Inference on Reliability in Two-parameter Exponential Stress–strength Model

Estimation for the P(X > Y) of Lomax distribution under accelerated life tests

The system or unit survives when strength is more significant than the stress enjoined. This procedure is usually used in many companies to test their product. The reliability or the quality of the scheme or component is described by the parameters of stress-strength reliability (R = P ( X > Y )) where X denotes strength and Y indicates stress. In this article, we adopted the statistical inference of R while the two arbitrary factors X and Y are independent and approach the Lomax lifetime distribution with common scale parameters. Also, the strength and stress variables are subjected to a partial step-stress-quickened life experiment. The classical estimation and Bayes method create the point estimate of R. Confidence intervals of R are computed with asymptotic distribution, bootstrap technique, and Bayesian credible intervals. All results are evaluated and compared under an extensive simulation study. Finally, the lifetime data sets generated from the Lomax distribution are used to analyze the system's reliability by estimating R.

Estimating average wind speed in Thailand using confidence intervals for common mean of several Weibull distributions

The Weibull distribution has been used to analyze data from many fields, including engineering, survival and lifetime analysis, and weather forecasting, particularly wind speed data. It is useful to measure the central tendency of wind speed data in specific locations using statistical parameters for instance the mean to accurately forecast the severity of future catastrophic events. In particular, the common mean of several independent wind speed samples collected from different locations is a useful statistic. To explore wind speed data from several areas in Surat Thani province, a large province in southern Thailand, we constructed estimates of the confidence interval for the common mean of several Weibull distributions using the Bayesian equitailed confidence interval and the highest posterior density interval using the gamma prior. Their performances are compared with those of the generalized confidence interval and the adjusted method of variance estimates recovery based on their coverage probabilities and expected lengths. The results demonstrate that when the common mean is small and the sample size is large, the Bayesian highest posterior density interval performed the best since its coverage probabilities were higher than the nominal confidence level and it provided the shortest expected lengths. Moreover, the generalized confidence interval performed well in some scenarios whereas adjusted method of variance estimates recovery did not. The approaches were used to estimate the common mean of real wind speed datasets from several areas in Surat Thani province, Thailand, fitted to Weibull distributions. These results support the simulation results in that the Bayesian methods performed the best. Hence, the Bayesian highest posterior density interval is the most appropriate method for establishing the confidence interval for the common mean of several Weibull 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.

Confidence intervals for the difference between the coefficients of variation of Weibull distributions for analyzing wind speed dispersion

Wind energy is an important renewable energy source for generating electricity that has the potential to replace fossil fuels. Herein, we propose confidence intervals for the difference between the coefficients of variation of Weibull distributions constructed using the concepts of the generalized confidence interval (GCI), Bayesian methods, the method of variance estimates recovery (MOVER) based on Hendricks and Robey's confidence interval, a percentile bootstrap method, and a bootstrap method with standard errors. To analyze their performances, their coverage probabilities and expected lengths were evaluated via Monte Carlo simulation. The simulation results indicate that the coverage probabilities of GCI were greater than or sometimes close to the nominal confidence level. However, when the Weibull shape parameter was small, the Bayesian- highest posterior density interval was preferable. All of the proposed confidence intervals were applied to wind speed data measured at 90-meter wind energy potential stations at various regions in Thailand.

Estimation of the Reliability of a Stress-Strength System from Poisson Half Logistic Distribution

This paper discussed the estimation of stress-strength reliability parameter R=P(Y<X) based on complete samples when the stress-strength are two independent Poisson half logistic random variables (PHLD). We have addressed the estimation of R in the general case and when the scale parameter is common. The classical and Bayesian estimation (BE) techniques of R are studied. The maximum likelihood estimator (MLE) and its asymptotic distributions are obtained; an approximate asymptotic confidence interval of R is computed using the asymptotic distribution. The non-parametric percentile bootstrap and student’s bootstrap confidence interval of R are discussed. The Bayes estimators of R are computed using a gamma prior and discussed under various loss functions such as the square error loss function (SEL), absolute error loss function (AEL), linear exponential error loss function (LINEX), generalized entropy error loss function (GEL) and maximum a posteriori (MAP). The Metropolis–Hastings algorithm is used to estimate the posterior distributions of the estimators of R. The highest posterior density (HPD) credible interval is constructed based on the SEL. Monte Carlo simulations are used to numerically analyze the performance of the MLE and Bayes estimators, the results were quite satisfactory based on their mean square error (MSE) and confidence interval. Finally, we used two real data studies to demonstrate the performance of the proposed estimation techniques in practice and to illustrate how PHLD is a good candidate in reliability studies.

Estimation of the reliability of all-ceramic crowns using finite element models and the stress-strength interference theory

The reliability of all-ceramic crowns is of concern to both patients and doctors. This study introduces a new methodology for quantifying the reliability of all-ceramic crowns based on the stress-strength interference theory and finite element models. The variables selected for the reliability analysis include the magnitude of the occlusal contact area, the occlusal load and the residual thermal stress. The calculated reliabilities of crowns under different loading conditions showed that too small occlusal contact areas or too great a difference of the thermal coefficient between veneer and core layer led to high failure possibilities. There results were consistent with many previous reports. Therefore, the methodology is shown to be a valuable method for analyzing the reliabilities of the restorations in the complicated oral environment.