Abstract
Sequential order statistics is an extension of ordinary order statistics. They model the successive failure times in sequential k-out-of-n systems, where the failures of components possibly affect the residual lifetimes of the remaining ones. In this paper, we consider the residual lifetime of the components after the kth failure in the sequential (n − k + 1)-out-of-n system. We extend some results on the joint distribution of the residual lifetimes of the remaining components in an ordinary (n − k + 1)-out-of-n system presented in Bairamov and Arnold (Stat Probab Lett 78(8):945–952, 2008) to the case of the sequential (n − k + 1)-out-of-n system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. Wiley, New York
Asadi M, Bairamov I (2006) The mean residual life function of a k-out-of-n structure at the system level. IEEE Trans Reliab 55(2): 314–318
Bairamov I, Arnold BC (2008) On the residual lifelengths of the remaining components in an n − k + 1 out of n system. Stat Probab Lett 78(8): 945–952
Barlow RE, Proschan F (1975) Statistical theory of reliability and life testing. Holt-Rinehart and Winston, New York
Cramer E, Kamps U (1996) Sequential order statistics and k-out-of-n systems with sequentially adjusted failure rates. Ann Inst Statist Math 48: 535–549
Cramer E, Kamps U (2001) Estimation with sequential order statistics from exponential distributions. Ann Inst Statist Math 53: 307–324
David HA (1981) Order statistics, 2nd edn. Wiley, New York
Franco M, Ruiz MC, Ruiz JM (2003) Note on closure of the ILR and DLR classes under formation of coherent systems. Stat Pap 44: 279–288
Høyland A, Rausand M (1994) System reliability theory: models and statistical methods. Wiley, New York
Hu T, Jin W, Khaledi BE (2007) Ordering conditional distributions of generalized order statistics. Probab Eng Inf Sci 21: 401–417
Kamps U (1995) A concept of generalized order statistics. Teubner, Stuttgart
Khaledi BE, Shaked M (2007) Ordering conditional lifetimes of coherent systems. J Stat Plann Infer 137: 1173–1184
Li X, Chen J (2004) Aging properties of the residual life length of k-out-of-n systems with independent but nonidentical components. Appl Stoch Models Bus Ind 20: 143–153
Li X, Zhang Z (2008) Some stochastic comparisons of conditional coherent systems. Appl Stoch Models Bus Ind 24: 541–549
Meeker WQ, Escobar LA (1998) Statistical methods for reliability data. Wiley, New York
Navarro J, Balakrishnan N, Samaniego FJ (2008) Mixture representations of residual lifetimes of used systems. J Appl Probab 45(4): 1097–1112
Navarro J, Eryilmaz S (2007) Mean residual lifetimes of consecutive-k-out-of-n systems. J Appl Probab 44: 82–98
Navarro J, Shaked M (2006) Hazard rate ordering of order statistics and systems. J Appl Probab 43(2): 391–408
Poursaeed MH (2009) A note on the mean past and the mean residual life of a (n − k + 1)-out-of-n system under multi monitoring. Stat Pap. doi:10.1007/s00362-009-0207-y
Rao CR, Shanbhag DN (1994) Choquet-Deny type functional equations with applications to stochastic models. Wiley, Chichester
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gurler, S. On residual lifetimes in sequential (n − k + 1)-out-of-n systems. Stat Papers 53, 23–31 (2012). https://doi.org/10.1007/s00362-010-0305-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-010-0305-x