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Accounting for measurement error in log regression models with applications to accelerated testing.

Robert Richardson1, H Dennis Tolley1, William E Evenson2

  • 1Department of Statistics, Brigham Young University, Provo, UT, United States of America.

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Summary

Parameter estimates in regression models can be biased due to measurement errors, impacting predictions in accelerated lifetime testing. This study introduces a weighted regression approach to address both measurement and additive errors in log regression models.

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Area of Science:

  • Statistics
  • Reliability Engineering

Background:

  • Parameter estimates in regression models are prone to bias when explanatory variables contain measurement errors.
  • This bias is particularly problematic in accelerated lifetime testing, where extrapolation amplifies prediction errors.
  • Additive stochastic components in log regression models can also introduce bias if incorrectly modeled as multiplicative.

Purpose of the Study:

  • To develop and evaluate a robust log regression model that accounts for both measurement error and additive error.
  • To improve the accuracy of parameter estimation and prediction in accelerated lifetime testing.
  • To provide a more reliable method for analyzing accelerated testing data.

Main Methods:

  • Approximation of a log regression model with measurement error and additive error using a weighted regression model.
  • Estimation of the weighted regression model via Iteratively Re-weighted Least Squares (IRLS).
  • Application and comparison of the proposed model to existing methods using the reduced Eyring equation in accelerated testing scenarios.

Main Results:

  • The proposed weighted regression approach effectively mitigates bias caused by measurement and additive errors.
  • Simulations and real-world data analysis demonstrate the superiority of the new model over previously accepted methods.
  • Improved accuracy in parameter estimates and extrapolated predictions for accelerated lifetime testing data.

Conclusions:

  • The developed weighted regression model offers a significant advancement for analyzing accelerated testing data.
  • Accounting for both measurement and additive errors is crucial for reliable modeling and prediction in reliability engineering.
  • This method provides a more accurate and robust alternative for practitioners in accelerated lifetime testing.