Fuzzy Lifetime Data Research Articles

Bayesian reliability estimation of weighted exponential-lindley distribution with intuitionistic fuzzy lifetime data

Bayesian reliability estimation of weighted exponential-lindley distribution with intuitionistic fuzzy lifetime data

Reliability Estimation of Inverse Weibull Distribution Based on Intuitionistic Fuzzy Lifetime Data

As a commonly used model in reliability analysis, the inverse Weibull distribution (IWD) is widely applied in various scientific fields. This paper considers the reliability estimation of the IWD based on intuitionistic fuzzy lifetime data. Firstly, the related concepts of the fuzzy set theory are reviewed, and the concepts of the intuitionistic fuzzy conditional density, intuitionistic fuzzy likelihood function, and intuitionistic fuzzy conditional expectation are obtained by extension. In classical estimations, the maximum likelihood estimators of parameters and reliability are derived. Due to the nonlinearity, the EM algorithm is used to obtain the maximum likelihood estimates. In the Bayesian estimation, the gamma prior is selected, and the Bayesian estimation of the parameters and reliability is conducted under the symmetric entropy and the scale square error loss function, respectively. Since the integrals are complicated, the Lindley approximation is used to approximate the Bayesian estimates. Then, the performance of these estimators is evaluated by the Monte Carlo simulation. The simulation results show that the Bayesian estimation is more suitable than the maximum likelihood estimation for the reliability estimation. Finally, a set of real data is used to prove the effectiveness of these proposed methods. Through these methods, the reliability of the intuitive fuzzy life data is accurately estimated, which provides an important reference for the reliability analysis in the scientific field.

Parameters and reliability estimation for the weibull distribution based on intuitionistic fuzzy lifetime data

In this paper, the definition of probability, conditional probability and likelihood function are generalized to the intuitionistic fuzzy observations. We focus on different estimation approaches of two-parameter Weibull (TW) distribution based on the intuitionistic fuzzy lifetime data including, maximum likelihood (ML) and Bayesian estimation methodology. The ML estimation of the parameters and reliability function of TW distribution is provided using the Newton–Raphson (NR) and Expectation–Maximization (EM) algorithms. The Bayesian estimates are provided via Tierney and Kadane’s approximation. In the Bayesian estimation approach, for the shape and scale parameters, the Gamma and inverse-Gamma priors are considered, respectively. Finally, a simulated data set is analyzed for illustrative purposes to show the applicability of the proposed estimation methods. The Monte Carlo simulations are performed to find the more efficient estimator in the intuitionistic fuzzy environment. The performances of the ML and Bayesian estimates of the parameters and reliability function are compared based on the mean biased (MB) and mean squared errors (MSE) criteria.

Competing Risk Analysis of Fuzzy Lifetime Data

Competing Risk Analysis of Fuzzy Lifetime Data

Statistical Inferences of Type-II Progressively Hybrid Censored Fuzzy Data with Rayleigh Distribution

This article presents the procedures for the estimation of the parameter of Rayleighdistribution based on Type-II progressive hybrid censored fuzzy lifetime data. Classicalas well as the Bayesian procedures for the estimation of unknown model parameters has been developed. The estimators obtained here are Maximum likelihood (ML) estimator, Method of moments (MM) estimator, Computational approach (CA) estimator and Bayes estimator. Highest posterior density (HPD) credible intervals of the unknown parameter are obtained by using Markov Chain Monte Carlo (MCMC) technique. For numerical illustration, a real data set has been considered.

BATHTUB HAZARD RATE DISTRIBUTIONS AND FUZZY LIFE TIMES

The development of life time analysis started back in the $20^{textit{th}}$ century and since then comprehensive developments have been made to model life time data efficiently. Recent development in measurements shows that all continuous measurements can not be measured as precise numbers but they are more or less fuzzy. Life time is also a continuous phenomenon, and has already been shown that life time observations are not precise measurements but fuzzy. Therefore, the corresponding analysis techniques employed on the data require to consider fuzziness of the observations to obtain appropriate estimates.In this study generalized estimators for the parameters and hazard rates are proposed for bathtub failure rate distributions to model fuzzy life time data effectively.

On the estimation of parameters, survival functions, and hazard rates based on fuzzy life time data

ABSTRACTLife time data analysis is regarded as one of the significant out-shoots of statistics. Classical statistical techniques reckon life time observations as precise numbers and solely cover variation among the observations. In fact, there are two types of uncertainty in data: variation among the observations and the fuzziness. To this effect, the analysis techniques, which do not consider fuzziness and are only based on precise life time observations, use incomplete information; hence lead to pseudo results. This study aimed at generalizing parameters estimation, survival functions, and hazard rates for fuzzy life time data.

