×

A note on comparisons among coherent systems with dependent components using signatures. (English) Zbl 1068.60026

S. Kochar, H. Mukerjee and F. J. Samaniego [Nav. Res. Logist. 46, No. 5, 507–523 (1999; Zbl 0948.90067)] obtained some results that stochastically compare the lifetimes of coherent systems with independent and identically distributed component lifetimes. The authors extend the results to coherent systems with (possibly) dependent component lifetimes. The notion of the Samaniego’s signatures is used in the derivation of the new results.

MSC:

60E15 Inequalities; stochastic orderings
60K10 Applications of renewal theory (reliability, demand theory, etc.)
62N05 Reliability and life testing

Citations:

Zbl 0948.90067
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Barlow, R.E.; Proschan, F., Statistical theory of reliability and life testing, (1975), Holt, Rinehart and Winston New York · Zbl 0379.62080
[2] Boland, P.J., Signatures of direct and indirect majority systems, J. appl. probab., 38, 2, 597-603, (2001) · Zbl 1042.62090
[3] Boland, P.J., Samaniego, F., 2003. The signature of a coherent system and its applications in reliability. In: Refik Soyer, Thomas Mazzuchi, Nozer Singpurwalla (Eds.), Mathematical Reliability: An Expository Perspective, vol. 67, International Series in Operational Research and Management Science. Kluwer, Dordrecht, pp. 1-29.
[4] Esary, J.D.; Marshall, A.W., Coherent life functions, SIAM J. appl. math., 18, 810-814, (1970) · Zbl 0198.24804
[5] Hu, T.; Hu, J., Comparison of order statistics between dependent and independent random variables, Statist. probab. lett., 37, 1, 1-6, (1998) · Zbl 0888.62048
[6] Karlin, S., Total positivity, (1968), Stanford University Press Stanford, CA · Zbl 0219.47030
[7] Kochar, S.; Mukerjee, H.; Samaniego, F.J., The “signature” of a coherent system and its application to comparison among systems, Naval res. logist., 46, 507-523, (1999) · Zbl 0948.90067
[8] Mi, J.; Shaked, M., Stochastic dominance of random variables implies the dominance of their order statistics, J. Indian statist. assoc., 40, 161-168, (2002)
[9] Papadatos, N., Distribution and expectation bounds on order statistics from possibly dependent variates, Statist. probab. lett., 54, 1, 21-31, (2001) · Zbl 1052.62057
[10] Rychlik, T., Distributions and expectations of order statistics for possibly dependent random variables, J. multivariate anal., 48, 1, 31-42, (1994) · Zbl 0790.62048
[11] Rychlik, T., Bounds for order statistics based on dependent variables with given nonidentical distributions, Statist. probab. lett., 23, 4, 351-358, (1995) · Zbl 0830.62050
[12] Rychlik, T., Mean-variance bounds for order statistics from dependent DFR, IFR, DFRA and IFRA samples, J. statist. plann. inference, 92, 1,2, 21-38, (2001) · Zbl 0973.62092
[13] Samaniego, F., On closure of the IFR class under formation of coherent systems, IEEE trans. reliab., R-34, 69-72, (1985) · Zbl 0585.62169
[14] Shaked, M.; Shanthikumar, J.G., Stochastic orders and their applications, (1994), Academic Press San Diego · Zbl 0806.62009
[15] Shaked, M.; Suarez-Llorens, A., On the comparison of reliability experiments based on the convolution order, J. amer. statist. assoc., 98, 463, 693-702, (2003) · Zbl 1040.62093
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.