Data and Parameter Interval Estimation

2021 ◽  
pp. 89-104
Author(s):  
R. Russell Rhinehart ◽  
Robert M. Bethea
Keyword(s):  
Interval Estimation ◽  
Parameter Interval

scholarly journals Parameter Interval Estimation of System Reliability for Repairable Multistate Series-Parallel System with Fuzzy Data

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wimonmas Bamrungsetthapong ◽  
Adisak Pongpullponsak
Keyword(s):  
Confidence Interval ◽  
System Reliability ◽  
Fuzzy System ◽  
Estimation Method ◽  
Interval Estimation ◽  
Parallel System ◽  
Expected Length ◽  
Parameter Interval ◽  
Sets Theory ◽  
Triangular Membership Function

The purpose of this paper is to create an interval estimation of the fuzzy system reliability for the repairable multistate series–parallel system (RMSS). Two-sided fuzzy confidence interval for the fuzzy system reliability is constructed. The performance of fuzzy confidence interval is considered based on the coverage probability and the expected length. In order to obtain the fuzzy system reliability, the fuzzy sets theory is applied to the system reliability problem when dealing with uncertainties in the RMSS. The fuzzy number with a triangular membership function is used for constructing the fuzzy failure rate and the fuzzy repair rate in the fuzzy reliability for the RMSS. The result shows that the good interval estimator for the fuzzy confidence interval is the obtained coverage probabilities the expected confidence coefficient with the narrowest expected length. The model presented herein is an effective estimation method when the sample size isn≥100. In addition, the optimalα-cut for the narrowest lower expected length and the narrowest upper expected length are considered.

scholarly journals Reliability Parameter Interval Estimation of NC Machine Tools considering Working Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Li Hongzhou ◽  
Sun Lixia
Keyword(s):  
Working Conditions ◽  
Machine Tools ◽  
Estimation Method ◽  
Interval Estimation ◽  
Point Estimation ◽  
Test Field ◽  
Reliability Parameter ◽  
Nc Machine ◽  
Nc Machine Tools ◽  
Parameter Interval

Aiming at the problem that the parameter interval estimation of NC machine tool’s reliability model considering working conditions established by Hongzhou is difficult to implement, given that it has several independent variables, an improved interval estimation method based on Bootstrap is proposed. Firstly, the two-step estimation method was used to calculate the point estimation of NC machine tool’s reliability parameter in test field, based on which B resamplings are generated based on the point estimation. The reliability parameter’s point estimation of the resamplings was obtained by maximum likelihood estimation. Permutation of B point estimations was made in ascending order and the interval estimations were obtained by the α quantile of the permutation. Case study indicated that the location and length of the interval estimation of NC machine tools’ reliability parameter, under different levels of working condition covariates, vary obviously.

scholarly journals INTERVAL ESTIMATION OF DISTRIBUTION PARAMETER BY STATISTICAL TRIALS OF EXPECTED VALUE

2019 ◽  
pp. 138-143
Author(s):  
V.O. Barannik
Keyword(s):  
Numerical Approximation ◽  
Interval Estimation ◽  
Random Variable ◽  
Expected Value ◽  
Distribution Parameter ◽  
Upper And Lower Bounds ◽  
Distribution Parameters ◽  
Estimation Of Distribution ◽  
Parameter Interval ◽  
Interval Estimators

The distribution parameter interval estimators are obtained by direct numerical approximation of the expected value for infinite and finite populations under the known upper and lower bounds of the random variable domain. Like in Bayesian approach, the distribution parameters are treated as random variables, and their uncertainty is described as a distribution. The Monte Carlo procedure is involved to get the correspondent confidence interval endpoints. The model does not impose any restrictions on the type of distributions. In contrast to other nonparametric interval assessments of distribution parameters, the model is operable for samples of any size.

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