Skip to main content Accessibility help
×
Home
Hostname: page-component-5bf98f6d76-rs6k2 Total loading time: 0.32 Render date: 2021-04-20T14:34:51.788Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Univariate and multivariate stochastic orderings of residual lifetimes of live components in sequential (𝑛-π‘Ÿ+ 1)-out-of-𝑛 systems

Published online by Cambridge University Press:Β  16 November 2018

Ghobad Barmalzan
Affiliation:
University of Zabol
Abedin Haidari
Affiliation:
Shahid Beheshti University
Narayanaswamy Balakrishnan
Affiliation:
McMaster University
Corresponding

Abstract

Sequential order statistics can be used to describe the ordered lifetimes of components of a system when the failure of a component may affect the reliability of the remaining components. After a reliability system consisting of n components fails, some of its components may still be alive. In this paper we first establish some univariate stochastic orderings and ageing properties of the residual lifetimes of the live components in a sequential (n-r+1)-out-of-n system. We also obtain a characterizing result for the exponential distribution based on uncorrelated residual lifetimes of live components. Finally, we provide some sufficient conditions for comparing vectors of residual lifetimes of the live components from two sequential (n-r+1)-out-of-n systems. The results established here extend some well-known results in the literature.

Type
Research Papers
Copyright
Copyright Β© Applied Probability Trust 2018Β 

Access options

Get access to the full version of this content by using one of the access options below.

References

Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1992). A First Course in Order Statistics. John Wiley, New York.Google Scholar
Bairamov, I. and Arnold, B. C. (2008). On the residual lifelengths of the remaining components in an n-k+1 out of n system. Statist. Prob. Lett. 78, 945–952.CrossRefGoogle Scholar
Balakrishnan, N. and Rao, C. R. (eds) (1998a). Order Statistics: Theory and Methods (Handbook Statist. 16). North-Holland, Amsterdam.Google Scholar
Balakrishnan, N. and Rao, C. R. (eds) (1998b). Order Statistics: Applications (Handbook Statist. 17). North-Holland, Amsterdam.Google Scholar
Balakrishnan, N., Barmalzan, G. and Haidari, A. (2014). Stochastic orderings and ageing properties of residual life lengths of live components in (n-k+1)-out-of-n systems. J. Appl. Prob. 51, 58–68.CrossRefGoogle Scholar
Balakrishnan, N., Beutner, E. and Kamps, U. (2008). Order restricted inference for sequential k-out-of-n systems. J. Multivariate Anal. 99, 1489–1502.CrossRefGoogle Scholar
Balakrishnan, N., Beutner, E. and Kamps, U. (2011). Modeling parameters of a load-sharing system through link functions in sequential order statistics models and associated inference. IEEE Trans. Reliab. 60, 605–611.CrossRefGoogle Scholar
Balakrishnan, N. et al. (2015). Reliability inference on composite dynamic systems based on Burr type-XII distribution. IEEE Trans. Reliab. 64, 144–153.CrossRefGoogle Scholar
Belzunce, F., Mercader, J.-A., Ruiz, J.-M. and Spizzichino, F. (2009). Stochastic comparisons of multivariate mixture models. J. Multivariate Anal. 100, 1657–1669.CrossRefGoogle Scholar
Burkschat, M. and Navarro, J. (2011). Aging properties of sequential order statistics. Prob. Eng. Inf. Sci. 25, 449–467.CrossRefGoogle Scholar
Burkschat, M. and Navarro, J. (2013). Dynamic signature of coherent systems based on sequential order statistics. J. Appl. Prob. 50, 272–287.CrossRefGoogle Scholar
Casella, G. and Berger, R. L. (2002). Statistical Inference, 2nd edn. Thomson, Pacific Grove, CA.Google Scholar
Cramer, E. (2006). Sequential order statistics. In Encyclopedia of Statistical Sciences, Vol. 12, John Wiley, Hoboken, NJ, pp. 7629–7634.Google Scholar
Cramer, E. and Kamps, U. (2001). Sequential k-out-of-n systems. In Advances in Reliability (Handbook Statist. 20), North-Holland, Amesterdam, pp. 301–372.Google Scholar
David, H. A. and Nagaraja, H. N. (2003). Order Statistics, 3rd edn. John Wiley, Hoboken, NJ.CrossRefGoogle Scholar
Gurler, S. (2012). On residual lifetimes in sequential (n-k+1)-out-of-n systems. Statist. Papers 53, 23–31.CrossRefGoogle Scholar
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, Vol. 1, 2nd edn. John Wiley, New York.Google Scholar
Kamps, U. (1995). A Concept of Generalized Order Statistics. Teubner, Stuttgart.CrossRefGoogle Scholar
Kvam, P. H. and PeΓ±a, E. A. (2005). Estimating load-sharing properties in a dynamic reliability system. J. Amer. Statist. Assoc. 100, 262–272.CrossRefGoogle Scholar
Lai, C.-D. and Xie, M. (2006). Stochastic Ageing and Dependence for Reliability. Springer, New York.Google Scholar
Marshall, A. W. and Olkin, I. (2007). Life Distributions. Springer, New York.Google Scholar
MΓΌller, A. and Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. John Wiley, Chichester.Google Scholar
Murthy, D. N. P., Xie, M. and Jiang, R. (2004). Weibull Models. John Wiley, Hoboken, NJ.Google Scholar
Navarro, J. and Burkschat, M. (2011). Coherent systems based on sequential order statistics. Naval Res. Logistics 58, 123–135.CrossRefGoogle Scholar
Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.CrossRefGoogle Scholar
Torrado, N., Lillo, R. E. and Wiper, M. P. (2012). Sequential order statistics: ageing and stochastic orderings. Methodol. Comput. Appl. Prob. 14, 579–596.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 47 *
View data table for this chart

* Views captured on Cambridge Core between 16th November 2018 - 20th April 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the β€˜name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. β€˜@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. β€˜@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Univariate and multivariate stochastic orderings of residual lifetimes of live components in sequential (𝑛-π‘Ÿ+ 1)-out-of-𝑛 systems
Available formats
Γ—

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Univariate and multivariate stochastic orderings of residual lifetimes of live components in sequential (𝑛-π‘Ÿ+ 1)-out-of-𝑛 systems
Available formats
Γ—

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Univariate and multivariate stochastic orderings of residual lifetimes of live components in sequential (𝑛-π‘Ÿ+ 1)-out-of-𝑛 systems
Available formats
Γ—
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *