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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Models and estimation for systems with recurrent events and usage processes.

Jerald F Lawless1, Martin J Crowder

  • 1Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada. jlawless@uwaterloo.ca

Lifetime Data Analysis
|March 12, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces joint models to analyze recurrent event failures and usage patterns, improving failure prediction even with incomplete usage data. The models offer insights into the relationship between usage and failure events.

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Last Updated: Jun 15, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Area of Science:

  • Reliability Engineering
  • Survival Analysis
  • Statistical Modeling

Background:

  • Understanding recurrent event processes and usage intensity is crucial for predicting system failures.
  • Incomplete usage data presents a significant challenge in analyzing the relationship between usage and failures.
  • Existing models may not adequately capture the complex interplay between recurrent events and usage dynamics.

Purpose of the Study:

  • To develop and present joint models for recurrent event processes and usage, enabling a comprehensive analysis of their relationship.
  • To provide a robust statistical framework for predicting failures based on usage patterns.
  • To address the challenge of incomplete usage data through effective statistical estimation techniques.

Main Methods:

  • Development of joint models for recurrent events (failures) and usage processes.
  • Implementation of maximum likelihood estimation for handling incomplete usage data.
  • Exploration of random effects models, including linear and gamma usage processes.

Main Results:

  • The proposed joint models effectively capture the relationship between unit usage and recurrent failures.
  • Maximum likelihood estimation provides a viable method for analyzing data with missing usage information.
  • Demonstrated the utility of the models using real-world automobile warranty claims data.

Conclusions:

  • Joint modeling of recurrent events and usage offers a powerful approach for failure analysis and prediction.
  • The methodology is effective even when usage data is incomplete, enhancing its practical applicability.
  • The study provides a valuable tool for reliability engineering and warranty analysis.