Hostname: page-component-7dd5485656-wjfd9 Total loading time: 0 Render date: 2025-10-30T18:51:09.312Z Has data issue: false hasContentIssue false
  • English
  • Français

On ordered system signature and its dynamic version for coherent systems with applications

Part of: Survival analysis and censored data Nonparametric inference Operations research and management science

Published online by Cambridge University Press:  28 February 2023

He Yi ,
Narayanaswamy Balakrishnan  and
Xiang Li
He Yi*
Affiliation:
Beijing University of Chemical Technology
Narayanaswamy Balakrishnan*
Affiliation:
McMaster University
Xiang Li*
Affiliation:
Beijing University of Chemical Technology
*
*Postal address: School of Economics and Management, Beijing University of Chemical Technology, North Third Ring Road 15, Chaoyang District, 100029, Beijing, China.
***Postal address: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4K1, Canada.
*Postal address: School of Economics and Management, Beijing University of Chemical Technology, North Third Ring Road 15, Chaoyang District, 100029, Beijing, China.
Get access Rights & Permissions [Opens in a new window]

Abstract

The notion of ordered system signature, originally defined for independent and identical coherent systems, is first extended to the case of independent and non-identical coherent systems, and then some key properties that help simplify its computation are established. Through its use, a dynamic ordered system signature is defined next, which facilitates a systematic study of dynamic properties of several coherent systems under a life test. The theoretical results established here are then illustrated through some specific examples. Finally, the usefulness in the evaluation of aging used systems of the concepts introduced is demonstrated.

Keywords

Ordered system signaturecoherent systemdynamic ordered system signatureused systemagingstochastic ordering

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 90B25: Reliability, availability, maintenance, inspection 62G30: Order statistics; empirical distribution functions

