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On the life and work of Cyrus Derman. (English) Zbl 1274.90007

Summary: This article provides a brief biographical synopsis of the life of Cyrus Derman and a comprehensive summary of his research. Professor Cyrus Derman was known among his friends as Cy.

MSC:

90-03 History of operations research and mathematical programming
01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Derman, Cyrus
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[1] Albright, S. C., & Derman, C. (1972). Asymptotic optimal policies for the stochastic sequential assignment problem. Management Science, 19(1), 46–51. · Zbl 0255.90022 · doi:10.1287/mnsc.19.1.46
[2] Brodheim, E., Derman, C., & Keyfitz, B. L. (1974). On the stationary probabilities for a certain class of denumerable Markov chains. Jnanabha (Sec. A), 4, 93–103. · Zbl 0319.60040
[3] Brodheim, E., Derman, C., & Prastacos, G. (1975). On the evaluation of a class of inventory policies for perishable products such as blood. Management Science, 21(11), 1320–1325. · Zbl 0307.90022 · doi:10.1287/mnsc.21.11.1320
[4] Chung, K., & Derman, C. (1956). Non-recurrent random walks. Pacific Journal of Mathematics, 6(3), 441–447. · Zbl 0072.35301 · doi:10.2140/pjm.1956.6.441
[5] Derman, C. (1954a). Ergodic property of the Brownian motion process. Proceedings of the National Academy of Sciences of the United States of America, 40(12), 1155–1158. · Zbl 0056.36206 · doi:10.1073/pnas.40.12.1155
[6] Derman, C. (1954b). A solution to a set of fundamental equations in Markov chains. Proceedings of the American Mathematical Society, 5(2), 332–334. · Zbl 0058.34504 · doi:10.1090/S0002-9939-1954-0060757-0
[7] Derman, C. (1955). Some contributions to the theory of denumerable Markov chains. Transactions of the American Mathematical Society, 79(2), 541–555. · Zbl 0065.11405 · doi:10.1090/S0002-9947-1955-0070883-3
[8] Derman, C. (1956a). Some asymptotic distribution theory for Markov chains with a denumerable number of states. Biometrika, 43(3–4), 285–294. · Zbl 0074.12704
[9] Derman, C. (1956b). An application of Chung’s lemma to the Kiefer–Wolfowitz stochastic approximation procedure. The Annals of Mathematical Statistics, 27(2), 532–536. · Zbl 0074.35502 · doi:10.1214/aoms/1177728277
[10] Derman, C. (1956c). Stochastic approximation. The Annals of Mathematical Statistics, 27(4), 879–886. · Zbl 0072.36403 · doi:10.1214/aoms/1177728065
[11] Derman, C. (1957). Non-parametric up-and-down experimentation. The Annals of Mathematical Statistics, 28(3), 795–798. · Zbl 0084.14801 · doi:10.1214/aoms/1177706895
[12] Derman, C. (1959). A simple allocation problem. Management Science, 5(4), 453–459. · Zbl 0995.90577 · doi:10.1287/mnsc.5.4.453
[13] Derman, C. (1961a). On minimax surveillance schedules. Naval Research Logistics Quarterly, 8(4), 415–419. · Zbl 0106.33802 · doi:10.1002/nav.3800080409
[14] Derman, C. (1961b). Remark concerning two-state semi-Markov processes. The Annals of Mathematical Statistics, 32(2), 615–616. · Zbl 0115.13704 · doi:10.1214/aoms/1177705070
[15] Derman, C. (1962a). On sequential decisions and Markov chains. Management Science, 9(1), 16–24. · Zbl 0995.90621 · doi:10.1287/mnsc.9.1.16
[16] Derman, C. (1962b). The sequencing of tests. In Columbia engineering quarterly (pp. 1175–1191).
