Four Common Properties of Repairable Systems Calculated with the Boltzmann-Like Entropy

Paolo Rocchi, Gurami Tsitsiashvili

IBM, Roma, Italy&Institute of Applied Mathematics Far Eastern Branch of RAS.
Institute of Applied Mathematics Far Eastern Branch of RAS, Vladivostok, Russia.

DOI: 10.4236/am.2012.312A279                

Abstract

Gnedenko, the father of the modern Reliability Theory, first derived some fundamental properties of reliable systems following rigid deductive logic. This paper shares the deductive method and infers four principal properties of repairable/maintainable systems using the Boltzmann-like entropy. In particular we calculate the reparability function and next discuss the physical meanings of the formal results. Lastly we comment on the broad range of applications and researches which can relate to this study.

Keywords

Repairable System; Boltzmann-Like Entropy

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	B. V. Gnedenko, Yu. K. Beliaev and A. D. Soloviev, “Mathematical Methods in Reliability Theory,” Science, Moscow, 1965.
[2]	P. Rocchi, “Boltzmann-Like Entropy in Reliability Theory,” Entropy, Vol. 4, No. 5, 2002, pp. 142-150.
[3]	P. Rocchi, “Calculations of System Aging through the Stochastic Entropy,” Entropy, Vol. 8, 2006, pp. 134-142.
[4]	V. L. Bengtson, D. Gans, N. Putney and M. Silverstein, “Handbook of Theories of Aging,” Springer, Berlin, 2008.
[5]	H. Z. Wang, “A Survey of Maintenance Policies of Deteriorating Systems,” European Journal of Operational Research, Vol. 139, No. 3, 2002, pp. 469-489.
[6]	M. Brown and F. Proschan, “Imperfect Repair,” Journal of Applied Probability, Vol. 20, No. 4, 1983, pp. 851-859.
[7]	C. H. Lie and Y. H. Chun, “An Algorithm for Preventive Maintenance Policy,” IEEE Transactions on Reliability, Vol. 35, No. 1, 1986, pp. 71-75. doi:10.1109/TR.1986.4335352
[8]	H. W. Block, W. S. Borges and T. H. Savits, “A General Age Replacement Model with Minimal Repair,” Naval Research Logistics, Vol. 35, No. 5, 1988, pp. 365-372.
[9]	L. R. Whitaker and F. J. Samaniego, “Estimating the Reliability of Systems Subject to Imperfect Repair,” Journal of American Statistical Association, Vol. 84, No. 405, 1989, pp. 301-309. doi:10.1080/01621459.1989.10478770
[10]	M. A. K. Malik, “Reliable Preventive Maintenance Policy,” AIIE Transactions, Vol. 11, No. 3, 1979, pp. 221-228.
[11]	W. H. Cole, “Operability in the Young and Aged,” Annals of Surgery, Vol. 138, No. 2, 1953, pp. 145-157. doi:10.1097/00000658-195308000-00001
[12]	J. M. Wilmoth and K. F. Ferraro, “Gerontology: Perspectives and Issues,” Springer, Berlin, 2006.
[13]	S. Kinugasa, M. Tachibana, H. Yoshimura, D. Kumar Dhar, M. Shibakita, S. Ohno, H. Kubota, R. Masunaga and N. Nagasue, “Esophageal Resection in Elderly Esophageal Carcinoma Patients: Improvement in Postoperative Complications,” Annals of Thoracic Surgery, Vol. 71, No. 2, 2001, pp. 414-418. doi:10.1016/S0003-4975(00)02333-X