scholarly journals Reliability and Inference for Multi State Systems: The Generalized Kumaraswamy Case

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1834
Author(s):  
Vlad Stefan Barbu ◽  
Alex Karagrigoriou ◽  
Andreas Makrides
Keyword(s):  
General Class ◽  
Asymptotic Theory ◽  
Continuous Distribution ◽  
Parameter Estimate ◽  
State System ◽  
Parameter Estimates ◽  
Reliability Parameter ◽  
Sojourn Times ◽  
Reliability Characteristics ◽  
Semi Markov Processes

Semi-Markov processes are typical tools for modeling multi state systems by allowing several distributions for sojourn times. In this work, we focus on a general class of distributions based on an arbitrary parent continuous distribution function G with Kumaraswamy as the baseline distribution and discuss some of its properties, including the advantageous property of being closed under minima. In addition, an estimate is provided for the so-called stress–strength reliability parameter, which measures the performance of a system in mechanical engineering. In this work, the sojourn times of the multi-state system are considered to follow a distribution with two shape parameters, which belongs to the proposed general class of distributions. Furthermore and for a multi-state system, we provide parameter estimates for the above general class, which are assumed to vary over the states of the system. The theoretical part of the work also includes the asymptotic theory for the proposed estimators with and without censoring as well as expressions for classical reliability characteristics. The performance and effectiveness of the proposed methodology is investigated via simulations, which show remarkable results with the help of statistical (for the parameter estimates) and graphical tools (for the reliability parameter estimate).

Standard Asymptotic Theory

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Asymptotic Theory ◽  
Asymptotic Variance ◽  
Statistical Significance ◽  
Regularity Conditions ◽  
Parameter Estimates ◽  
Asymptotic Results ◽  
Ml Estimation ◽  
True Parameter ◽  
Log Likelihood ◽  
Ml Estimator

This book relies on maximum likelihood (ML) estimation of parameters. Asymptotic theory assumes regularity conditions hold when the ML estimator is consistent. Typically an additional third derivative condition is assumed to ensure that the ML estimator is also asymptotically normally distributed. Standard asymptotic results that then hold are summarized in this chapter; for example, the asymptotic variance of the ML estimator is then given by the Fisher information formula, and the log-likelihood ratio, the Wald and the score statistics for testing the statistical significance of parameter estimates are all asymptotically equivalent. Also, the useful profile log-likelihood then behaves exactly as a standard log-likelihood only in a parameter space of just one dimension. Further, the model can be reparametrized to make it locally orthogonal in the neighbourhood of the true parameter value. The large exponential family of models is briefly reviewed where a unified set of regular conditions can be obtained.

scholarly journals Analysis of reliability of systems with component-wise storages

2018 ◽  
Vol 58 ◽  
pp. 02024 ◽  
Author(s):  
Yuriy E. Obzherin ◽  
Stanislav M Sidorov ◽  
Mikhail M Nikitin
Keyword(s):  
Phase Space ◽  
Energy Systems ◽  
Two Component System ◽  
Additional Time ◽  
Component System ◽  
Time Redundancy ◽  
Reliability Characteristics ◽  
Two Component ◽  
Semi Markov Processes ◽  
Time Reserve

Time redundancy is a method of increasing the reliability and efficiency of the operation of systems for various purposes, in particular, energy systems. A system with time redundancy is given additional time (a time reserve) for restoring characteristics. In this paper, based on the theory of semi-Markov processes with a common phase space of states, a semi-Markov model of a two-component system with a component-wise instantly replenished time reserve is constructed. The stationary reliability characteristics of the system under consideration are determined.

A discrete formulation of the theory of sojourn times in a two-state system

2001 ◽  
Vol 289 (3-4) ◽  
pp. 307-320 ◽  
Author(s):  
Marian Boguñá ◽  
Jaume Masoliver ◽  
George H. Weiss
Keyword(s):  
State System ◽  
Sojourn Times ◽  
Discrete Formulation

Adaptive Estimation Using Multiagent Network Identifiers With Undirected and Directed Graph Topologies

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Teymur Sadikhov ◽  
Michael A. Demetriou ◽  
Wassim M. Haddad ◽  
Tansel Yucelen
Keyword(s):  
Directed Graph ◽  
Adaptive Estimation ◽  
Parameter Estimate ◽  
The State ◽  
Adaptive Observer ◽  
Parameter Estimates ◽  
Communication Architecture ◽  
Adaptive Identifier ◽  
The Mean ◽  
Additive Term

In this paper, we present an adaptive estimation framework predicated on multiagent network identifiers with undirected and directed graph topologies. Specifically, the system state and plant parameters are identified online using N agents implementing adaptive observers with an interagent communication architecture. The adaptive observer architecture includes an additive term which involves a penalty on the mismatch between the state and parameter estimates. The proposed architecture is shown to guarantee state and parameter estimate consensus. Furthermore, the proposed adaptive identifier architecture provides a measure of agreement of the state and parameter estimates that is independent of the network topology and guarantees that the deviation from the mean estimate for both the state and parameter estimates converge to zero. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.

