Estimation Of Reliability Function Research Articles

Pre-test Shrinkage Estimation for Reliability Function of Burr XII Distribution Using Progressive Type II Censored Sample under Precautionary Loss Function (PLF)

This article deal with the proposal of suggest and study of the properties of pre-test shrinkage estimators of Reliability Function for the Burr XII distribution using Progressive Type II censored sample. Since some difficulties to derive equations of risk function for proposed shrinkage estimators of reliability function under Precautionary Loss Function (PLF), we to study properties by using Monte-Carlo simulation. The numerical and Monte-Carlo simulations show that the performance of the proposed estimators is better than classical estimators in terms of relative risk.

Comparing of the Reliability for two-parameters Lomax distribution using Lindley method Estimation

Bayesian analysis of two-parameters Lomax distribution's reliability has been examined in this search using three prior functions [ Gamma, assumption &Inverted Levy] , the estimation was produced under squared errors loss function used idea of Lindley. The simulation study was carried out to assess the performance of the three alternative estimators of reliability function by 6 assumed experiments for different values of distributions parameters with small, moderate, and large sample sizes using mean squared error criteria. The best performance, according to the reported results showed that the best performance was for Inverted Levy prior with squared error loss function.

Comparing of the Reliability for two-parameters Lomax distribution using Lindley method Estimation

Bayesian analysis of two-parameters Lomax distribution's reliability has been examined in this search using three prior functions [ Gamma, assumption &Inverted Levy] , the estimation was produced under squared errors loss function used idea of Lindley. The simulation study was carried out to assess the performance of the three alternative estimators of reliability function by 6 assumed experiments for different values of distributions parameters with small, moderate, and large sample sizes using mean squared error criteria. The best performance, according to the reported results showed that the best performance was for Inverted Levy prior with squared error loss function.

On Estimation of Reliability Functions for the Extended Rayleigh Distribution under Progressive First-Failure Censoring Model

When conducting reliability studies, the progressive first-failure censoring (PFFC) method is useful in situations in which the units of the life testing experiment are separated into groups consisting of k units each with the intention of seeing only the first failure in each group. Using progressive first-failure censored samples, the statistical inference for the parameters, reliability, and hazard functions of the extended Rayleigh distribution (ERD) are investigated in this study. The asymptotic normality theory of maximum likelihood estimates (MLEs) is used in order to acquire the maximum likelihood estimates (MLEs) together with the asymptotic confidence intervals (Asym. CIs). Bayesian estimates (BEs) of the parameters and the reliability functions under different loss functions may be produced by using independent gamma informative priors and non-informative priors. The Markov chain Monte Carlo (MCMC) approach is used so that Bayesian computations are performed with ease. In addition, the MCMC method is used in order to create credible intervals (Cred. CIs) for the parameters, which may be used for either informative or non-informative priors. Additionally, computations for the reliability functions are carried out. A Monte Carlo simulation study is carried out in order to provide a comparison of the behaviour of the different estimations that were created for this work. At last, an actual data set is dissected for the purpose of providing an example.

Software Reliability Modelling and Application in Software Development Life Cycle

<div class="section abstract"><div class="htmlview paragraph">With the accelerating demands of new features in embedded software viz diagnostic services, infotainment instigate complex software development. Ever-increasing software complexity gives rise to unreliable behaviours in the vehicle system. Software reliability model reinforces the confidence of the end-user about the compliant operation of the provided software with respect to requirements. This paper describes the application of software reliability engineering in the Software development life cycle. Further, we are demonstrating means to compute the software operational reliability by acquiring defects observed at the software testing phase. A detailed software reliability model selection process led us to conclude to a software reliability model based on the Nonhomogeneous Poisson process (NHPP) by Schneidewind. The discussed Software reliability model considers both fault detection and correction process for modelling and uses historical defect data of the software for the estimation of fault rate, here the reliability model considers a subset of defect data to incorporate the “data aging” in the estimation. Obtain the correct estimates of the software reliability model parameters we used the Statistical Modelling and Estimation of Reliability Functions for Software (SMERFS V3) software tool. The software reliability engineering aids the project planning team by estimating the target operation reliability of software as well as the necessary time to evaluate the software & defects to be resolved to achieve the target. Software Reliability helps the organization by maintaining the balance between defect escape rate and cost incurred on software testing. Subsequently, employing effective software reliability techniques facilitate the organization to put forward software quality, quantitatively to the customers.</div></div>

Estimation of reliability function based on the upper record values for generalized gamma Lindley stress–strength model: Case study COVID-19

In this paper, the problem of estimation when X and Y are two independent upper record values from gamma Lindley distribution is considered. Maximum likelihood and the Bayesian estimator methods were used to set the best-estimated reliability function. The importance of this research is because this model, when applied, can obtain reliability values that depend on upper record values, which is an interesting problem in many real-life applications. Also, based on WHO data on the COVID-19 pandemic, a stress-strength model was applied based on the upper recorded values for Mont-Carlo simulation data.

