An extension of the cosine generalized family is presented in this paper by using the cosine trigonometric function and method of parameter induction concurrently. Prominent characteristics of the proposed family along with useful results are extracted. Moreover, two new subfamilies and several special models are also deduced. A four-parameter model called an Extended Cosine Weibull (ECW) with its mathematical properties is studied deeply. Graphical study reveals that the new model adopts right- and left-skewed, symmetrical, and reversed-J density shapes, while all possible monotone and nonmonotone shapes are exhibited by the hazard rate function. The maximum likelihood technique is exercised for parametric estimation, while estimation performance is accessed via Monte Carlo simulation study graphically and numerically. The superiority of the presented model over several outstanding and competing models is confirmed via three reliability and survival dataset applications.

We focus on estimating the stress-strength reliability model when the strength variable is subjected to the step-stress partially accelerated life test. Based on the assumption that both stress and strength random variables follow Weibull distribution with a common first shape parameter, the inferences for this reliability system are constructed. The maximum likelihood, two parametric bootstraps, and Bayes estimates are obtained. Moreover, approximate confidence intervals, asymptotic variance-covariance matrix, and highest posterior density credible intervals are derived. A simulation study and application to real-life data are conducted to compare the proposed estimation methods developed here and also check the accuracy of the results.

The present research mainly aims to use a mathematical formula to determine the optimal intervals for conducting preventive maintenance operations for machines to reduce the expected failure time when the malfunction data follow the Weibull distribution. The reliability function, failure rate, and the average time between machine failures were derived after performing preventive maintenance operations and before conducting preventive maintenance operations to state the amelioration that happens to machines. These rely on real data of performing preventive maintenance operations and the downtime required to repair machine or device faults that occur between preventive maintenance periods and the downtime necessary to perform preventive maintenance operations on the machine or device. Thus, the study concluded that preventive maintenance operations are working to increase the reliability of the machine and improve it, as well as to increase the average period of time for the machine to operate between faults.

In the survival data analysis, competing risks are commonly overlooked, and conventional statistical methods are used to analyze the event of interest. There may be more than one cause of death or failure in many experimental investigations of survival analysis. A competing risks model will be derived statistically applying Type-II half logistic weibull sub-distributions. Type-II half logistic weibull life?times failure model with independent causes. It is possible to estimate parameters and parametric functions using Bayesian and classical methods. A Bayes estimation is obtained by the Markov chain Monte-Carlo method. The posterior density function and the Metropolis-Hasting algorithm are used to calculate the Markov chain Monte-Carlo samples. Simulation data is used to evaluate the performance of the two methods according to the Type-II censored system. As a test of the discussed model, a real data set is provided.

This study introduces a novel trigonometric-based family of distributions for modeling continuous data through a newly proposed framework known as the ASP family, where ‘ASP’ represents the initials of the authors Aadil, Shamshad, and Parvaiz. A specific subclass of this family, termed the “ASP Rayleigh distribution” (ASPRD), is introduced that features two parameters. We conducted a comprehensive statistical analysis of the ASPRD, exploring its key properties and demonstrating its superior adaptability. The model parameters are estimated using four classical estimation methods: maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), and maximum product of spaces estimation (MPSE). Extensive simulation studies confirm these estimation techniques’ robustness, showing that biases, mean squared errors, and root mean squared errors consistently decrease as sample sizes increase. To further validate its applicability, we employ ASPRD on three real-world engineering datasets, showcasing its effectiveness in modeling complex data structures. This work not only strengthens the theoretical framework of probability distributions but also provides valuable tools for practical applications, paving the way for future advancements in statistical modeling.

The inverse Lomax distribution has been extensively used in many disciplines, including stochastic modelling, economics, actuarial sciences, and life testing. It is among the most recognizable lifetime models. The purpose of this research is to look into a new and important aspect of the inverse Lomax distribution: the calculation of the fuzzy stress-strength reliability parameter RF = P(Y < X), as­suming X and Y are random independent variables that follow the inverse Lomax probability distribution. The properties of structural for the proposed reliability model are studied along with the Bayesian estimation methods, maximum product of the spacing and maximum likelihood. Extensive simulation studies are achieved to explore the performance of the various estimates. Subsequently, two sets of real data are considered to highlight the practicability of the model.