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Keywords:
failure extropy; Jensen divergence; mixed system; redundancy; stochastic orders; system signature
failure extropy; Jensen divergence; mixed system; redundancy; stochastic orders; system signature
Summary:
Recent research has shown growing interest in quantifying uncertainty in system lifetimes. This paper investigates the failure extropy (FEx) of an $n$-component mixed system, conditioned on the failure of all components by a given time $t$. Using the concept of system signature, explicit expressions for the FEx of the system lifetime are derived, along with key properties and informative bounds. To extend this framework, a divergence measure based on FEx is proposed to assess the complexity of system structures. A new discrimination measure is also proposed, serving as a valuable tool to assess how closely a system resembles a parallel system. An application to redundancy allocation has been carried out to demonstrate the practical relevance of the proposed results and provide insights into optimal system design under uncertainty.
References:
[1] Asadi, M., Ebrahimi, N., Soofi, E. S., Zohrevand, Y.: Jensen-Shannon information of the coherent system lifetime. Reliab. Eng. Syst. Safety 156 (2016), 244-255. DOI 10.1016/j.ress.2016.07.015
[2] Barlow, R. E., Proschan, F.: Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York (1975). MR 0438625 | Zbl 0379.62080
[3] Chakraborty, S., Pradhan, B.: On cumulative residual extropy of coherent and mixed systems. Ann. Oper. Res. 340 (2024), 59-81. DOI 10.1007/s10479-023-05727-2 | MR 4791486 | Zbl 1547.94197
[4] Jose, J., Sathar, E. I. Abdul: An ordered approach on cumulative extropy measures for information analysis. Commun. Stat., Theory Methods 52 (2023), 1512-1532. DOI 10.1080/03610926.2021.1928706 | MR 4546528 | Zbl 07706293
[5] Kamari, O., Buono, F.: On extropy of past lifetime distribution. Ric. Mat. 70 (2021), 505-515. DOI 10.1007/s11587-020-00488-7 | MR 4342690 | Zbl 1494.94026
[6] Kayal, S.: On a generalized entropy of mixed systems. J. Stat. Management Syst. 22 (2019), 1183-1198. DOI 10.1080/09720510.2019.1580899
[7] Kayal, S.: Failure extropy, dynamic failure extropy and their weighted versions. Stoch. Qual. Control 36 (2021), 59-71. DOI 10.1515/eqc-2021-0008 | MR 4265194 | Zbl 1479.62003
[8] Kayid, M.: Further results involving residual and past extropy with their applications. Stat. Probab. Lett. 214 (2024), Article ID 110201, 7 pages. DOI 10.1016/j.spl.2024.110201 | MR 4773161 | Zbl 07913930
[9] Kayid, M., Shrahili, M.: Rényi entropy for past lifetime distributions with application in inactive coherent systems. Symmetry 15 (2023), Article ID 1310, 15 pages. DOI 10.3390/sym15071310
[10] Khaledi, B.-E., Shaked, M.: Ordering conditional lifetimes of coherent systems. J. Stat. Plann. Inference 137 (2007), 1173-1184. DOI 10.1016/j.jspi.2006.01.012 | MR 2301471 | Zbl 1111.60012
[11] Kochar, S., Mukerjee, H., Samaniego, F. J.: The ''signature'' of a mixed system and its application to comparisons among systems. Naval Res. Logistics 46 (1999), 507-523. DOI 10.1002/(SICI)1520-6750(199908)46:5<507::AID-NAV4>3.0.CO;2-D
[12] Kundu, C.: On cumulative residual (past) extropy of extreme order statistics. Commun. Stat., Theory Methods 52 (2023), 5848-5865 \99999DOI99999 10.1080/03610926.2021.2021238 . DOI 10.1080/03610926.2021.2021238 | MR 4608920 | Zbl 07711346
[13] Lad, F., Sanfilippo, G., Agrò, G.: Extropy: Complementary dual of entropy. Stat. Sci. 30 (2015), 40-58. DOI 10.1214/14-STS430 | MR 3317753 | Zbl 1332.62027
[14] Nair, R. D., Sathar, E. I. Abdul: On dynamic failure extropy. J. Indian Soc. Probab. Stat. 21 (2020), 287-313. DOI 10.1007/s41096-020-00083-x
[15] Pakdaman, Z., Noughabi, R. Alizadeh: On the study of the cumulative residual extropy of mixed used systems and their complexity. Probab. Eng. Inf. Sci. 39 (2025), 122-140. DOI 10.1017/S0269964824000196 | MR 4861610
[16] Qiu, G.: The extropy of order statistics and record values. Stat. Probab. Lett. 120 (2017), 52-60. DOI 10.1016/j.spl.2016.09.016 | MR 3567921 | Zbl 1349.62165
[17] Qiu, G., Jia, K.: Extropy estimators with applications in testing uniformity. J. Nonparametric Stat. 30 (2018), 182-196. DOI 10.1080/10485252.2017.1404063 | MR 3756237 | Zbl 1388.62133
[18] Qiu, G., Jia, K.: The residual extropy of order statistics. Stat. Probab. Lett. 133 (2018), 15-22. DOI 10.1016/j.spl.2017.09.014 | MR 3732347 | Zbl 1440.62164
[19] Qiu, G., Wang, L., Wang, X.: On extropy properties of mixed systems. Probab. Eng. Inf. Sci. 33 (2019), 471-486. DOI 10.1017/S0269964818000244 | MR 3947267 | Zbl 1557.62033
[20] Samaniego, F. J.: System Signatures and Their Applications in Engineering Reliability. International Series in Operations Research & Management Science 110. Springer, New York (2007). DOI 10.1007/978-0-387-71797-5 | MR 2380178 | Zbl 1154.62075
[21] Saranya, P., Sunoj, S. M.: On relative cumulative extropy, its residual (past) measures and their applications in estimation and testing. J. Indian Soc. Probab. Stat. 25 (2024), 199-225. DOI 10.1007/s41096-024-00176-x
[22] Shaked, M., Shanthikumar, J. G.: Stochastic Orders. Springer Series in Statistics. Springer, New York (2007). DOI 10.1007/978-0-387-34675-5 | MR 2265633 | Zbl 1111.62016
[23] Shannon, C. E.: A mathematical theory of communication. Bell Syst. Tech. J. 27 (1948), 623-656. DOI 10.1002/j.1538-7305.1948.tb01338.x | MR 0026286 | Zbl 1154.94303
[24] Toomaj, A.: Renyi entropy properties of mixed systems. Commun. Stat., Theory Methods 46 (2017), 906-916. DOI 10.1080/03610926.2015.1006785 | MR 3557542 | Zbl 1360.62499
[25] Toomaj, A., Sunoj, S. M., Navarro, J.: Some properties of the cumulative residual entropy of coherent and mixed systems. J. Appl. Probab. 54 (2017), 379-393. DOI 10.1017/jpr.2017.6 | MR 3668472 | Zbl 1401.62018
[26] Yang, J., Xia, W., Hu, T.: Bounds on extropy with variational distance constraint. Probab. Eng. Inf. Sci. 33 (2018), 186-204. DOI 10.1017/S0269964818000098 | MR 3923353 | Zbl 1557.60037
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