Cumulative constrained sojourn times in semi-Markov processes with an application to pensionable service

1978 ◽  
Vol 15 (3) ◽  
pp. 531-542 ◽  
Author(s):  
Izzet Sahin
Keyword(s):  
Markov Processes ◽  
Sojourn Time ◽  
Working Life ◽  
Partial Coverage ◽  
Sojourn Times ◽  
Semi Markov Processes

This paper is concerned with the characterization of the cumulative pensionable service over an individual's working life that is made up of random lengths of service in different employments in a given industry, under partial coverage, transferability, and a uniform vesting rule. This characterization uses some results that are developed in the paper involving a functional and cumulative constrained sojourn times (constrained in the sense that if a sojourn time is less than a given constant it is not counted) in semi-Markov processes.

A Two-Stage Conditional Estimation Procedure for Unrestricted Latent Class Models

1980 ◽  
Vol 5 (2) ◽  
pp. 129-156 ◽  
Author(s):  
George B. Macready ◽  
C. Mitchell Dayton
Keyword(s):  
General Class ◽  
Latent Class ◽  
Estimation Procedure ◽  
Error Rates ◽  
Latent Class Models ◽  
Parameter Estimates ◽  
Probability Models ◽  
Two Stage ◽  
Conditional Estimation ◽  
Class Models

A variety of latent class models has been presented during the last 10 years which are restricted forms of a more general class of probability models. Each of these models involves an a priori dependency structure among a set of dichotomously scored tasks that define latent class response patterns across the tasks. In turn, the probabilities related to these latent class patterns along with a set of “Omission” and “intrusion” error rates for each task are the parameters used in defining models within this general class. One problem in using these models is that the defining parameters for a specific model may not be “identifiable.” To deal with this problem, researchers have considered curtailing the form of the model of interest by placing restrictions on the defining parameters. The purpose of this paper is to describe a two-stage conditional estimation procedure which results in reasonable estimates of specific models even though they may be nonidentifiable. This procedure involves the following stages: (a) establishment of initial parameter estimates and (b) step-wise maximum likelihood solutions for latent class probabilities and classification errors with iteration of this process until stable parameter estimates across successive iterations are obtained.

Cumulative constrained sojourn times in semi-Markov processes with an application to pensionable service

1978 ◽  
Vol 15 (03) ◽  
pp. 531-542
Author(s):  
Izzet Sahin
Keyword(s):  
Markov Processes ◽  
Sojourn Time ◽  
Working Life ◽  
Partial Coverage ◽  
Sojourn Times ◽  
Semi Markov Processes

This paper is concerned with the characterization of the cumulative pensionable service over an individual's working life that is made up of random lengths of service in different employments in a given industry, under partial coverage, transferability, and a uniform vesting rule. This characterization uses some results that are developed in the paper involving a functional and cumulative constrained sojourn times (constrained in the sense that if a sojourn time is less than a given constant it is not counted) in semi-Markov processes.

scholarly journals Sample Size and Test Length for Item Parameter Estimate and Exam Parameter Estimate

2021 ◽  
Vol 9 (1) ◽  
pp. 69-78
Author(s):  
Riswan Riswan
Keyword(s):  
Item Response Theory ◽  
Sample Size ◽  
Item Response ◽  
Parameter Estimate ◽  
Test Theory ◽  
Item Parameter ◽  
Parameter Estimates ◽  
Test Length ◽  
Response Theory ◽  
The Stability

The Item Response Theory (IRT) model contains one or more parameters in the model. These parameters are unknown, so it is necessary to predict them. This paper aims (1) to determine the sample size (N) on the stability of the item parameter (2) to determine the length (n) test on the stability of the estimate parameter examinee (3) to determine the effect of the model on the stability of the item and the parameter to examine (4) to find out Effect of sample size and test length on item stability and examinee parameter estimates (5) Effect of sample size, test length, and model on item stability and examinee parameter estimates. This paper is a simulation study in which the latent trait (q) sample simulation is derived from a standard normal population of ~ N (0.1), with a specific Sample Size (N) and test length (n) with the 1PL, 2PL and 3PL models using Wingen. Item analysis was carried out using the classical theory test approach and modern test theory. Item Response Theory and data were analyzed through software R with the ltm package. The results showed that the larger the sample size (N), the more stable the estimated parameter. For the length test, which is the greater the test length (n), the more stable the estimated parameter (q).

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