Information

Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 3 , September 2023 , pp. 982 - 1002
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Ashrafi, S. and Asadi, M. (2014). Dynamic reliability modeling of three-state networks. J. Appl. Prob. 51, 999–1020.CrossRefGoogle Scholar
Balakrishnan, N., Beutner, E. and Cramer, E. (2010). Exact two-sample non-parametric confidence, prediction, and tolerance intervals based on ordinary and progressively Type-II right censored data. Test 19, 68–91.CrossRefGoogle Scholar
Balakrishnan, N., Ng, H. K. T. and Navarro, J. (2011). Linear inference for Type-II censored system lifetime data with signatures available. IEEE Trans. Rel. 60, 426–440.CrossRefGoogle Scholar
Balakrishnan, N., Ng, H. K. T. and Navarro, J. (2011). Exact nonparametric inference for component lifetime distribution based on lifetime data from systems with known signature. J. Nonpar. Statist. 23, 741–752.CrossRefGoogle Scholar
Balakrishnan, N., and Volterman, W. (2014). On the signatures of ordered system lifetimes. J. Appl. Prob. 51, 82–91.CrossRefGoogle Scholar
Coolen, F. P. A. and Coolen-Maturi, T. (2012). Generalizing the signature to systems with multiple types of components. In Complex Systems and Dependability, eds W. Zamojski, J. Mazurkiewicz, J. Sugier, T. Walkowiak, and J.‘Kacprzyk. Springer, Berlin, pp. 115–130.Google Scholar
Coolen-Maturi, T., Coolen, F. P. A. and Balakrishnan, N. (2021). The joint survival signature of coherent systems with shared components. Reliab. Eng. Syst. Safety 207, 107350.CrossRefGoogle Scholar
Cramer, E., and Navarro, J. (2015). Progressive Type-II censoring and coherent systems. Naval Res. Logistics 62, 512–530.CrossRefGoogle Scholar
Cramer, E., and Navarro, J. (2016). The progressive censoring signature of coherent systems. Appl. Stoch. Models Business Industry 32, 697–710.CrossRefGoogle Scholar
Da, G. and Hu, T. (2013). On bivariate signatures for systems with independent modules. In Stochastic Orders in Reliability and Risk, eds H. Li and X. Li. Springer, New York, pp. 143–166.CrossRefGoogle Scholar
Eryilmaz, S., Coolen, F. P. A. and Coolen-Maturi, T. (2018). Mean residual life of coherent systems consisting of multiple types of dependent components. Naval Res. Logistics 65, 86–97.CrossRefGoogle Scholar
Eryilmaz, S. and Tuncel, A. (2016). Generalizing the survival signature to unrepairable homogeneous multi-state systems. Naval Res. Logistics 63, 593–599.CrossRefGoogle Scholar
Gertsbakh, I. and Shpungin, Y. (2012). Multidimensional spectra of multistate systems with binary components. In Recent Advances in System Reliability, eds A. Lisnianski and I. Frenkel. Springer, London, pp. 49–61.CrossRefGoogle Scholar
Kelkinnama, M., Tavangar, M. and Asadi, M. (2015). New developments on stochastic properties of coherent systems. IEEE Trans. Rel. 64, 1276–1286.CrossRefGoogle Scholar
Kochar, S., Mukerjee, H. and Samaniego, F. J. (1999). The ‘signature’ of a coherent system and its application to comparisons among systems. Naval Res. Logistics 46, 507–523.3.0.CO;2-D>CrossRefGoogle Scholar
Lindqvist, B. H., Samaniego, F. J. and Wang, N. (2019). Preservation of the mean residual life order for coherent and mixed systems. J. Appl. Prob. 56, 153–173.CrossRefGoogle Scholar
Mahmoudi, M. and Asadi, M. (2011). The dynamic signature of coherent systems. IEEE Trans. Rel. 60, 817–822.CrossRefGoogle Scholar
Navarro, J., Balakrishnan, N. and Samaniego, F. J. (2008). Mixture representations for residual lifetimes of used systems. J. Appl. Prob. 45, 1097–1112.CrossRefGoogle Scholar
Navarro, J., Ruiz, J. M. and Sandoval, C. J. (2007). Properties of coherent systems with dependent components. Commun. Statist. Theory Meth. 36, 175–191.CrossRefGoogle Scholar
Navarro, J., Samaniego, F. J. and Balakrishnan, N. (2013). Mixture representations for the joint distribution of lifetimes of two coherent systems with shared components. Adv. Appl. Prob. 45, 1011–1027.CrossRefGoogle Scholar
Navarro, J., Samaniego, F. J., Balakrishnan, N. and Bhattacharya, D. (2008). On the application and extension of system signatures in engineering reliability. Naval Res. Logistics 55, 313–327.CrossRefGoogle Scholar
Samaniego, F. J. (1985). On closure of the IFR class under formation of coherent systems. IEEE Trans. Rel. 34, 69–72.CrossRefGoogle Scholar
Samaniego, F. J. (2007). System Signatures and Their Applications in Engineering Reliability. Springer, New York.CrossRefGoogle Scholar
Samaniego, F. J., Balakrishnan, N. and Navarro, J. (2009). Dynamic signatures and their use in comparing the reliability of new and used systems. Naval Res. Logistics 56, 577–591.CrossRefGoogle Scholar
Toomaj, A., Chahkandi, M. and Balakrishnan, N. (2021). On the information properties of working used systems using dynamic signature. Appl. Stoch. Models Business Industry 37, 318–341.CrossRefGoogle Scholar
Yang, Y., Ng, H. K. T. and Balakrishnan, N. (2016). A stochastic expectation-maximization algorithm for the analysis of system lifetime data with known signature. Comput. Statist. 31, 609–641.CrossRefGoogle Scholar
Yang, Y., Ng, H. K. T. and Balakrishnan, N. (2019). Expectation-maximization algorithm for system-based lifetime data with unknown system structure. AStA Adv. Statist. Anal. 103, 69–98.CrossRefGoogle Scholar
Yi, H., Balakrishnan, N. and Cui, L. R. (2020). On the multi-state signatures of ordered system lifetimes. Adv. Appl. Prob. 52, 291–318.CrossRefGoogle Scholar
Yi, H., Balakrishnan, N. and Cui, L. R. (2021). Computation of survival signatures for multi-state consecutive-k systems. Reliab. Eng. Syst. Safety 208, 107429.CrossRefGoogle Scholar
Yi, H., Balakrishnan, N. and Cui, L. R. (2022). On dependent multi-state semi-coherent systems based on multi-state joint signature. To appear in Methodology Comput. Appl. Prob., DOI: 10.1007/s11009-021-09877-3.CrossRefGoogle Scholar
Yi, H. and Cui, L. R. (2018). A new computation method for signature: Markov process method. Naval Res. Logistics 65, 410–426.CrossRefGoogle Scholar
Zarezadeh, S., Asadi, M. and Balakrishnan, N. (2014). Dynamic network reliability modeling under nonhomogeneous Poisson processes. Eur. J. Operat. Res. 232, 561–571.CrossRefGoogle Scholar