Hybrid Fuzzy Estimation of System Reliability for Multi-State System

2017 ◽  
Vol 866 ◽  
pp. 387-391
Author(s):  
Wimonmas Bamrungsetthapong ◽  
Adisak Pongpullponsak
Keyword(s):  
Confidence Interval ◽  
System Reliability ◽  
Fuzzy System ◽  
Coverage Probability ◽  
Interval Estimation ◽  
Point Estimate ◽  
Hybrid Estimation ◽  
Expected Length ◽  
Fuzzy Parameter ◽  
Fuzzy Parameters

This article is purpose a hybrid estimation of the fuzzy system reliability for the Non-repairable multi-state series-parallel system (NMSS). Considering the fuzzy parameter of NMSS are prior fuzzy parameters. Then the posterior fuzzy parameters of NMSS are constructed by fuzzy Bayesian point estimate of fuzzy system reliability. Moreover, an approach to construct interval estimation of the fuzzy system reliability of NMSS will be used in estimation of the prior fuzzy confidence interval and posterior fuzzy confidence interval of fuzzy system reliability. Finally, the coverage probability and the expected length that it is used to interpret the efficiency of both fuzzy confidence intervals are presented.

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.

Fuzzy System Reliability Analysis Based on Confidence Interval

2012 ◽  
Vol 433-440 ◽  
pp. 4908-4914 ◽  
Author(s):  
Ezzatallah Baloui Jamkhaneh ◽  
Azam Nozari
Keyword(s):  
Confidence Interval ◽  
System Reliability ◽  
Fuzzy System ◽  
Statistical Data ◽  
Parallel Systems ◽  
Fuzzy Data ◽  
Statistical Methodology ◽  
Fuzzy Reliability ◽  
Numerical Examples ◽  
Cut Set

This paper proposes a new method for analyzing the fuzzy system reliability of a parallel-series and series-parallel systems using fuzzy confidence interval, where the reliability of each component of each system is unknown. To compute system reliability, we are estimated reliability of each component of the systems using fuzzy statistical data with both tools appropriate for modeling fuzzy data and suitable statistical methodology to handle these data. Numerical examples are given to compute fuzzy reliability and its cut set and the calculating was performed by using programming in software R.

scholarly journals Confidence Intervals for the Coefficient of Variation in a Normal Distribution with a Known Population Mean

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Wararit Panichkitkosolkul
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Coverage Probability ◽  
Normal Approximation ◽  
Monte Carlo Simulation Study ◽  
Population Mean ◽  
Expected Length ◽  
Simulation Results

This paper presents three confidence intervals for the coefficient of variation in a normal distribution with a known population mean. One of the proposed confidence intervals is based on the normal approximation. The other proposed confidence intervals are the shortest-length confidence interval and the equal-tailed confidence interval. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence intervals with the existing confidence intervals. Simulation results have shown that all three proposed confidence intervals perform well in terms of coverage probability and expected length.

Interval estimation of proportion ratios for stratified bilateral correlated binary data

2019 ◽  
Vol 29 (7) ◽  
pp. 1987-2014
Author(s):  
Yuqing Xue ◽  
Chang-Xing Ma
Keyword(s):  
Clinical Trials ◽  
Confidence Interval ◽  
Coverage Probability ◽  
Binary Data ◽  
Interval Estimation ◽  
Correlated Binary Data ◽  
Empirical Results ◽  
Estimation Of Proportion ◽  
Score Statistics ◽  
Interval Width

Confidence interval (CI) methods for the ratio of two proportions in the presence of correlated bilateral binary data are constructed for comparative clinical trials with stratified design. Simulations are conducted to evaluate the performance of the presented CIs with respect to mean coverage probability (MCP), mean interval width (MIW), and the ratio of mesial non-coverage probability to the distal non-coverage probability (RMNCP). Based on the empirical results, we suggest the use of the proposed CI method based on the complete score statistics (CS) for general applications. An example from a rheumatology study is used to demonstrate the proposed methodologies.

VALID CONFIDENCE INTERVALS IN REGRESSION AFTER VARIABLE SELECTION

1998 ◽  
Vol 14 (4) ◽  
pp. 463-482 ◽  
Author(s):  
Paul Kabaila
Keyword(s):  
Confidence Interval ◽  
Variable Selection ◽  
Confidence Intervals ◽  
Coverage Probability ◽  
Risk Function ◽  
Selection Procedure ◽  
Error Variance ◽  
Regression Parameters ◽  
Variable Selection Procedure ◽  
Expected Length

We consider a linear regression model with regression parameters (θ1,...,θp) and error variance parameter σ2. Our aim is to find a confidence interval with minimum coverage probability 1 − α for a parameter of interest θ1 in the presence of nuisance parameters (θ2,...,θp,σ2). We consider two confidence intervals, the first of which is the standard confidence interval for θ1 with coverage probability 1 − α. The second confidence interval for θ1 is obtained after a variable selection procedure has been applied to θp. This interval is chosen to be as short as possible subject to the constraint that it has minimum coverage probability 1 − α. The confidence intervals are compared using a risk function that is defined as a scaled version of the expected length of the confidence interval. We show that, subject to certain conditions including that [(dimension of response vector) − p] is small, the second confidence interval is preferable to the first when we anticipate (without being certain) that |θp|/σ is small. This comparison of confidence intervals is shown to be mathematically equivalent to a corresponding comparison of prediction intervals.

scholarly journals The Safety of COVID-19 Vaccinations—We Should Rethink the Policy

Vaccines ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 693
Author(s):  
Harald Walach ◽  
Rainer J. Klement ◽  
Wouter Aukema
Keyword(s):  
Side Effects ◽  
Confidence Interval ◽  
Field Study ◽  
Adverse Reactions ◽  
Safety Data ◽  
European Medicines Agency ◽  
Point Estimate ◽  
Drug Reactions ◽  
Vaccination Policy ◽  
Risks And Benefits

Background: COVID-19 vaccines have had expedited reviews without sufficient safety data. We wanted to compare risks and benefits. Method: We calculated the number needed to vaccinate (NNTV) from a large Israeli field study to prevent one death. We accessed the Adverse Drug Reactions (ADR) database of the European Medicines Agency and of the Dutch National Register (lareb.nl) to extract the number of cases reporting severe side effects and the number of cases with fatal side effects. Result: The NNTV is between 200–700 to prevent one case of COVID-19 for the mRNA vaccine marketed by Pfizer, while the NNTV to prevent one death is between 9000 and 50,000 (95% confidence interval), with 16,000 as a point estimate. The number of cases experiencing adverse reactions has been reported to be 700 per 100,000 vaccinations. Currently, we see 16 serious side effects per 100,000 vaccinations, and the number of fatal side effects is at 4.11/100,000 vaccinations. For three deaths prevented by vaccination we have to accept two inflicted by vaccination. Conclusions: This lack of clear benefit should cause governments to rethink their vaccination policy.

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