[17] Derman, C. (1963a). On optimal replacement rules when changes of state are Markovian. In R. Bellman (Ed.), Mathematical optimization techniques (Vol. 396, pp. 201–210). California: University of California Press. · Zbl 0173.46702
[18] Derman, C. (1963b). Optimal replacement and maintenance under Markovian deterioration with probability bounds on failure. Management Science, 9(3), 478–481. · doi:10.1287/mnsc.9.3.478
[19] Derman, C. (1963c). Stable sequential control rules and Markov chains. Journal of Mathematical Analysis and Applications, 6(2), 257–265. · Zbl 0129.30703 · doi:10.1016/0022-247X(63)90007-6
[20] Derman, C. (1964a). Markovian sequential decision processes. Proceedings of Symposia in Applied Mathematics, 16, 281–289. · Zbl 0203.17801
[21] Derman, C. (1964b). On sequential control processes. The Annals of Mathematical Statistics, 35(1), 341–349. · Zbl 0142.14402 · doi:10.1214/aoms/1177703757
[22] Derman, C. (1966). Denumerable state Markovian decision processes-average cost criterion. The Annals of Mathematical Statistics, 37(6), 1545–1553. · Zbl 0144.43102 · doi:10.1214/aoms/1177699146
[23] Derman, C. (1970a). Markovian decision processes–average cost criterion. Mathematics of the decision sciences, Part 2. American Mathematical Society, 11, 139–149.
[24] Derman, C. (1970b). Finite state Markovian decision processes. New York: Academic Press. · Zbl 0262.90001
[25] Derman, C., & Ignall, E. (1969). On getting close to but not beyond a boundary(optimal rule for decision to stop or continue observation of random variables after observing sequence of variables with continuous distribution function). Journal of Mathematical Analysis and Applications, 28, 128–143. · Zbl 0186.50002 · doi:10.1016/0022-247X(69)90116-4
[26] Derman, C., & Ignall, E. (1975). On the stochastic ordering of Markov chains. Operations Research, 23(3), 574–576. · Zbl 0307.60057 · doi:10.1287/opre.23.3.574
[27] Derman, C., & Klein, M. (1958a). Inventory depletion management. Management Science, 4(4), 450–456. · doi:10.1287/mnsc.4.4.450
[28] Derman, C., & Klein, M. (1958b). On the feasibility of using a multiple linear regression model for verifying a declared inventory. In S. Melman (Ed.), Inspection for disarmament (pp. 220–229). Columbia: Columbia University Press.
[29] Derman, C., & Klein, M. (1959). Discussion: a note on the optimal depletion of inventory. Management Science, 5(2), 210–213. · doi:10.1287/mnsc.5.2.210
[30] Derman, C., & Klein, M. (1965). Some remarks on finite horizon Markovian decision models. Operations Research, 13(2), 272–278. · Zbl 0137.13901 · doi:10.1287/opre.13.2.272
[31] Derman, C., & Klein, M. (1966). Surveillance of multi-component systems: a stochastic traveling salesman’s problem. Naval Research Logistics Quarterly, 13(2), 103–111. · Zbl 0144.43103 · doi:10.1002/nav.3800130202
[32] Derman, C., & Klein, M. (1970). Probability and statistical inference for engineers: a first course. Oxford: Oxford University Press. · Zbl 0086.34305
[33] Derman, C., & Koh, S. P. (1988). On the comparison of two software reliability estimators. Probability in the Engineering and Informational Sciences, 2(1), 15–21. · Zbl 1134.68346 · doi:10.1017/S0269964800000589
[34] Derman, C., & Lieberman, G. (1967). A Markovian decision model for a joint replacement and stocking problem. Management Science, 13(9), 609–617. · Zbl 0158.38701 · doi:10.1287/mnsc.13.9.609
