Geodesic
A counting process model of survival of parallel load-sharing system
Kybernetika, Tome 37 (2001) no. 1, pp. 47-60 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

A system composed from a set of independent and identical parallel units is considered and its resistance (survival) against an increasing load is modelled by a counting process model, in the framework of statistical survival analysis. The objective is to estimate the (nonparametrized) hazard function of the distribution of loads breaking the units of the system (i. e. their breaking strengths), to derive the large sample properties of the estimator, and to propose a goodness-of-fit test. We also examine the relationship between the survival of the system and the survival of its components.
A system composed from a set of independent and identical parallel units is considered and its resistance (survival) against an increasing load is modelled by a counting process model, in the framework of statistical survival analysis. The objective is to estimate the (nonparametrized) hazard function of the distribution of loads breaking the units of the system (i. e. their breaking strengths), to derive the large sample properties of the estimator, and to propose a goodness-of-fit test. We also examine the relationship between the survival of the system and the survival of its components.
Classification : 60G10, 60K10, 62M05, 62N02, 62N05
Keywords: hazard function; goodness-of-fit test 
@article{KYB_2001_37_1_a3,
     author = {Volf, Petr and Linka, Ale\v{s}},
     title = {A counting process model of survival of parallel load-sharing system},
     journal = {Kybernetika},
     pages = {47--60},
     year = {2001},
     volume = {37},
     number = {1},
     zbl = {1265.62021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2001_37_1_a3/}
}
TY  - JOUR
AU  - Volf, Petr
AU  - Linka, Aleš
TI  - A counting process model of survival of parallel load-sharing system
JO  - Kybernetika
PY  - 2001
SP  - 47
EP  - 60
VL  - 37
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/KYB_2001_37_1_a3/
LA  - en
ID  - KYB_2001_37_1_a3
ER  - 
%0 Journal Article
%A Volf, Petr
%A Linka, Aleš
%T A counting process model of survival of parallel load-sharing system
%J Kybernetika
%D 2001
%P 47-60
%V 37
%N 1
%U http://geodesic.mathdoc.fr/item/KYB_2001_37_1_a3/
%G en
%F KYB_2001_37_1_a3
Volf, Petr; Linka, Aleš. A counting process model of survival of parallel load-sharing system. Kybernetika, Tome 37 (2001) no. 1, pp. 47-60. http://geodesic.mathdoc.fr/item/KYB_2001_37_1_a3/

[1] Andersen P. K., Borgan O.: Counting process models for life history data: A review. Scand. J. Statist. 12 (1985), 97–158 | MR | Zbl

[2] Andersen P. K., Borgan O., Gill R. D., Keiding N.: Statistical Models Based on Counting Processes. Springer, New York 1993 | MR | Zbl

[3] Andersen P. K., Gill R. D.: Cox’s regression model for counting processes: A large sample study. Ann. Statist. 10 (1982), 1100–1120 | DOI | MR | Zbl

[4] Belyaev, Yu. K., Rydén P.: Non-parametric estimators of the distribution of tensile strengths for wires. Research Report 1997-15, University of Umea 1997

[5] Crowder M. J., Kimber A. C., Smith R. L., Sweeting T. L.: Statistical Analysis of Reliability Data. Chapman and Hall, London 1991 | MR

[6] Daniels H. E.: The maximum of a Gaussian process whose mean path has a maximum, with an application to the strength of bundles of fibres. Adv. in Appl. Probab. 21 (1991), 315–333 | DOI | MR

[7] Fleming T. R., Harrington D. P.: Counting Processes and Survival Analysis. Wiley, New York 1991 | MR | Zbl

[8] Hoffmann–Jørgensen J.: Probability with a View Towards Statistics, Volume II. Chapman and Hall, London 1994 | MR

[9] Rao C. R.: Linear Statistical Inference and Its Application. Wiley, New York 1965 | MR

[10] Suh M. W., Bhattacharyya B. B., Grandage A.: On the distribution and moments of the strength of a bundle of filaments. J. Appl. Probab. 7 (1970), 712–720 | DOI | MR | Zbl

[11] Volf P.: Analysis of generalized residuals in hazard regression models. Kybernetika 32 (1996), 501–510 | MR | Zbl