search for


Analysis of degradation data using double hierarchical generalized linear model
Journal of the Korean Data & Information Science Society 2018;29:217-28
Published online January 31, 2018
© 2018 Korean Data and Information Science Society.

Maengseok Noh1 · You-Jin Ok2 · Myung Hwan Na3 · Chi Tim Ng4

1Department of Statistics, Pukyong University
234Department of Statistics, Chonnam National University
Correspondence to: Professor, Department of Statistics, Chonnam National University, 77, Yongbong-ro, Buk-gu, Gwangju 61186, Korea. E-mail:
Received December 26, 2017; Revised January 10, 2018; Accepted January 11, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
To estimate the expected lifetime of tires on a car, we use the field experiment data which report the degradation depths according to driving distance for each of four experiment cars. Ordinary linear model does not allow correlation within repeated experiment data and gives parameter estimates sensitive to outliers. For analysis of data, in this paper we consider a double hierarchical generalized linear model (DHGLM) in which the mean and dispersion parameters can be modeled as random-effects models. In DHGLMs, we can allow the heterogeneity between different cars in the mean as well as the dispersion parameters. The introduction of random effects to dispersion parameters provides estimates that are less sensitive to the presence of outliers. For statistical inferences, we use the hierarchical likelihood approach. In this paper, by showing various statistical tools such as model selection criteria and residual plots with real data analysis, DHGLM is very useful model for degradation data with correlation and outliers.
Keywords : Degradation data, double hierarchical generalized linear models, dierarchical likelihood approach, outlier, random effects.