[35] Derman, C., & Robbins, H. (1955). The strong law of large numbers when the first moment does not exist. Proceedings of the National Academy of Sciences of the United States of America, 41(8), 586–587. · Zbl 0064.38202 · doi:10.1073/pnas.41.8.586
[36] Derman, C., & Ross, S. (1995). An improved estimator of {\(\sigma\)} in quality control. Probability in the Engineering and Informational Sciences, 9(3), 411–416. · Zbl 1335.62150 · doi:10.1017/S0269964800003946
[37] Derman, C., & Ross, S. (1996). Statistical aspects of quality control. New York: Prentice Hall. · Zbl 0889.62085
[38] Derman, C., & Sacks, J. (1959). On Dvoretzky’s stochastic approximation theorem. The Annals of Mathematical Statistics, 30(2), 601–606. · Zbl 0161.15603 · doi:10.1214/aoms/1177706277
[39] Derman, C., & Sacks, J. (1960). Replacement of periodically inspected equipment (an optimal optional stopping rule). Naval Research Logistics Quarterly, 7(4), 597–607. · Zbl 0173.46701 · doi:10.1002/nav.3800070429
[40] Derman, C., & Smith, D. (1979). Renewal decision problem-random horizon. Mathematics of Operations Research, 4(3), 225–232. · Zbl 0443.90039 · doi:10.1287/moor.4.3.225
[41] Derman, C., & Smith, D. (1980). An alternative proof of the IFRA property of some shock models. Naval Research Logistics Quarterly, 27(4), 703–707. · Zbl 0448.60062 · doi:10.1002/nav.3800270416
[42] Derman, C., & Solomon, H. (1958). Development and evaluation of surveillance sampling plans. Management Science, 5(1), 72–88. · Zbl 0995.62501 · doi:10.1287/mnsc.5.1.72
[43] Derman, C., & Strauch, R. (1966). A note on memoryless rules for controlling sequential control processes. The Annals of Mathematical Statistics, 37(1), 276–278. · Zbl 0138.13604 · doi:10.1214/aoms/1177699618
[44] Derman, C., & Veinott, A. F. Jr. (1967). A solution to a countable system of equations arising in Markovian decision processes. The Annals of Mathematical Statistics, 38(2), 582–584. · Zbl 0171.16004 · doi:10.1214/aoms/1177698973
[45] Derman, C., & Veinott, A. F. Jr. (1972). Constrained Markov decision chains. Management Science, 19(4-Part-1), 389–390. · Zbl 0246.90051 · doi:10.1287/mnsc.19.4.389
[46] Derman, C., Littauer, S., & Solomon, H. (1957). Tightened multi-level continuous sampling plans. The Annals of Mathematical Statistics, 28(2), 395–404. · Zbl 0088.11709 · doi:10.1214/aoms/1177706967
[47] Derman, C., Johns, M. Jr., & Lieberman, G. (1959). Continuous sampling procedures without control. The Annals of Mathematical Statistics, 30(4), 1175–1191. · Zbl 0095.13001 · doi:10.1214/aoms/1177706103
[48] Derman, C., Lieberman, G., & Ross, S. (1972a). A sequential stochastic assignment problem. Management Science, 18(7), 349–355. · Zbl 0238.90054 · doi:10.1287/mnsc.18.7.349
[49] Derman, C., Lieberman, G., & Ross, S. (1972b). On optimal assembly of systems. Naval Research Logistics Quarterly, 19(4), 569–574. · Zbl 0251.90019 · doi:10.1002/nav.3800190402
[50] Derman, C., Gleser, L. J., & Olkin, I. (1973). A guide to probability theory and application. Holt, Rinehart and Winston. · Zbl 0428.60001
[51] Derman, C., Lieberman, G., & Ross, S. (1974a). Assembly of systems having maximum reliability. Naval Research Logistics Quarterly, 21(1), 1–12. · Zbl 0286.90033 · doi:10.1002/nav.3800210102
[52] Derman, C., Lieberman, G., & Ross, S. (1974b). Optimal allocations in the construction of k-out-of-n reliability systems. Management Science, 21(3), 241–250. · Zbl 0322.90027 · doi:10.1287/mnsc.21.3.241