Estimation of reliability function and mean time to system failure for k-out-of-n systems using Weibull failure time model

Estimation of reliability function and mean time to system failure for k-out-of-n systems using Weibull failure time model

Bayes and Empirical Bayesian Estimator of Reliability Function in Multicomponent Stress-Strength System based on Generalized Rayleigh Distribution

Bayes and Empirical Bayesian Estimator of Reliability Function in Multicomponent Stress-Strength System based on Generalized Rayleigh Distribution

Some Further Properties and Bayesian Inference for Inverse xgamma Distribution Under Progressive Type-II Censored Scheme

Inverse xgamma distribution is recently proposed by Yadav et al. (J Ind Prod Eng 35(1):48–55, 2018) as an inverted version of xgamma distribution. In the present article, some more statistical properties (such as, characteristic and generating functions, distributions of extreme order statistics, important entropy measures) and some additional survival and/or reliability characteristics (such as, conditional moments, mean deviation, Bonferroni and Lorenz curves, entropy, ageing intensity) of inverse xgamma distribution have been studied in detail. Classical and Bayesian inferential procedures to estimate the unknown parameter, reliability function, hazard rate function under progressively censored schemes have been investigated. Further, asymptotic confidence interval (ACI), bootstrap confidence interval (BCI) and highest posterior density (HPD) credible interval for the parameter have also been calculated. A Monte-Carlo simulation study has been performed to compare the performances of classical and Bayesian estimators of reliability function and hazard rate function. The performances of ACI, BCI and HPD credible intervals have been compared in terms of estimated average widths and coverage probabilities for the parameter. Lastly, a data set is analyzed for illustrating the proposed methodology.

Comparison of some reliability estimation methods for Laplace distribution using simulations

In this paper, we derived an estimator of reliability function for Laplace distribution with two parameters using Bayes method with square error loss function, Jeffery’s formula and conditional probability random variable of observation. The main objective of this study is to find the efficiency of the derived Bayesian estimator compared to the maximum likelihood of this function and moment method using simulation technique by Monte Carlo method under different Laplace distribution parameters and sample sizes. The consequences have shown that Bayes estimator has been more efficient than the maximum likelihood estimator and moment estimator in all samples sizes.

Minimum Variance Unbiased Estimation of Reliability Function for a Class of Generalizations of Lindley Distribution

Uniformly minimum variance unbiased (UMVU) estimators of reliability function (both stress–strength and mission time) and the associated variance are derived for a class of generalization of Lindley distribution. The application of the results is further validated by a real data study. AMS 2020 subject classification: 62N05 62F10

The robust estimators of reliability function for some compound distribution

This paper investigates the use of the POT technique for natural phenomena weather. Their data contain extreme values (high or rare values) by applying two methods. The first method is based on the estimate using the order statistical, and the second method is based on likelihood ratio. The comparative model is based on MSE of the estimated parameters, the probability density function for each distribution of the mixed distributions, and their reliability function. The POT sample has shown significant improvement in data and its superiority, especially in simple exponential distribution.

On Estimation of Stress-Strength Reliability Using Lower Record Values from Proportional Reversed Hazard Family

In this article, a study on the stress-strength parameter based on lower record values from one parameter proportional reversed hazard family (PRHF) has been conducted. The classical and Bayesian results of Khan and Arshad (UMVU Estimation of Reliability Function and Stress-Strength Reliability from Proportional Reversed Hazard Family Based on Lower Records. American Journal of Mathematical and Management Sciences, 35(2), 171–181) and Condino et al. (Likelihood and Bayesian estimation of P(Y < X) using lower record values from a general class of distributions. Statistical Papers), when the strength and stress variables belong to different family of distributions from PRHF have been generalized. Uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE) and Bayes estimator (BE) are obtained for the powers of the parameter and reliability functions and The estimators of three parametric functions, namely, powers of parameter, and are interrelated, whereas, in the literature, researchers have handled the three estimation problems separately. Moreover, it is has been shown that the expressions for and are not required to estimate them. In this article, the technique of obtaining estimators of and is simpler as it does not require Rao-Blackwellization. Simulation studies have been performed for analyzing the behavior of the proposed estimators. An example using real data has also been considered as an illustration.

Comparing Different Estimators of Reliability Function for Stress-Strength Models with Applications

Comparing Different Estimators of Reliability Function for Stress-Strength Models with Applications

Estimation of Reliability Function for Complete Data - Article Review

The theory of reliability is one of the important theories that is attracting great interest in many researchers at present because of its importance in various fields of life especially in determining the age of a particular device and its efficiency and the addition of applications in the field of radar and atmospheric and astronomical observation. The growing interest in reliability studies is due to the rapid technical and technological development and the use of complex systems in various fields. This paper reviews the article of reliability in terms of the reliability function for complete data of one of the failure time distributions (weibull distribution) and its parameters in different methods using simulation.

Estimation of Reliability Function for Complete Data - Article Review

Estimation of Reliability Function for Complete Data - Article Review

Generalized Gamma - Maxwell distribution: Properties and estimation of reliability functions

In this article, a new three parameter generalized distribution named as Generalized Gamma-Maxwell distribution is introduced. The proposed generalization can be seen as an extension of the Gamma-Maxwell distribution with more flexibility in terms of parameters. The basic properties of the distribution and its reliability characteristics are studied. We consider two types of reliability functions namely R(t) and stress-strength reliability function ‘P’. Maximum likelihood estimation of parameters and reliability functions is performed through numerical methods. A real data application is presented showing that the proposed distribution provides a better fit to real data as compared to other distributions.

Unbiased estimation of reliability function from a mixture of two exponential distributions based on a single observation

In this paper we investigate an aspect of unbiased estimation of the reliability function, based on a single observation from a mixture of two exponential distributions with known mixing proportions. We introduce a few equivalent versions of unbiased estimators, and find that they give proper estimates only if negative weights on component mixture distributions are allowed.

English

English

UMVU Estimation of Reliability Function and Stress–Strength Reliability from Proportional Reversed Hazard Family Based on Lower Records

SYNOPTIC ABSTRACTIn this study, we have obtained the uniformly minimum variance unbiased estimator (UMVUE) of reliability function and stress–strength reliability for one parameter proportional reversed hazard rate family of distribution based on lower record values. Further, the results are reduced for power function distribution, exponentiated Weibull distribution, generalized exponential distribution, generalized Rayleigh (also known as Burr type X) distribution and Topp–Leone distribution. Also, the UMVU estimator and maximum likelihood estimator are compared through simulation.