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In [[mathematics]], a '''continuum structure function (CSF)''' is defined by [[Laurence Baxter]] as a nondecreasing [[map (mathematics)|map]]ping from the unit [[hypercube]] to the unit [[interval (mathematics)|interval]]. It is used by Baxter to help in the [[Mathematical model]]ling of the level of performance of a system in terms of the performance levels of its components.<ref>Baxter, L A (1984) Continuum structures I., ''Journal of Applied Probability'', 21 (4), pp. 802–815 {{JSTOR|3213697}}</ref><ref>Baxter, L A, (1986), Continuum structures. II, ''Math. Proc. Camb. Phil. Soc''.99, 331 331</ref><ref>Kim, Chul; Baxter, Laurence A.(1987) Reliability importance for continuum structure functions. ''Journal of Applied Probability'', 24, 779–785 {{JSTOR|3214108}}</ref>
In [[mathematics]], a '''continuum structure function (CSF)''' is defined by [[Laurence Baxter]] as a nondecreasing [[map (mathematics)|map]]ping from the unit [[hypercube]] to the unit [[interval (mathematics)|interval]]. It is used by Baxter to help in the [[Mathematical model]]ling of the level of performance of a system in terms of the performance levels of its components.<ref>{{cite journal
| last1=Baxter | first1=Laurence A. | authorlink1=Laurence Baxter
| date=1984
| title=Continuum structures I
| journal=Journal of Applied Probability
| volume=21
| issue=4
| pages=802–815
| jstor=3213697
| doi=10.2307/3213697}}</ref><ref>{{cite journal
| last1=Baxter | first1=Laurence A. | authorlink1=Laurence Baxter
| date=1986
| title=Continuum structures. II
| journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]]
| volume=99
| issue=2
| pages=331–338
| doi=10.1017/S0305004100064240}}</ref><ref>{{cite journal
| last1=Kim | first1=Chul
| last2=Baxter | first2=Laurence A. | authorlink2=Laurence Baxter
| date=1987
| title=Reliability importance for continuum structure functions
| journal=Journal of Applied Probability
| volume=24
| issue=3
| pages=779—785
| jstor=3214108
| doi=10.2307/3214108}}</ref>


==References==
==References==
{{Reflist}}
{{Reflist}}
{{refbegin}}
{{refbegin}}

* Kim, C., Baxter. L. A. (1987) "Axiomatic characterizations of continuum structure functions", ''Operations Research Letters'', 6 (6), 297&ndash;300, {{doi| 10.1016/0167-6377(87)90047-2}}.
==Further reading==
*{{Cite journal | last1 = Baxter | first1 = L. A. | last2 = Lee | first2 = S. M. | doi = 10.1017/S026996480000111X | title = Further Properties of Reliability Importance for Continuum Structure Functions | journal = Probability in the Engineering and Informational Sciences | volume = 3 | issue = 2 | pages = 237 | year = 2009 | s2cid = 122033755 }}
*{{cite journal
| last1=Kim | first1=Chul
| last2=Baxter | first2=Laurence A. | authorlink2=Laurence Baxter
| date=1987
| title=Axiomatic characterizations of continuum structure functions
| journal=[[Operations Research Letters]]
| volume=6
| issue=6
| pages=297&ndash;300
| doi=10.1016/0167-6377(87)90047-2}}
*{{Cite journal | last1 = Baxter | first1 = Laurence A. | authorlink1=Laurence Baxter | last2 = Lee | first2 = Seung Min | doi = 10.1017/S026996480000111X | title = Further Properties of Reliability Importance for Continuum Structure Functions | journal = Probability in the Engineering and Informational Sciences | volume = 3 | issue = 2 | pages = 237 | year = 2009 | s2cid = 122033755 }}
{{refend}}
{{refend}}



Revision as of 18:54, 27 November 2024

In mathematics, a continuum structure function (CSF) is defined by Laurence Baxter as a nondecreasing mapping from the unit hypercube to the unit interval. It is used by Baxter to help in the Mathematical modelling of the level of performance of a system in terms of the performance levels of its components.[1][2][3]

References

  1. ^ Baxter, Laurence A. (1984). "Continuum structures I". Journal of Applied Probability. 21 (4): 802–815. doi:10.2307/3213697. JSTOR 3213697.
  2. ^ Baxter, Laurence A. (1986). "Continuum structures. II". Mathematical Proceedings of the Cambridge Philosophical Society. 99 (2): 331–338. doi:10.1017/S0305004100064240.
  3. ^ Kim, Chul; Baxter, Laurence A. (1987). "Reliability importance for continuum structure functions". Journal of Applied Probability. 24 (3): 779–785. doi:10.2307/3214108. JSTOR 3214108.

Further reading