This paper investigates the statistical inference of inverse power Lomax distribution parameters under progressive first-failure censored samples. The maximum likelihood estimates (MLEs) and the asymptotic confidence intervals are derived based on the iterative procedure and asymptotic normality theory of MLEs, respectively. Bayesian estimates of the parameters under squared error loss and generalized entropy loss function are obtained using independent gamma priors. For Bayesian computation, Tierney–Kadane’s approximation method is used. In addition, the highest posterior credible intervals of the parameters are constructed based on the importance sampling procedure. A Monte Carlo simulation study is carried out to compare the behavior of various estimates developed in this paper. Finally, a real data set is analyzed for illustration purposes.

Predicting remaining useful life (RUL) plays a crucial role in predictive maintenance, improving system reliability, availability, and safety. However, obtaining data from the target domain is often challenging in real-world industrial applications. This article focuses on the domain generalization (DG) problem, where the attention is directed toward adapting algorithms to unseen domains. Building upon the popular algorithm domain adversarial neural network (DANN) for DG, we extend the contrastive adversarial domain adaptation method using a multiple source–source adversarial network to learn domain-invariant features from multiple source domains. In addition, we incorporate the swin-transformer structure into our model to enhance its capability in extracting time–frequency features, leveraging its excellent performance in visual DG problems. Furthermore, to expand the training dataset, we propose a novel augmentation algorithm for time–frequency data. Through predictive experiments in scenarios with unknown domain labels, we validate the contribution of the proposed methods to RUL prediction performance.

Entropy measures the uncertainty associated with a random variable. It has important applications in cybernetics, probability theory, astrophysics, life sciences and other fields. Recently, many authors focused on the estimation of entropy with different life distributions. However, the estimation of entropy for the generalized Bilal (GB) distribution has not yet been involved. In this paper, we consider the estimation of the entropy and the parameters with GB distribution based on adaptive Type-II progressive hybrid censored data. Maximum likelihood estimation of the entropy and the parameters are obtained using the Newton–Raphson iteration method. Bayesian estimations under different loss functions are provided with the help of Lindley’s approximation. The approximate confidence interval and the Bayesian credible interval of the parameters and entropy are obtained by using the delta and Markov chain Monte Carlo (MCMC) methods, respectively. Monte Carlo simulation studies are carried out to observe the performances of the different point and interval estimations. Finally, a real data set has been analyzed for illustrative purposes.