EMPIRICAL ACCELERATION FUNCTIONS AND FUZZY INFORMATION

In accelerated life testing approaches lifetime data are obtained under various conditions which are considered more severe than the usual condition. Classical analysis techniques are based on obtained precise measurements, and used to model variation among the observations. In fact, data have two types of uncertainty: variation among the observations and fuzziness of the single observation. Analysis techniques, which do not consider fuzziness and are only based on precise lifetime observations, lead to pseudo results. The aim of this study was to examine the behavior of empirical acceleration functions using fuzzy lifetime data. Furthermore the results showed an increased fuzziness in the transformed lifetimes compared to the input data.

On the survival models for step-stress experiments based on fuzzy life time data

In statistical methodologies of life time analyses accelerated life testing (ALT) has a significant importance. In accelerated life testing the measurements of life times are recorded under various conditions which are more severe than usual environment. The techniques related to the inference of life times in ALT are usually based on precise measurements. In practical applications life time data have two types of uncertainty, one is stochastic variation and the other is fuzziness. Classical stochastic models are developed to draw inference based on the variation among observations, and do nothing with fuzziness. By doing so the analyses are based on incomplete information and can lead to misleading conclusions. In this study estimators are proposed to cover fuzziness in addition to stochastic variation of the life times. The results based on the proposed methods are more suitable for realistic life time data.

Empirical reliability functions based on fuzzy life time data

Reliability analysis is one of the significant applications of statistics. Many parametric and non-parametric techniques are available for reliability estimation based on precise life time observations, without considering the uncertainty of individual observations. But life time observations are not precise measurements but more or less fuzzy. Therefore by considering life time measurements as precise numbers we may lose information and get misleading results. This study is aimed to present some non-parametric estimates for reliability functions based on fuzzy life time data.

Reliability estimation in Rayleigh distribution based on fuzzy lifetime data

Some work has been done in the past on the estimation of reliability characteristics of Rayleigh distribution based on complete and censored samples. But, traditionally it is assumed that the available data are performed in exact numbers. However, in real world situations, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. Thus, it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers. In this paper, we present a Bayesian approach to estimate the parameter and reliability function of Rayleigh distribution from fuzzy lifetime data. Based on fuzzy data, the Bayes estimates can not be obtained in explicit forms; therefore, we provide two approximations, namely Lindley’s approximation and Tierney and Kadane’s approximation as well as a Markov Chain Monte Carlo method to compute the Bayes estimates of the parameter and reliability function. Their performance is then assessed through Monte Carlo simulations. Finally, one real data set is analyzed for illustrative purposes.

On reliability estimation based on fuzzy lifetime data

Real lifetime data are never precise numbers but more or less non-precise, also called fuzzy. This kind of imprecision is connected with all measurement results of continuous variables, therefore also with time observations. Imprecision is different from errors and variability. Therefore estimation methods for reliability characteristics have to be adapted to the situation of fuzzy lifetimes in order to obtain realistic results.

An evaluation of the reliability of complex systems using shadowed sets and fuzzy lifetime data

In this paper, we consider the problem of the evaluation of system reliability using statistical data obtained from reliability tests of its elements, in which the lifetimes of elements are described using an exponential distribution. We assume that this lifetime data may be reported imprecisely and that this lack of precision may be described using fuzzy sets. As the direct application of the fuzzy sets methodology leads in this case to very complicated and time consuming calculations, we propose simple approximations of fuzzy numbers using shadowed sets introduced by Pedrycz (1998). The proposed methodology may be simply extended to the case of general lifetime probability distributions.

Bayesian reliability analysis for fuzzy lifetime data

Lifetime data are important in reliability analysis. Classical reliability estimation is based on precise lifetime data. It is usually assumed that observed lifetime data are precise real numbers. However, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. Thus, it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers. Bayesian methods have proved to be very useful when the sample size is small. There is little study on Bayesian reliability estimation based on fuzzy lifetime data. Most of the reported works in this area is limited to single parameter lifetime distributions. In this paper, we propose a new method to determine the membership function of the estimates of the parameters and the reliability function of multi-parameter lifetime distributions. An artificial neural network is used to approximate the calculation process of parameter estimation and reliability prediction. The genetic algorithm is used to find the boundary values of the membership function of the estimate of interest at any cut level. This method can be used to determine the membership functions of the Bayesian estimates of multi-parameter distributions. The effectiveness of the proposed method is illustrated with normal and Weibull distributions.