Abstract
In recent years, stochastic orders in general and stochastic convexity in particular have been demonstrated as playing a central role in the optimal design and control of stochastic systems (refer to the wide-ranging applications presented in a recent monograph by Shaked and Shanthikumar [16]; also, refer to Shaked and Shanthikumar [15] and Shanthikumar and Yao [17], among many others). A somewhat less known but equally useful property, stochastic submodularity, and its many applications have been illustrated in Chang and Yao [4] and in Chang, Shanthikumar, and Yao [5].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albin, S. L., and Friedman, D. J. The impact of clustered defect distributions in 1C fabrication. Management Sci. 35, 1066–1078, 1989.
Blischke, W. R. Mathematical models for analysis of warranty policies. Math. Comput. Modeling 13, 1–16, 1990.
Beutler, F. X, and Ross, K. W. Optimal policies for controlled Markov chains with a constraint. J. Math. Ana. Appl. 112, 236–252, 1985.
Chang, C. S., and Yao, D. D. Rearrangement, majorization, and stochastic scheduling. Math. Oper. Res. 18, 658–684, 1993.
Chang, C. S., Shanthikumar, J. G., and Yao, D. D. Stochastic convexity and stochastic majorization. In: Yao, D. D. (ed.), Stochastic Modeling and Analysis of Manufacturing Systems, Chapter 5. Springer-Verlag, New York, 1994.
Chen, J., Yao, D. D., and Zheng, S. Quality control for products supplied with warranty. Oper. Res, to appear.
Chen, J., Yao, D. D., and Zheng, S. Sequential Inspection of Components in an Assembly System. Working Paper, IEOR Department, Columbia University, New York, NY 10027, 1997.
Derman, C. Finite State Markovian Decision Processes. Academic Press, New York, 1970.
Feinberg, E. A. Constrained semi-Markov decision processes with average rewards. ZOR Math. Meth. Oper. Res. 39, 257–288, 1994.
Kallenberg, L. Linear Programming and Finite Markovian Control Problems. Math Centre Tracts 148, Mathematisch Centrum, Amsterdam, 1983.
Keilson, J., and Sumita, U. Uniform stochastic ordering and related inequalities. Can. J. Stat. 10, 181–198, 1982.
Ross, S. M. Stochastic Processes. Wiley, New York, 1983.
Ross, S. M. Introduction to Stochastic Dynamic Programming. Academic Press, New York, 1983.
Scarf, H. The optimality of (S, s) policies in the dynamic inventory problem. In: Arrow, K. J., Karlin, S., and Suppes, P. (eds.), Mathematical Methods in the Social Sciences. Stanford University Press, Stanford, CA, 1960, pp. 196–202.
Shaked, M., and Shanthikumar, J. G. Stochastic convexity and its applications. Adv. Appl. Prob. 20, 427–446, 1988.
Shaked, M., and Shanthikumar, J. G. Stochastic Orders and Their Applications. Academic Press, New York, 1994.
Shanthikumar, J. G, and Yao, D. D. Strong stochastic convexity: closure properties and applications. J. Appl. Prob. 28, 131–145, 1991.
Shanthikumar, J. G., and Yao, D. D. Bivariate characterization of some stochastic order relations. Adv. Appl. Prob. 23, 642–659, 1991.
Topkis, D. M. Minimizing a submodular function on a lattice. Oper. Res. 26, 305–321, 1978.
Yao, D. D., and Zheng, S. Sequential inspection under capacity constraints. Oper. Res., to appear.
Editor information
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Yao, D.D., Zheng, S. (1999). Optimality of Sequential Quality Control via Stochastic Orders. In: Shanthikumar, J.G., Sumita, U. (eds) Applied Probability and Stochastic Processes. International Series in Operations Research & Management Science, vol 19. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5191-1_10
Download citation
DOI: https://doi.org/10.1007/978-1-4615-5191-1_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7364-3
Online ISBN: 978-1-4615-5191-1
eBook Packages: Springer Book Archive