scholarly journals Reliability

2021 ◽  
pp. 81-94
Author(s):  
Lisa Jackson ◽  
Frank P. A. Coolen
Keyword(s):  
Statistical Inference ◽  
System Reliability ◽  
Likelihood Function ◽  
Reliability Data ◽  
Key Concepts

AbstractThis chapter introduces key concepts for quantification of system reliability. In addition, basics of statistical inference for reliability data are explained, in particular, the derivation of the likelihood function.

Missing Data Assumptions

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Roderick J. Little
Keyword(s):  
Missing Data ◽  
Statistical Inference ◽  
Missing Values ◽  
Likelihood Function ◽  
Sufficient Conditions ◽  
Annual Review ◽  
Publication Date ◽  
Missing Completely At Random ◽  
Missingness Mechanism ◽  
Original Definition

I review assumptions about the missing-data mechanism that underlie methods for the statistical analysis of data with missing values. I describe Rubin's original definition of missing at random, (MAR), its motivation and criticisms, and his sufficient conditions for ignoring the missingness mechanism for likelihood-based, Bayesian, and frequentist inference. Related definitions, including missing completely at random, always MAR, always missing completely at random, and partially MAR are also covered. I present a formal argument for weakening Rubin's sufficient conditions for frequentist maximum likelihood inference with precision based on the observed information. Some simple examples of MAR are described, together with an example where the missingness mechanism can be ignored even though MAR does not hold. Alternative approaches to statistical inference based on the likelihood function are reviewed, along with non-likelihood frequentist approaches, including weighted generalized estimating equations. Connections with the causal inference literature are also discussed. Finally, alternatives to Rubin's MAR definition are discussed, including informative missingness, informative censoring, and coarsening at random. The intent is to provide a relatively nontechnical discussion, although some of the underlying issues are challenging and touch on fundamental questions of statistical inference. Expected final online publication date for the Annual Review of Statistics, Volume 8 is March 7, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

AN INTRODUCTION TO ECONOMETRIC THEORY

1998 ◽  
Vol 14 (6) ◽  
pp. 795-798
Author(s):  
Oliver B. Linton
Keyword(s):  
Graduate Students ◽  
Statistical Inference ◽  
Conditional Expectation ◽  
First Year ◽  
Mathematical Background ◽  
Special Cases ◽  
Key Concepts

This book is a modern introduction to measure theoretic probability and statistical inference well targeted for graduate students in econometrics at top institutions. It would make an excellent textbook for first year graduate students who intend to specialize in econometrics or who have an advanced mathematical background, and it would also be a useful part of any graduate econometrics course. It is concise and intensely focused on the key conceptual points, thus counteracting the tendency toward long-windedness apparent in some recent econometric texts. Nevertheless, it provides many valuable insights into difficult material. In particular, the discussions of sigma fields and conditional expectation given a sigma field are very helpful. The coverage of multivariate concepts alongside univariate ones is particularly useful to econometricians and something that is missing from most comparable statistical texts. The author has a mature attitude to proof, providing complete and illuminating proofs of some results but making liberal use of simplifications provided by special cases, for example in Theorems 4.1 and 4.5 and Section 5.2.2, to shorten and focus the arguments. The proofs themselves are very clear and well presented. Carefully chosen diagrams are given throughout the book that nicely illustrate many of the key concepts. In addition, each chapter contains a long list of problems of varying complexity, which will be useful to instructors.

Maximum Likelihood Parameter Estimation of CNC System Reliability

2014 ◽  
Vol 487 ◽  
pp. 282-285
Author(s):  
Yan Gu ◽  
Yi Qiang Wang ◽  
Xiao Qin Zhou ◽  
Xiu Hua Yuan
Keyword(s):  
Genetic Algorithm ◽  
Parameter Estimation ◽  
Maximum Likelihood ◽  
System Reliability ◽  
Simulated Annealing Algorithm ◽  
Likelihood Function ◽  
Estimation Method ◽  
Distribution Model ◽  
Improved Genetic Algorithm ◽  
Cnc System

In order to increase calculation accuracy of CNC system reliability, this paper proposed a maximum likelihood parameter estimation method based on improved genetic algorithm. In the parameter estimation process for CNC system reliability distribution model, the maximum likelihood function value was gained by improving genetic algorithm through simulated annealing algorithm. Parameter estimation was carried out by setting Weibull distribution as an example. The result shows that the improved genetic algorithm can increase solution efficiency and convergence rate. Besides, it can effectively estimate parameters of reliability distribution model.

