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Equivalency of multi-state survival signatures of multi-state systems of different sizes and its use in the comparison of systems

Published online by Cambridge University Press:  10 June 2022

He Yi Open the ORCID record for He Yi [Opens in a new window] ,
Narayanaswamy Balakrishnan  and
Xiang Li
He Yi
Affiliation:
School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China. E-mail: [email protected]
Narayanaswamy Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton L8S 4K1, Ontario, Canada. E-mail: [email protected]
Xiang Li
Affiliation:
School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China. E-mail: [email protected]
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Abstract

In this paper, the multi-state survival signature is first redefined for multi-state coherent or mixed systems with independent and identically distributed (i.i.d.) multi-state components. With the assumption of independence of component lifetimes at different state levels, transformation formulas of multi-state survival signatures of different sizes are established through the use of equivalent systems and a generalized triangle rule for order statistics from several independent and non-identical distributions. The results obtained facilitate stochastic comparisons of multi-state coherent or mixed systems with different numbers of i.i.d. multi-state components. Specific examples are finally presented to illustrate the transformation formulas established here, and also their use in comparing systems of different sizes.

Keywords

equivalent systemgeneralized triangle rulemulti-state survival signaturemulti-state systemorder statistics
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 3 , July 2023 , pp. 801 - 817
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

