Main Article Content
This paper is devoted to study a new four- parameter additive model. The newly suggested model is referred to as the flexible Weibull extension-Burr XII distribution. It is derived by considering a serial system with one component following a flexible Weibull extension distribution and another following a Burr XII distribution. The usefulness of the model stems from the flexibility of its failure rate which accommodates bathtub and modified bathtub among other risk patterns. These two patterns have been widely accepted in several fields, especially reliability and engineering fields. In addition, the importance of the new distribution is that it includes new sub-models which are not known in the literature. Some statistical properties of the proposed distribution such as quantile function, the mode, the rth moment, the moment generating function and the order statistics are discussed. Moreover, the method of maximum likelihood is used to estimate the parameters of the model. Also, to evaluate the performance of the estimators, a simulation study is carried out. Finally, the performance of the proposed distribution is compared through a real data set to some well-known distributions including the new modified Weibull, the additive Burr and the additive Weibull distributions. It is shown that the proposed model provides the best fit for the used real data set.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- Almalki, S.J. and Yuan, J. (2013). The New Modified Weibull Distribution. Reliability Engineering and System Safety, 111, 164-170. DOI: https://doi.org/10.1016/j.ress.2012.10.018
- Bebbington, M., Lai, C.D., and Zitikis, R. (2007). A Flexible Weibull Extension. Reliability Engineering and System Safety, 92, 719-726. DOI: https://doi.org/10.1016/j.ress.2006.03.004
- Burr, I.W. (1942). Cumulative Frequency Functions. Annals of Mathematical Statistics, 13, 215-232. DOI: https://doi.org/10.1214/aoms/1177731607
- El-Desouky, B.S., Mustafa, A. and Al-Garash, S. (2017). The Exponential Flexible Weibull Extension Distribution. Open Journal of Modelling and Simulation, 5, 83-97. DOI: https://doi.org/10.4236/ojmsi.2017.51007
- He, B., Cui, W., and Du, X. (2016), "An Additive Modified Weibull Distribution", Reliability Engineering and System Safety, 154, 28-37. DOI: https://doi.org/10.1016/j.ress.2015.08.010
- Kuo W and Kuo Y. (1983). Facing the headaches of early failures: a state of the art review of burn-in decisions. Proceedings of the IEEE, 71,1257–66. DOI: https://doi.org/10.1109/PROC.1983.12763
- Lai, C.D., Xie, M. and Murthy, D.N.P. (2003). A modified Weibull distribution. Reliability, IEEE Transactions on, 52, 33–37. DOI: https://doi.org/10.1109/TR.2002.805788
- Mudholkar, G. S. and Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. Reliability, IEEE Transactions on, 42, 299-302. DOI: https://doi.org/10.1109/24.229504
- Nelson. W. (1982). Applied Life Data Analysis. John Wiley & Sons. New York. NY. DOI: https://doi.org/10.1002/0471725234
- Singh, B. (2016), "An Additive Perks–Weibull Model with Bathtub-Shaped Hazard Rate Function", Communications in Mathematics and Statistics, 4, 473–493. DOI: https://doi.org/10.1007/s40304-016-0096-z
- Tarvirdizade, B. and Ahmadpour, M. (2019), “A New Extension of Chen Distribution with Applications to Lifetime Data”, Communications in Mathematics and Statistics, DOI: 10.1007/s40304-019-00185-4. DOI: https://doi.org/10.1007/s40304-019-00185-4
- Wang, F.K. (2000). A new Model with Bathtub-Shaped Failure Rate Using an Additive Burr XII Distribution. Reliability Engineering and System Safety, 70, 305–312. DOI: https://doi.org/10.1016/S0951-8320(00)00066-1
- Xie, M. and 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. DOI: https://doi.org/10.1016/0951-8320(95)00149-2
- Xie, M., Tang, Y. and Goh, T.N. (2002). A modified Weibull extension with bathtub failure rate function. Reliability Engineering System Safety, 76, 279–285. DOI: https://doi.org/10.1016/S0951-8320(02)00022-4
- Xie M, Lai CD and Murthy DNP. (2003). Weibull-related distributions for modelling bathtub-shaped failure rate functions. Mathematical and statistical methods in reliability. Singapore: World Scientific Publishing, 283–97. DOI: https://doi.org/10.1142/9789812795250_0019