Markov Chain Monte Carlo-Based Estimation of Stress–Strength Reliability Parameter for Generalized Linear Failure Rate Distributions

2021 ◽  
pp. 2150031
Author(s):  
F. Shahsanaei ◽  
A. Daneshkhah
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Failure Rate ◽  
Interval Estimate ◽  
Reliability Parameter ◽  
Bayes Estimates ◽  
Squared Error ◽  
Classical Inference ◽  
Strength Models

This paper provides Bayesian and classical inference of Stress–Strength reliability parameter, [Formula: see text], where both [Formula: see text] and [Formula: see text] are independently distributed as 3-parameter generalized linear failure rate (GLFR) random variables with different parameters. Due to importance of stress–strength models in various fields of engineering, we here address the maximum likelihood estimator (MLE) of [Formula: see text] and the corresponding interval estimate using some efficient numerical methods. The Bayes estimates of [Formula: see text] are derived, considering squared error loss functions. Because the Bayes estimates could not be expressed in closed forms, we employ a Markov Chain Monte Carlo procedure to calculate approximate Bayes estimates. To evaluate the performances of different estimators, extensive simulations are implemented and also real datasets are analyzed.

scholarly journals Fuzzy Rule Interpolation and Extrapolation Techniques: Criteria and Evaluation Guidelines

2011 ◽  
Vol 15 (3) ◽  
pp. 254-263 ◽  
Author(s):  
Domonkos Tikk ◽  
◽  
Zsolt Csaba Johanyák ◽  
Szilveszter Kovács ◽  
Kok Wai Wong ◽  
...  
Keyword(s):  
Fuzzy Rule ◽  
Complexity Reduction ◽  
Control Problems ◽  
Approximation Techniques ◽  
Initial Investigation ◽  
Classical Inference ◽  
Rule Bases

This paper comprehensively analyzes Fuzzy Rule Interpolation and extrapolation Techniques (FRITs). Because extrapolation techniques are usually extensions of fuzzy rule interpolation, we treat them both as approximation techniques designed to be applied where sparse or incomplete fuzzy rule bases are used, i.e., when classical inference fails. FRITs have been investigated in the literature from aspects such as applicability to control problems, usefulness regarding complexity reduction and logic. Our objectives are to create an overall FRIT standard with a general set of criteria and to set a framework for guiding their classification and comparison. This paper is our initial investigation of FRITs. We plan to analyze details in later papers on how individual techniques satisfy the groups of criteria we propose. For analysis,MATLAB FRI Toolbox provides an easy-to-use testbed, as shown in experiments.

scholarly journals Contrasts and Classical Inference

2007 ◽  
pp. 126-139 ◽  
Author(s):  
J. Poline ◽  
F. Kherif ◽  
C. Pallier ◽  
W. Penny
Keyword(s):  
Classical Inference

scholarly journals Asymptotic inference for partially observed branching processes

2011 ◽  
Vol 43 (04) ◽  
pp. 1166-1190 ◽  
Author(s):  
Andrea Kvitkovičová ◽  
Victor M. Panaretos
Keyword(s):  
Branching Processes ◽  
Dependence Structure ◽  
Detection Mechanism ◽  
Nonparametric Estimators ◽  
Stochastic Epidemic ◽  
Partially Observed ◽  
Asymptotic Confidence Intervals ◽  
Interaction Scheme ◽  
Classical Inference ◽  
Spreading Potential

We consider the problem of estimation in a partially observed discrete-time Galton-Watson branching process, focusing on the first two moments of the offspring distribution. Our study is motivated by modelling the counts of new cases at the onset of a stochastic epidemic, allowing for the facts that only a part of the cases is detected, and that the detection mechanism may affect the evolution of the epidemic. In this setting, the offspring mean is closely related to the spreading potential of the disease, while the second moment is connected to the variability of the mean estimators. Inference for branching processes is known for its nonstandard characteristics, as compared with classical inference. When, in addition, the true process cannot be directly observed, the problem of inference suffers significant further perturbations. We propose nonparametric estimators related to those used when the underlying process is fully observed, but suitably modified to take into account the intricate dependence structure induced by the partial observation and the interaction scheme. We show consistency, derive the limiting laws of the estimators, and construct asymptotic confidence intervals, all valid conditionally on the explosion set.

scholarly journals OPTIMAL DISCRETE STOPPING TIMES FOR RELIABILITY GROWTH TESTS

2005 ◽  
Vol 12 (05) ◽  
pp. 365-383
Author(s):  
JOHN QUIGLEY
Keyword(s):  
Fault Detection ◽  
Likelihood Function ◽  
Growth Models ◽  
Minimum Variance ◽  
Stopping Times ◽  
Optimal Time ◽  
Reliability Growth ◽  
Time Intervals ◽  
Moderate Number ◽  
Classical Inference

Often, the duration of a reliability growth development test is specified in advance and the decision to terminate or continue testing is conducted at discrete time intervals. These features are normally not captured by reliability growth models. This paper adapts a standard reliability growth model to determine the optimal time for which to plan to terminate testing. The underlying stochastic process is developed from an Order Statistic argument with Bayesian inference used to estimate the number of faults within the design and classical inference procedures used to assess the rate of fault detection. Inference procedures within this framework are explored where it is shown the Maximum Likelihood Estimators possess a small bias and converges to the Minimum Variance Unbiased Estimator after few tests for designs with moderate number of faults. It is shown that the Likelihood function can be bimodal when there is conflict between the observed rate of fault detection and the prior distribution describing the number of faults in the design. An illustrative example is provided.

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