[53] Derman, C., Lieberman, G., & Ross, S. (1975a). Optimal allocation of resources in systems. In SIAM, conference volume on reliability and fault tree analysis (pp. 307–317). · Zbl 0319.90024
[54] Derman, C., Lieberman, G., & Ross, S. (1975b). A stochastic sequential allocation model. Operations Research, 23(6), 1120–1130. · Zbl 0353.90018 · doi:10.1287/opre.23.6.1120
[55] Derman, C., Lieberman, G., & Ross, S. (1976). Optimal system allocations with penalty cost. Management Science, 23(4), 399–403. · Zbl 0356.90070 · doi:10.1287/mnsc.23.4.399
[56] Derman, C., Lieberman, G., & Ross, S. (1978). A renewal decision problem. Management Science, 24(5), 554–561. · Zbl 0371.90045 · doi:10.1287/mnsc.24.5.554
[57] Derman, C., Lieberman, G., & Ross, S. (1979a). Adaptive disposal models. Naval Research Logistics Quarterly, 26(1), 33–40. · Zbl 0396.90049 · doi:10.1002/nav.3800260104
[58] Derman, C., Lieberman, G., & Ross, S. (1979b). On renewal decisions. In Dynamic programming and its applications (pp. 307–317). New York: Academic Press. · Zbl 0459.90027
[59] Derman, C., Lieberman, G., & Ross, S. (1979c). On the candidate problem with a random number of candidates. Tech. Rep. 192, Stanford University.
[60] Derman, C., Lieberman, G., & Ross, S. (1980). On the optimal assignment of servers and a repairman. Journal of Applied Probability, 17(2), 577–581. · Zbl 0428.60096 · doi:10.2307/3213050
[61] Derman, C., Lieberman, G., & Ross, S. (1982). On the consecutive-k-of-n: F system. IEEE Transactions on Reliability, 31(1), 57–63. · Zbl 0478.90029 · doi:10.1109/TR.1982.5221229
[62] Derman, C., Ross, S., & Schechner, Z. (1983). A note on first passage times in birth and death and nonnegative diffusion processes. Naval Research Logistics Quarterly, 30(2), 283–285. · Zbl 0525.60091 · doi:10.1002/nav.3800300209
[63] Derman, C., Lieberman, G., & Ross, S. (1984a). On the use of replacements to extend system life. Operations Research, 32(3), 616–627. · Zbl 0544.90039 · doi:10.1287/opre.32.3.616
[64] Derman, C., Lieberman, G., & Schechner, Z. (1984b). Prematurely terminated sequential tests for MILil-std 781c. In Frontiers in statistical quality control. Berlin: Springer.
[65] Derman, C., Lieberman, G., & Ross, S. (1987). On sampling inspection in the presence of inspection errors. Probability in the Engineering and Informational Sciences, 1(02), 237–249. · Zbl 1133.90323 · doi:10.1017/S0269964800000437
[66] Katehakis, M., & Derman, C. (1984). Optimal repair allocation in a series system. Mathematics of Operations Research, 9(4), 615–623. · Zbl 0562.90026 · doi:10.1287/moor.9.4.615
[67] Katehakis, M., & Derman, C. (1986). Computing optimal sequential allocation rules in clinical trials. In J. Van Ryzin (Ed.), Lecture notes-monograph series: Vol. 8. Adaptive statistical procedures and related topics (pp. 29–39). · Zbl 0691.62075
[68] Katehakis, M., & Derman, C. (1987). Optimal repair allocation in a series system, expected discounted operation time criterion. Stochastic Analysis and Applications, 5(4), 387–394. · Zbl 0628.60093 · doi:10.1080/07362998708809126
[69] Katehakis, M. N., & Derman, C. (1989). On the maintenance of systems composed of highly reliable components. Management Science, 35(5), 551–560. · Zbl 0676.90026 · doi:10.1287/mnsc.35.5.551
[70] Olkin, I., Gleser, L. J., & Derman, C. (1994). Probability models and applications. New York: Prentice Hall. · Zbl 0428.60001
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