Research Article RobustAssessingtheLifetimePerformanceofProductswith InverseGaussianDistributioninBayesianandClassicalSetup AbdullahAliH.Ahmadini , 1 AmaraJaved, 2 SohailAkhtar , 3 ChristopheChesneau , 4 FarrukhJamal , 5 ShokryaS.Alshqaq, 1 MohammedElgarhy , 6 SanaaAl-Marzouki, 7 M.H.Tahir , 5 andWaleedAlmutiry 8 1 Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia 2 School of Statistics, Minhaj University, Lahore, Pakistan 3 Department of Mathematics and Statistics, University of Haripur, Haripur, Khyber Pakhtunkhwa, Pakistan 4 Department of Mathematics, Universit´ e de Caen, LMNO, Campus II, Science 3, 14032 Caen, France 5 Department of Statistics, e Islamia University Bahawalpur, Bahawalpur, Pakistan 6 e Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, Algarbia 31951, Egypt 7 Statistics Department, Faculty of Science, King Abdul Aziz University, Jeddah 21551, Saudi Arabia 8 Department of Mathematics, College of Science and Arts in Ar Rass, Qassim University, Ar Rass, Saudi Arabia Correspondence should be addressed to Farrukh Jamal; farrukh.jamal@iub.edu.pk Received 7 July 2021; Revised 6 September 2021; Accepted 15 September 2021; Published 4 October 2021 Academic Editor: Amer Al-Omari Copyright © 2021 Abdullah Ali H. Ahmadini et al. is 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. e inverse Gaussian (Wald) distribution belongs to the two-parameter family of continuous distributions having a range from 0 to ∞ and is considered as a potential candidate to model diffusion processes and lifetime datasets. Bayesian analysis is a modern inferential technique in which we estimate the parameters of the posterior distribution obtained by formally combining a prior distribution with an observed data distribution. In this article, we have attempted to perform the Bayesian and classical analyses of the Wald distribution and compare the results. Jeffreys’ and uniform priors are used as noninformative priors, while the ex- ponential distribution is used as an informative prior. e analysis comprises finding joint posterior distributions, the posterior means, predictive distributions, and credible intervals. To illustrate the entire estimation procedure, we have used real and simulated datasets, and the results thus obtained are discussed and compared. We have used the Bayesian specialized Open BUGS software to perform Markov Chain Monte Carlo (MCMC) simulations using a real dataset. 1.Introduction In probability theory, the inverse Gaussian distribution (IGD), also known as the Wald distribution, belongs to the two-parameter family of continuous distributions with support 0 to ∞ [1]. e concept of Brownian motion is applicable in describing the inherent process of many phenomena, particularly in the natural and physical sciences. e time in which a Brownian motion with a positive drift reaches a fixed value is distributed as an IGD. e probability density function, or density for short, of the IGD is given by f(x; μ, λ)� λ 2πx 3   1/2 exp − λ(x − μ) 2 2μ 2 x  , x > 0, μ > 0, λ > 0. (1) Here, μ is the location and λ is the shape parameter. e IGD approaches the normal distribution as λ ⟶∞. Hindawi Mathematical Problems in Engineering Volume 2021, Article ID 4582958, 9 pages https://doi.org/10.1155/2021/4582958