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
Bagdonavičius, Vilijandas 1; Bikelis, Algimantas 1; Kazakevičius, Vytautas 1; Nikulin, Mikhail 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
@article{CRMATH_2006__342_1_63_0,
     author = {Bagdonavi\v{c}ius, Vilijandas and Bikelis, Algimantas and Kazakevi\v{c}ius, Vytautas and Nikulin, Mikhail},
     title = {Non-parametric estimation from simultaneous renewal{\textendash}failure{\textendash}degradation data with competing risks},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {63--68},
     publisher = {Elsevier},
     volume = {342},
     number = {1},
     year = {2006},
     doi = {10.1016/j.crma.2005.11.001},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2005.11.001/}
}
TY  - JOUR
AU  - Bagdonavičius, Vilijandas
AU  - Bikelis, Algimantas
AU  - Kazakevičius, Vytautas
AU  - Nikulin, Mikhail
TI  - Non-parametric estimation from simultaneous renewal–failure–degradation data with competing risks
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 63
EP  - 68
VL  - 342
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2005.11.001/
DO  - 10.1016/j.crma.2005.11.001
LA  - en
ID  - CRMATH_2006__342_1_63_0
ER  - 
%0 Journal Article
%A Bagdonavičius, Vilijandas
%A Bikelis, Algimantas
%A Kazakevičius, Vytautas
%A Nikulin, Mikhail
%T Non-parametric estimation from simultaneous renewal–failure–degradation data with competing risks
%J Comptes Rendus. Mathématique
%D 2006
%P 63-68
%V 342
%N 1
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2005.11.001/
%R 10.1016/j.crma.2005.11.001
%G en
%F CRMATH_2006__342_1_63_0
Bagdonavičius, Vilijandas; Bikelis, Algimantas; Kazakevičius, Vytautas; Nikulin, Mikhail. 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. http://www.numdam.org/articles/10.1016/j.crma.2005.11.001/

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

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

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

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

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

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

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

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

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

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

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

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

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

Cited by Sources: