { 10.5120/ijca2020920820 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2020
                        %A S.E. Abu-Youssef
                        %A A.A. El-Toony
                        %T Testing of UBAC(2) Class of Life Distributions based on TTT - Transform%T 
                        %J International Journal of Computer Applications
                        %V 175
                        %N 29
                        %P 9-12
                        %R 10.5120/ijca2020920820
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, a new test statistic for testing exponentiality against used better than aged in increasing concave ordering UBAC(2) is constructed based on total time on test (TTT)-Transform. Critical values are tabulated for sample size n = 10(5)100. The power of the test is estimated for some commonly used distributions in reliability. Finally, medical applications for real data are proposed to illustrate the theoretical results.

References
  • Bryson, M. C. and Siddiqui, M. M. 1969. Some criteria for aging. Journal of the American Statistical Association, Vol. 64, No. 328, pp. 1472-1483.
  • Barlow, R. E. and Proschan, F. 1981. Mathematical theory of reliability. To Begin With: Silver-Spring, MD.
  • Abu-Youssef, S. E. 2004. Non-parametric Test for Monotone Variance Residual Life Class of Life Distributions with Hypothesis Testing Applications. Applied Mathematics and Computations, Vol. 158, No. 3, pp. 817-826.
  • Ahmed, I. A. 2004. Some Properties of Classes of Life Distributions with Unknown Age. Statistics and Probability Letters, Vol. 69, No. 3, pp. 333-342.
  • Barlow, R. E. and Campo, R. 1975. Total Time on Test Processes and Application to Failure Data Analysis. Reliab. Fault Tree Analysis, SIAM, Philadephia, Vol. 8, No. 4, pp. 451-481.
  • Klefsjo, B. 1980. Some Aging Properties and The Total Time on Test Transform. Res. Rep., Dept. of Math. Statist. Univ. of Umea, Sweden.
  • Klefsjo, B. 1982. The HNBUE and HNWUE classes of life distributions. Naval Logist Res. Quart, Vol. 29, pp. 331-344.
  • Klefsjo, B. 1983. Some Tests Against Aging Based on Total Time on Test Transform. Comm. Statist., Theor. Meth., Vol.12, No. 8, pp. 907-927.
  • Bergman, B. and Klefsjo, B. 1984. The total time on test concept and its use in reliability theory. Operat. Res., Vol. 32, No. 3, pp. 596-606.
  • Pham, T. G. and Turkkan, M. 1994. The Lorenz and the scaled total-time-on-test transform curves: a unified approach. IEEE Trans. Reliab., Vol. 43, No. 1, PP. 76-84.
  • Bartoszewicz, J. 1995. Stochastic order relations and the total time on test transform.
  • S
  • tatist. Prob. Lett., Vol. 22, No. 2, pp. 103-110.
  • Bartoszewicz, J. 1996. Tail orderings and the total time on test transform. Appl. Math., Vol, 24, No. 1,pp. 77-86.
  • Haupt, E. and Schabe, H. 1997. The TTT transformation and a new bathtab distribution model. J. Statist. Planning Infer., Vol. 60, No. 2, pp. 229-240.
  • Kochar, S. C., Li, X., and Shaked, M. 2002. The total time on test transform and the excess wealth stochastic orders of distributions. Adv. Appl. Prob., Vol. 34, No. 4, pp. 826-845.
  • Li, X. and Zou, M. 2004. Preservation of stochastic orders for random minima and maxima with applications. Naval Res. Logistics., Vol. 51, No. 3, pp. 332-334.
  • Ahmed, I. A., Li, X. and Kayid, M. 2005. The NBUT class of life distributions. IEEE Trans. Reliab., Vol. 54, No. 3, pp. 396-401.
  • Li, H. and Shaked, M. 2007. A general family of univariate stochastic orders. J. Statist. Planning Infer., Vol. 137, No. 11, pp. 3601-3610.
  • Al-Nachawati, H. 2007. Test for Monotone Variance Residual Life Class of Life Distributions Based on Total Time on Test Transformation. J. King Saud Univ., Vol. 19, No. 2, pp. 109-117.
  • Nanda, A. K. and Shaked, M. 2008. Partial ordering and aging properties of order statistics when sample size is random: a brief review. Commun. Statist. Theory Meth., Vol. 37, No. 11, pp. 1710-1720.
  • Abu-Youssef, S. E., Mohie El-Din, M. M. and Hassan, M. KH. 2012. Testing Of EBELC Classes Of Life Distributions Based On TTT - Transform. International Journal of Reliability and Applications., Vol. 13, No. 1, pp. 49-56.
  • Mohie El-Din, M. M., Abu-Youssef, S. E. and 2013. Testing unknown age classes of life distributions based on TTT-transform. International Journal of Reliability and Applications., Vol. 14, No. 1, pp. 1-9.
  • Ali, N. S. A. 2018. On the Properties of the UBAC(2) Class of Life Distributions. Journal of Testing and Evaluation., Vol. 46, No. 2, pp.730-735.
  • Willmot, G. and Cai, J. 2000. On classes of life time distributions with unknown age. Probability in the engineering and informational sciences, Vol. 14, No. 4, pp. 473-484.
  • Dicrescenzo, A. 1999. Dual stochastic ordering, decreasing aging properties of divices of unknown age. it Communications in Statistics. Stochastic Models, Vol. 15, No. 3, pp. 561-576.
  • Mohie El-Din, M. M., Abu-Youssef, S. E. and Ali, N. S. A. 2015. A New Class of Life Distributions Based On Unknown Age, IJRA, Vol. 16, No. 1, pp. 27–34.
  • Deshpand, J. V., Kocher, S. C. and Singh, H. 1986. Aspects of Positive Aging. J. Appl. Probab., Vol. 28, No. 3, pp. 1472-1483.
  • Deshpand, J. V. and Purohit, S. G. 2005. Life Time: Statistical Models and Methods, World Scientific Publishing Co., Singapore. Vol. 11.
  • Barlow, R. E. and Doksum, K. 1972. Isotonic tests for convex ordering. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Prob. Univ. of Calif., Vol. 1, pp. 293-323.
  • Barlow, R. E., Bartholomew, D. J., Bremner, J. M. and Brunk, H. D. 1972. Statistical inference under order restriction. Wiley, New York, Vol. 27, No. 4, pp. 139-189.
  • Barlow, R. E. 1979. Geometry of the total time on test transform, Naval Res. Logist. Quart., Vol. 26, No. 3, pp. 393-402.
  • Hollander, M. and Prochan, F. 1975. Test for mean residual life. Biometrika. 62(3), pp. 585-593.
  • Abu-Youssef, S. E. 2009. A Goodness of Fit Approach to Monotone Variance Residual LifeClass of Life Distributions, Applied Mathematical Sciences., Vol. 3, no. 15, 715-724.
  • Kochar, S. C. 1985. Testing exponentiality against monotone failure rate average. Comm. in Stat. - Theo. and Meth., Vol. 14, No. 2, pp. 381-392.
  • Attia, A. F., Mahmoud, M. A. W. and Abdul-Moniem, I. B. 2004. On Testing for Exponential Better than Used in Average Class of Life Distributions Based on the U-Test. The proceeding of The 39 th Annual Conference on Statistics. Computer Sciences and Operation Research, ISSR Cairo University-Egypt, pp. 11-14.
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

UBAC(2) classes of life distributions Survival function Exponentiality Total time on test (TTT)-transform Monte Carlo method.

Powered by PhDFocusTM