Main Article Content

Abstract

In this study, we propose two estimators called the 3-step MML and the combined estimators of the parameters of the modified Weibull distribution which is used in reliability models with bathtub-shaped failure rate function. The simulations show the superiority of both estimators over the graphical estimators. Particularly, the combined estimators are the better of the two. Two real-life data applications also show the superiority of the proposed estimators compared to the graphical estimators.

Keywords

3-step modified maximum likelihood Combined estimators Graphical method Hazard function Reliability

Article Details

Author Biographies

Adam Abdelrahman Hussein Adam, Faculty of Economics and Administrative Sciences, Department of Applied Statistics and Population Studies, Portsudan Town, Red Sea University, Sudan

Red Sea University, Faculty of Economics and Administrative Sciences, Department of Applied Statistics and Population Studies, Portsudan Town, Sudan.

Hakan SavaÅŸ Sazak, Department of Statistics, Bornova, İzmir, Ege University, Turkey

Ege University, Faculty of Science, Department of Statistics, Bornova, İzmir, Turkey.

How to Cite
Hussein Adam, A. A., & Sazak, H. S. (2023). Estimation of the Parameters of the Modified Weibull Distribution with Bathtub-shaped Failure Rate Function. Pakistan Journal of Statistics and Operation Research, 19(4), 765-776. https://doi.org/10.18187/pjsor.v19i4.4185

References

    Aarset, M. V. (1987). How to identify a bathtub hazard rate. IEEE Transactions on Reliability, 36(1), 106-108.
    Almalki, S. J., & Yuan, J. (2013). A new modified Weibull distribution. Reliability Engineering and System Safety, 111, 164-170.
    Bebbington, M., Lai, C. D., & Zitikis, R. (2007). A flexible Weibull extension. Reliability Engineering and System Safety, 92, 719-726.
    Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics and Probability Letters, 49, 155-161.
    Hussein Adam, A. A. (2017). Estimation in Reliability Models with Distribution Having Bathtub Shaped Hazard Function. PhD thesis, İzmir, Ege University.
    Kay, S. M. (1993). Fundamental of Statistical Signal Processing Estimation Theory, Prentice Hall, New Jersey.
    Lai, C.D., Xie, M., & Murthy, D. N. P. (2003). A modified Weibull distribution. IEEE Transactions on Reliability, 52(1), 33-37.
    Peng, X., & Yan, Z. (2014). Estimation and application for a new extended Weibull distribution. Reliability Engineering and System Safety, 121, 34-42.
    Puthenpura, S., & Sinha, N. K. (1986). Modified maximum likelihood method for the robust estimation of system parameters from noisy data. Automatica, 22, 231-235.
    Sazak, H. S. (2019). The combined dynamically weighted modified maximum likelihood estimators of the location and scale parameters. Journal of Statistical Computation and Simulation, 89(5), 751-762.
    Sürücü, B., & Sazak, H. S. (2009). Monitoring reliability for a three-parameter Weibull distribution. Reliability Engineering and System Safety, 94(2), 503-508.
    Vaughan, D. C. (1992). On the Tiku-Suresh method of estimation. Communications in Statistics - Theory and Methods, 21, 451-469.
    Vaughan, D. C. (2002). The generalized secant hyperbolic distribution and its properties. Communications in Statistics - Theory and Methods, 31, 219-238.
    Vaughan, D. C., & Tiku, M. L. (2000). Estimation and hypothesis testing for a non-normal bivariate distribution and applications. Mathematical and Computer Modelling, 32, 53-67.
    Wang, F. K. (2000). A new model with bathtub-shaped failure rate using an additive Burr XII distribution. Reliability Engineering and System Safety, 70, 305-321.
    Xie, M., & Lai C. D. (1996). Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function. Reliability Engineering and System Safety, 52, 87-93.
    Xie, M., Tang, Y., & Goh, T. N. (2002). A modified Weibull extension with bathtub-shaped failure rate function. Reliability Engineering and System Safety, 76, 279-285.