Comptes Rendus
Statistics/Probability Theory
Non-parametric estimation from simultaneous renewal–failure–degradation data with competing risks
Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 63-68.

A joint model for linear degradation and competing failure data with partial renewals is proposed. Non-parametric estimation procedures for failure intensities and failure probabilities as functions of degradation level are given. Asymptotic properties of the estimators are investigated.

Nous proposons un modèle conjoint pour des données de dégradation linéaire à taux aléatoire et des défaillances à modalités multiples et compétitives, sous des hypothèses de renouvellement partiel. Les procédures d'estimation non-paramétrique pour les intensités et les probabilités de panne comme fonctions du niveau de dégradation sont données ce qui permet d'obtenir les propriétés asymptotiques des estimateurs.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.11.001
Vilijandas Bagdonavičius 1; Algimantas Bikelis 1; Vytautas Kazakevičius 1; Mikhail Nikulin 2, 3

1 University of Vilnius, 24, Naugarduko, Vilnius, Lithuania
2 Université Victor-Segalen Bordeaux 2, 146, rue Leo-Saignat, 33076 Bordeaux cedex, France
3 Mathematical Institute, Russian Academy of Sciences, Saint Petersbourg, Russia
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Vilijandas Bagdonavičius; Algimantas Bikelis; Vytautas Kazakevičius; Mikhail Nikulin. Non-parametric estimation from simultaneous renewal–failure–degradation data with competing risks. Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 63-68. doi : 10.1016/j.crma.2005.11.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.11.001/

[1] V. Bagdonavičius; A. Bikelis; V. Kazakevičius Statistical analysis of linear degradation and failure time data with multiple failure modes, Lifetime Data Anal., Volume 10 (2004), pp. 65-81

[2] V. Bagdonavicius; A. Bikelis; V. Kazakevicius; M. Nikulin Estimation from simultaneous degradation and failure data (B. Linquist; K.A. Doksum, eds.), Mathematical and Statistical Methods in Reliability, Series on Quality, Reliability and Engineering Statistics, vol. 7, World Scientific, 2003, pp. 301-318

[3] V. Bagdonavičius; M. Nikulin Accelerated Life Models, Chapman and Hall/CRC, Boca Raton, 2002

[4] V. Bagdonavičius; M. Nikulin Estimation in degradation models with explanatory variables, Lifetime Data Anal., Volume 7 (2001), pp. 85-103

[5] R. Henderson; P. Diggle; A. Dobson Joint modeling of longitudinal measurements and event time data, Biostatistics, Volume 1 (2002), pp. 465-480

[6] J. Hogan; N. Laird Mixture models for the joint distribution of repeated measures and event times, Statistics in Medicine, Volume 16 (1997), pp. 239-257

[7] P. Hu; A. Tsiatis; M. Davidian Estimating the parameters in the Cox model when covariate variables are measured with error, Biometrics, Volume 54 (1998), pp. 1407-1419

[8] J. Jacod; A.N. Shyriayev Limit Theorems for Stochastic Processes, Springer, New York, 1987

[9] W. Kahle, Statistical models for the degree of repair in incomplete repair models, in: Proceedings of the International Symposium on Stochastic Models in Reliability, Safety, Security and Logistics, Sami Shamoon College of Engineering, Beer Sheva, February 2005, pp. 15–17

[10] A. Lehmann On a degradation–failure models for repairable items (M. Nikulin; N. Balakrishnan; M. Mesbah; N. Limnios, eds.), Parametric and Semiparametric Models with Applications to Reliability Survival Analysis, and Quality of Life, Birkhäuser, Boston, 2004, pp. 65-80

[11] X. Song; M. Davidian; A. Tsiatis An estimator of the proportional hazards model with multiple longitudinal covariates measured with error, Biostatistics, Volume 3 (2002), pp. 511-528

[12] A. Tsiatis; M. Davidian A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error, Biometrika, Volume 88 (2001), pp. 447-458

[13] Y. Wang; J. Taylor Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome, J. Amer. Statist. Assoc., Volume 96 (2001), pp. 895-905

[14] M. Wulfsohn; A. Tsiatis A joint model for survival and longitudinal data measured with error, Biometrics, Volume 53 (1997), pp. 330-339

[15] J. Xu; S. Zeger Joint analysis of longitudinal data comprising repeated measures and times to events, Appl. Statist., Volume 50 (2001), pp. 375-387

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