Research Article New Rayleigh Flexible Weibull Extension (RFWE) Distribution with Applications to Real and Simulated Data Muneeb Javed, 1 Syed Muhammad Asim, 1 Alamgir Khalil, 1 Said Farooq Shah , 1 and Zahra Almaspoor 2 1 Department of Statistics, University of Peshawar, Peshawar, Pakistan 2 Department of Statistics, Yazd University, Yazd P.O. Box 89175-741, Iran Correspondence should be addressed to Zahra Almaspoor; z.almaspoor@stu.yazd.ac.ir Received 3 July 2022; Accepted 17 September 2022; Published 22 October 2022 Academic Editor: Giulia Pascoletti Copyright © 2022 Muneeb Javed et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Rayleigh flexible Weibull extension (RFWE) distribution, a new three-parameter model introduced in this paper, is a generalization of the flexible Weibull extension. This model produces best fit for failure time of electronic device obtained from power-linkage voltage spikes during electronic storms. We derive the statistical properties of the RFWE distribution. The parameters of this new distribution are estimated using the maximum likelihood method, which also yielded asymptotic confidence bounds. This model is examined using both real and simulated data. Under various priors, an additional Bayesian estimate is also carried out. The Bayes estimates and other posterior results are calculated using simulations. 1. Introduction To model the lifetime components, Weibull distribution is very useful in fields like physics and engineering. Farooq et al. [1] focused on investigations to derive a new probabil- ity model for data sets with extreme values in engineering. Ijaz et al. [2] developed a new modification with three parameters of the Lomax distribution. Kumaraswamy Wei- bull distribution is studied by Corderio et al. [3]. Moreover, El-Morshedy et al. [4] proposed a three-parameter model by exponentiating the inverse flexible Weibull extension distri- bution. They called it exponentiated inverse flexible Weibull extension (EIFW) distribution. Manisha and Tiensuwan [5] introduced a beta transmuted Weibull distribution, which contains several distributions as special cases, and properties of the distribution are also discussed. Mustafa et al. [6] intro- duced a four-parameter model called the Weibull general- ized flexible Weibull extension (WGFWE) distribution which exhibits a bathtub-shaped hazard rate. Bebbington et al. [7] discussed applications of the flexible Weibull distri- bution that includes life testing experiments and applied sta- tistics. Nadarajah and Kotz [8] and Murthy et al. [9] discussed the extensions of the Weibull distribution. In this article, a new generalization of the flexible Wei- bull extension (FWE) distribution called Rayleigh flexible Weibull extension (RFWE) distribution is constructed by using a method developed by Alzaatreh et al. [10] to gener- ate a family of distributions. This class of distributions is defined as Gz ðÞ = ð −ln 1−Fz ðÞ ð Þ 0 gx ðÞ dx: ð1Þ Alzaatreh et al. [10] derived the Weibull-Pareto distribu- tion by taking gðxÞ to be the probability density function (pdf) of the Weibull distribution and F ðzÞ to be the cumula- tive density function (cdf) of the Pareto distribution, and Alzaatreh et al. [11] derived the gamma-normal distribution by taking gðxÞ to be the pdf of the gamma distribution and F ðzÞ to be the cdf of the normal distribution. Now, we consider pdf gðxÞ of Rayleigh distribution as a parent distribution given as gx ðÞ =2θxe −θx 2 : ð2Þ Hindawi Modelling and Simulation in Engineering Volume 2022, Article ID 7718284, 11 pages https://doi.org/10.1155/2022/7718284