Parameter Estimation of Limited Failure Population Model With a Weibull Underlying Distribution

2020 ◽  
Vol 6 (2) ◽  
Author(s):  
Themistoklis Koutsellis ◽  
Zissimos P. Mourelatos
Keyword(s):  
Statistical Inference ◽  
Population Model ◽  
Likelihood Function ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Data Driven ◽  
Estimation Methods ◽  
Underlying Distribution ◽  
Function Fitting ◽  
Failure Statistics

Abstract For many data-driven reliability problems, the population is not homogeneous; i.e., its statistics are not described by a unimodal distribution. Also, the interval of observation may not be long enough to capture the failure statistics. A limited failure population (LFP) consists of two subpopulations, a defective and a nondefective one, with well-separated modes of the two underlying distributions. In reliability and warranty forecasting applications, the estimation of the number of defective units and the estimation of the parameters of the underlying distribution are very important. Among various estimation methods, the maximum likelihood estimation (MLE) approach is the most widely used. Its likelihood function, however, is often incomplete, resulting in an erroneous statistical inference. In this paper, we estimate the parameters of a LFP analytically using a rational function fitting (RFF) method based on the Weibull probability plot (WPP) of observed data. We also introduce a censoring factor (CF) to assess how sufficient the number of collected data is for statistical inference. The proposed RFF method is compared with existing MLE approaches using simulated data and data related to automotive warranty forecasting.

COMPARISON OF PROPORTIONAL HAZARDS MODELING, ADDITIVE HAZARDS MODELING AND PROPORTIONAL INTENSITY MODELING WHEN APPLIED TO REPAIRABLE SYSTEM RELIABILITY

1995 ◽  
Vol 02 (01) ◽  
pp. 23-34 ◽  
Author(s):  
DAVE WIGHTMAN ◽  
TONY BENDELL
Keyword(s):  
System Reliability ◽  
Proportional Hazards ◽  
Data Sets ◽  
Reliability Data ◽  
Data Set ◽  
Explanatory Variables ◽  
Additive Hazards ◽  
Proportional Intensity ◽  
Modeling Techniques ◽  
Selection Of

In an Industrial Reliability setting a number of modeling techniques are available which allow the incorporation of explanatory variables; for example, Proportional Hazards Modeling, Proportional Intensity Modeling and Additive Hazards Modeling. However, in many applied settings it is unclear what the form of the underlying process is, and thus which of the above modeling structures is the most appropriate, if any. In this paper we discuss the different modeling formulations with regard to such features as their appropriateness, flexibility, robustness and ease of implementation together with the author’s experience gained from application of the models to a wide selection of reliability data sets. In particular, a comparative study of the models when applied to a software reliability data set is provided.

Human Reliability in Industrial Systems: An Overview

1976 ◽  
Vol 20 (1) ◽  
pp. 12-16 ◽  
Author(s):  
David Embrey
Keyword(s):  
System Reliability ◽  
Human Error ◽  
Quantitative Assessment ◽  
Reliability Assessment ◽  
Human Reliability ◽  
Reliability Data ◽  
Industrial Systems ◽  
Areas Of Interest

This paper describes some of the major areas of interest in the field of human reliability. The nature of system reliability assessment is described, and the importance of considering human reliability emphasized. Human error is then discussed from several standpoints, and techniques for its quantitative assessment described. The review concludes with a description of the various sources of human reliability data and the research that is currently in progress.

scholarly journals Fisher information and statistical inference for phase-type distributions

2011 ◽  
Vol 48 (A) ◽  
pp. 277-293 ◽  
Author(s):  
Mogens Bladt ◽  
Luz Judith R. Esparza ◽  
Bo Friis Nielsen
Keyword(s):  
Em Algorithm ◽  
Statistical Inference ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Likelihood Function ◽  
Information Matrix ◽  
The Em Algorithm ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Newton Raphson

This paper is concerned with statistical inference for both continuous and discrete phase-type distributions. We consider maximum likelihood estimation, where traditionally the expectation-maximization (EM) algorithm has been employed. Certain numerical aspects of this method are revised and we provide an alternative method for dealing with the E-step. We also compare the EM algorithm to a direct Newton–Raphson optimization of the likelihood function. As one of the main contributions of the paper, we provide formulae for calculating the Fisher information matrix both for the EM algorithm and Newton–Raphson approach. The inverse of the Fisher information matrix provides the variances and covariances of the estimated parameters.

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