Amini-Seresht, E., Khaledi, B.E., & Kochar, S. (2020). Some new results on stochastic comparisons of coherent systems using signatures. Journal of Applied Probability 57(1): 156–173.CrossRefGoogle Scholar
Balakrishnan, N. & Volterman, W. (2014). On the signatures of ordered system lifetimes. Journal of Applied Probability 51(1): 82–91.CrossRefGoogle Scholar
Behrensdorf, J., Regenhardt, T.E., Broggi, M., & Beer, M. (2021). Numerically efficient computation of the survival signature for the reliability analysis of large networks. Reliability Engineering and System Safety 216: 107935.CrossRefGoogle Scholar
Burkschat, M. & Navarro, J. (2018). Stochastic comparisons of systems based on sequential order statistics via properties of distorted distributions. Probability in the Engineering and Informational Sciences 32(2): 246–274.10.1017/S0269964817000018CrossRefGoogle Scholar
Coolen, F.P.A. & Coolen-Maturi, T. (2012). Generalizing the signature to systems with multiple types of components. In Zamojski, W., Mazurkiewicz, J., Sugier, J., Walkowiak, T., & Kacprzyk, J. (eds), Complex systems and dependability. New York: Springer, pp. 115–130.Google Scholar
Coolen-Maturi, T., Coolen, F.P.A., & Balakrishnan, N. (2021). The joint survival signature of coherent systems with shared components. Reliability Engineering and System Safety 207: 107350.CrossRefGoogle Scholar
Cui, L.R., Gao, H.D., & Mo, Y.C. (2018). Reliability for k-out-of-n:F balanced systems with m sectors. IISE Transactions 50(5): 381–393.CrossRefGoogle Scholar
Da, G.F. & Hu, T.Z. (2013). On bivariate signatures for systems with independent modules. In Li, H.J. & Li, X.H. (eds), Stochastic orders in reliability and risk. New York: Springer, pp. 143–166.10.1007/978-1-4614-6892-9_7CrossRefGoogle Scholar
Ding, W.Y., Fang, R., & Zhao, P. (2021). An approach to comparing coherent systems with ordered components by using survival signatures. IEEE Transactions on Reliability 70(2): 495–506.CrossRefGoogle Scholar
Eryilmaz, S. & Tuncel, A. (2016). Generalizing the survival signature to unrepairable homogeneous multi-state systems. Naval Research Logistics 63(8): 593–599.CrossRefGoogle Scholar
Gertsbakh, I. & Shpungin, Y. (2012). Multidimensional spectra of multistate systems with binary components. In Lisnianski, A. & Frenkel, I. (eds), Recent advances in system reliability. London: Springer, pp. 49–61.CrossRefGoogle Scholar
Goli, S. (2019). On the conditional residual lifetime of coherent systems under double regularly checking. Naval Research Logistics 66(4): 352–363.CrossRefGoogle Scholar
Kochar, S., Mukerjee, H., & Samaniego, F.J. (1999). The “signature” of a coherent system and its application to comparisons among systems. Naval Research Logistics 46(5): 507–523.10.1002/(SICI)1520-6750(199908)46:5<507::AID-NAV4>3.0.CO;2-D3.0.CO;2-D>CrossRefGoogle Scholar
Lindqvist, B.H., Samaniego, F.J., & Huseby, A.B. (2016). On the equivalence of systems of different sizes, with applications to system comparisons. Advances in Applied Probability 48(2): 332–348.CrossRefGoogle Scholar
Lindqvist, B.H., Samaniego, F.J., & Wang, N.N. (2021). On the comparison of performance-per-cost for coherent and mixed systems. Probability in the Engineering and Informational Sciences 35(4): 867–884.10.1017/S0269964820000273CrossRefGoogle Scholar
Lisnianski, A., Frenkel, I., & Ding, Y. (2010). Multi-state system reliability analysis and optimization for engineers and industrial managers. London: Springer.CrossRefGoogle Scholar
Natvig, B. (2010). Multistate systems: Reliability theory with applications. Hoboken, New Jersey: Wiley.Google Scholar
Navarro, J. & Fernandez-Sanchez, J. (2020). On the extension of signature-based representations for coherent systems with dependent non-exchangeable components. Journal of Applied Probability 57(2): 429–440.CrossRefGoogle Scholar
Navarro, J., Ruiz, J.M., & Sandoval, C.J. (2007). Properties of coherent systems with dependent components. Communications in Statistics - Theory and Methods 36: 175–191.10.1080/03610920600966316CrossRefGoogle Scholar
Navarro, J., Samaniego, F.J., & Balakrishnan, N. (2013). Mixture representations for the joint distribution of lifetimes of two coherent systems with shared components. Advances in Applied Probability 45(4): 1011–1027.10.1239/aap/1386857855CrossRefGoogle Scholar
Navarro, J., Samaniego, F.J., Balakrishnan, N., & Bhattacharya, D. (2008). On the application and extension of system signatures in engineering reliability. Naval Research Logistics 55(4): 313–327.CrossRefGoogle Scholar
Samaniego, F.J. (1985). On closure of the IFR class under formation of coherent systems. IEEE Transactions on Reliability R 34(1): 69–72.CrossRefGoogle Scholar
Samaniego, F.J. (2007). System signatures and their applications in engineering reliability. New York: Springer.10.1007/978-0-387-71797-5CrossRefGoogle Scholar
Samaniego, F.J., Balakrishnan, N., & Navarro, J. (2009). Dynamic signatures and their use in comparing the reliability of new and used systems. Naval Research Logistics 56(6): 577–591.CrossRefGoogle Scholar
Yi, H., Balakrishnan, N., & Cui, L.R. (2020). On the multi-state signatures of ordered system lifetimes. Advances in Applied Probability 52(1): 291–318.10.1017/apr.2019.65CrossRefGoogle Scholar
Yi, H., Balakrishnan, N., & Cui, L.R. (2021). Comparisons of multi-state systems with binary components of different sizes. Methodology and Computing in Applied Probability 23(4): 1309–1321.CrossRefGoogle Scholar
Yi, H., Balakrishnan, N., & Cui, L.R. (2021). Computation of survival signatures for multi-state consecutive-k systems. Reliability Engineering and System Safety 208: 107429.CrossRefGoogle Scholar
Yi, H., Balakrishnan, N., & Cui, L.R. (2022). On dependent multi-state semi-coherent systems based on multi-state joint signature. Methodology and Computing in Applied Probability, to appear, DOI: 10.1007/s11009-021-09877-3CrossRefGoogle Scholar
Yi, H., Balakrishnan, N., & Li, X. (2022). Signatures of multi-state systems based on a series/parallel/recurrent structure of modules. Probability in the Engineering and Informational Sciences, to appear, DOI: 10.1017/S0269964821000103CrossRefGoogle Scholar
Yi, H., Balakrishnan, N., & Li, X. (2022). Equivalency in joint signatures for binary/multi-state systems of different sizes. Probability in the Engineering and Informational Sciences, to appear, DOI: 10.1017/S026996482100023110.1017/S0269964821000231CrossRefGoogle Scholar
Yi, H. & Cui, L.R. (2018). A new computation method for signature: Markov process method. Naval Research Logistics 65(5): 410–426.CrossRefGoogle Scholar
Zarezadeh, S., Asadi, M., & Eftekhar, S. (2019). Signature-based information measures of multi-state networks. Probability in the Engineering and Informational Sciences 33(3): 438–459.CrossRefGoogle Scholar