Geodesic
Application of Sedyakin's model and Birnbaum–Saunders family for statistical analysis of redundant systems with one warm stand-by unit
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 155-171 
M. S. Nikulin; R. Tahir. Application of Sedyakin's model and Birnbaum–Saunders family for statistical analysis of redundant systems with one warm stand-by unit. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 155-171. http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a9/
@article{ZNSL_2011_396_a9,
     author = {M. S. Nikulin and R. Tahir},
     title = {Application of {Sedyakin's} model and {Birnbaum{\textendash}Saunders} family for statistical analysis of redundant systems with one warm stand-by unit},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {155--171},
     year = {2011},
     volume = {396},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a9/}
}
TY  - JOUR
AU  - M. S. Nikulin
AU  - R. Tahir
TI  - Application of Sedyakin's model and Birnbaum–Saunders family for statistical analysis of redundant systems with one warm stand-by unit
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2011
SP  - 155
EP  - 171
VL  - 396
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a9/
LA  - en
ID  - ZNSL_2011_396_a9
ER  - 
%0 Journal Article
%A M. S. Nikulin
%A R. Tahir
%T Application of Sedyakin's model and Birnbaum–Saunders family for statistical analysis of redundant systems with one warm stand-by unit
%J Zapiski Nauchnykh Seminarov POMI
%D 2011
%P 155-171
%V 396
%U http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a9/
%G en
%F ZNSL_2011_396_a9

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The purpose of this paper is to determine the improved system reliability by introducing the redundancy of the components. This paper considers one warm stand-by unit with one main unit. We study the reliability of such systems using the probability models in terms of the Sedyakin's Model. Parametric family of Birnbaum–Saunders distributions is considered as the distribution of failure times of both main and stand-by units. Parametric point and interval estimation is obtained from censored data.

[1] V. Bagdonavičius, “Testing the hypothesis of the additive accumulation of damages”, Theory Probab. Appl., 23:2 (1978), 403–408 | MR | Zbl

[2] V. Bagdonavičius, M. Nikulin, “Transfer functional and semiparametric regression models”, Biometrika, 84 (1997), 365–378 | DOI | MR | Zbl

[3] V. Bagdonavičius, M. Nikulin, Accelerated Life Models: Modeling and Statistical Analysis, Chapman and Hall, 2002

[4] V. Bagdonavičius, I. Masiulaityle, M. Nikulin, “Statistical analysis of redundant system with “warm” stand-by units”, Stochastics: An International Journal of Probability and Stochastical Processes, 80:2–3 (2008), 115–128 | DOI | MR | Zbl

[5] V. Bagdonavičius, I. Masiulaityle, M. Nikulin, “Statistical analysis of redundant system with one stand-by unit”, Mathematical methods in Survival analysis, reliability and quality of life, eds. Huber C., Limnios N., Balakrishnan N., Messbah M., Nikulin M., ISTE Wiley, London, 2008, 189–202 | MR

[6] V. Bagdonavičius, I. Masiulaityle, M. Nikulin, “Asymptotic Properties of Redundant Systems Reliability Estimators”, Advances in Degradation Modeling: Applications to Reliability, Survival Analysis, and Finance, 1st Edition, eds. Nikulin M., Limnios N., Balakrishnan N., Kahle W., Huber C., Birkhäuser Boston, 2009, 293–310 | MR

[7] V. Bagdonavičius, I. Masiulaityle, M. Nikulin, “Parametric estimation of redundant system reliability from censored data”, Mathematical and Statistical Methods in Reliability, eds. Balakrishnan N., Nikulin M., Rykov V., Springer Verlag, Boston, 2010, 51–64 | MR

[8] N. Balakrishnan, V. Leiva, J. Lopez, “Acceptance sampling plans from truncated life tests based on the generalized Birnbaum-Saunders distribution”, Communications in Statistics: Simulation and Computation, 36 (2007), 643–656 | DOI | MR | Zbl

[9] N. Balakrishnan, V. Leiva, A. Sanhueza, F. Vilca, “Estimation in the Birnbaum–Saunders distribution based on scale-mixture of normals and the EM-algorithm”, SORT, 33:2 (2009), 171–192 | MR | Zbl

[10] Z. W. Birnbaum, S. C. Saunders, “A new family of life distributions”, J. Appl. Probab., 6 (1969), 637–652 | MR

[11] A. Desmond, “On the Relationship Between two Fatigue-lide Models”, Trans. Reliab., 35 (1986), 167–169 | DOI | Zbl

[12] D. Kundu, N. Kannan, N. Balakrishnan, “On the hazard function of Birnbaum-Saunders distribution and associated inference”, Comput. Statist. Data Anal., 52 (2008), 2692–2702 | DOI | MR | Zbl

[13] A. J. Lemonte, F. Cribari-Neto, K. L. P. Vasconcellos, “Improved statistical inference for the two-parameter Birnbaum–Saunders distribution”, Comput. Statist. Data Anal., 51 (2007), 4656–4681 | DOI | MR | Zbl

[14] W. Q. Meeker, L. Escobar, Statistical Methods for Reliability Data, Wiley, 1998 | Zbl

[15] M. Nikulin, N. Saaidia, R. Tahir, “Reliability analysis of redundant systems by simulation for data with unimodal hazard rate functions”, Math. Engin. Sci. Aerosp., 2:3 (2011), 105–114 | MR

[16] N. M. Sedyakin, “On one physical principle in reliability theory”, Techn. Cybernetics, 3 (1966), 80–87 (in russian)

[17] I. N. Volodin, O. A. Dzhungurova, “On limit distribution emerging in the generalized Birnbaum–Saunders model”, J. Math. Sc., 99 (2000), 1348–1366 | DOI | MR | Zbl