Stress-strength reliability under partially accelerated life testing using Weibull model

The reliability of a system is the probability that its strength exceeds its stress. This reliability is called as the stress-strength reliability. The inferences of the stress-strength reliability R=P(X>Y), when: (1) the strength (X) and stress (Y) are independent random variables follow one-parameter exponential distributions; and (2) the strength variable is subjected to the step-stress partially accelerated life test (SSPALT) are discussed recently. Exponential distribution has limitation to describe the strength and stress due to its constant failure rate. In this paper, we consider the estimate of R, when: (1) X and Y are independent random variables that follow two-parameter Weibull distributions; and (2) the strength variable X is subjected to the SSPALT. The maximum likelihood estimator of R and its asymptotic distribution are not obtained analytically and therefore the asymptotic confidence interval of R is discussed. A real data set is analyzed using the proposed model for illustrative and comparison purposes. Based on the numerical results, we would conclude that the exponential distribution is rejected to fit the strength and stress, at any significant level that is greater than or equal to 2.58%, against the Weibull model

A Unit Half-Logistic Geometric Distribution and Its Application in Insurance

A new one parameter distribution recently was proposed for modelling lifetime data called half logistic-geometric (HLG) distribution. In this paper, appropriate transformation is considered for HLG distribution and a new distribution is derived called unit half logistic-geometric (UHLG) distribution for modelling bounded data in the interval (0, 1). Some important statistical properties are investigated with a closed form quantile function. Some methods of parameter estimation are introduced to evaluate the distribution parameter and a simulation study is introduced to compare these different methods. A real data application in the insurance field is introduced to show the flexibility of the new distribution modelling such data comparing with other distributions

Inference of Reliability Analysis for Type II Half Logistic Weibull Distribution with Application of Bladder Cancer

The estimation of the unknown parameters of Type II Half Logistic Weibull (TIIHLW) distribution was analyzed in this paper. The maximum likelihood and Bayes methods are used as estimation methods. These estimators are used to estimate the fuzzy reliability function and to choose the best estimator of the fuzzy reliability function by comparing the mean square error (MSE). The simulation’s results showed that fuzziness is better than reality for all sample sizes, and fuzzy reliability at Bayes predicted estimates is better than the maximum likelihood technique. It produces the lowest average MSE until a sample size of n = 50 is obtained. A simulated data set is applied to diagnose the performance of the two techniques applied here. A real data set is used as a practice for the model discussed and developed the maximum likelihood estimate alternative model of TIIHLW as Topp Leone inverted Kumaraswamy, modified Kies inverted Topp–Leone, Kumaraswamy Weibull–Weibull, Marshall–Olkin alpha power inverse Weibull, and odd Weibull inverted Topp–Leone. We conclude that the TIIHLW is the best distribution fit for this data

Evaluating the system reliability of the bridge structure using the unit half-logistic geometric distribution

The concept of reliability has gained widespread use in various fields, including manufacturing. This paper examines a system consisting of five components, including a bridge network component. The components are assumed to be identical and have a varying failure rate over time, with a unit half-logistic geometric distribution. The study focuses on analyzing properties such as the mean time to failure (MTTF), α-fractiles, and reliability equivalence factor (REF). To improve the bridge system, the reduction and duplication methods are implemented. Numerical results are provided to demonstrate the effectiveness of these methods

The Unit Alpha-Power Kum-Modified Size-Biased Lehmann Type II Distribution: Theory, Simulation, and Applications

In order to represent the data with non-monotonic failure rates and produce a better fit, a novel distribution is created in this study using the alpha power family of distributions. This distribution is called the alpha-power Kum-modified size-biased Lehmann type II or, in short, the AP-Kum-MSBL-II distribution. This distribution is established for modeling bounded data in the interval (0,1). The proposed distribution’s moment-generating function, mode, quantiles, moments, and stress–strength reliability function are obtained, among other attributes. To estimate the parameters of the proposed distribution, estimation methods such as the maximum likelihood method and Bayesian method are employed to estimate the unknown parameters for the AP-Kum-MSBL-II distribution. Moreover, the confidence intervals, credible intervals, and coverage probability are calculated for all parameters. The symmetric and asymmetric loss functions are used to find the Bayesian estimators using the Markov chain Monte Carlo (MCMC) method. Furthermore, the proposed distribution’s usefulness is demonstrated using three real data sets. One of them is a medical data set dealing with COVID-19 patients’ mortality rate, the second is a trade share data set, and the third is from the engineering area, as well as extensive simulated data, which were applied to assess the performance of the estimators of the proposed distribution

Classical and Bayesian estimation for the extended odd Weibull power Lomax model with applications

A new continuous distribution called the extended odd Weibull power Lomax (ExOW-POLO) distribution is introduced and studied. Numerous reliability and statistical features are derived. Additionally studied are point estimates using maximum likelihood, maximum product space, least square, weighted least square, and Bayesian estimation techniques. The mean square error and bias of the maximum likelihood and Bayesian parameter estimators are computed using simulation approaches, such as Markov chain Monte Carlo. Two intraocular pressure (IOP) real datasets were conducted between January 2015 and February 2018 on 49 patients (84 eyes) under the age of two who presented with primary congenital glaucoma to the Paediatric Ophthalmology Unit of the Mansoura Ophthalmic Center of Mansoura University in Egypt have been fitted the ExOW-POLO distribution. Comparing the properties of the proposed distribution’s fitting of the data to recognized extensions of the Lomax distribution. The analysis revealed that the most well-known extensions of Lomax distribution were made by the ExOW-POLO distribution outfit. In addition, the correlation measures and independent sample test for the two IOP real datasets are introduced with (A) Levene’s test for equality of variances for the two cases and (B) the t-test for equality of means. For Levene’s test for equality of variances: the null hypothesis is that equal variances are assumed and the alternative hypothesis is that equal variances are not assumed

The odd lindley power rayleigh distribution: properties, classical and bayesian estimation with applications

In this paper, we propose and investigate the odd Lindley Power Rayleigh (OLPR) distribution, which is derived by combining the odd Lindley-G family and power Rayleigh distribution. The proposed distribution, which is comparable to the Lindley distribution, Rayleigh distribution and other Rayleigh generalizations have the desirable attribute of allowing greater flexibility than some of its well known extensions. A comprehensive account of the mathematical and statistical properties along with the estimation of parameters using classical and Bayesian estimation methodologies is presented. An extensive simulation study is carried out to assess the behaviour of estimators based on their biases and mean square errors. Finally, we consider two practical real-life applications, we observe that the proposed model outperforms other competing models using the Akaike information criterion (AIC), the Bayesian information criterion (BIC), Anderson-Darling (A*), Cramer-von Mises (W*) and other goodness-of-fit measures