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Number of successes in Markov trials

Published online by Cambridge University Press:  01 July 2016

U. Narayan Bhat  and
Ram Lal
U. Narayan Bhat*
Affiliation:
Southern Methodist University
Ram Lal*
Affiliation:
Southern Methodist University
*
Postal address for both authors: Department of Statistical Science, Southern Methodist University Dallas, TX 75275, USA.
Postal address for both authors: Department of Statistical Science, Southern Methodist University Dallas, TX 75275, USA.
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Abstract

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Markov trials are a sequence of dependent trials with two outcomes, success and failure, which are the states of a Markov chain. The distribution of the number of successes in n Markov trials and the first-passage time for a specified number of successes are obtained using an augmented Markov chain model.

Keywords

MARKOV CHAINFIRST-PASSAGE TIME
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 20 , Issue 3 , September 1988 , pp. 677 - 680
Copyright
Copyright © Applied Probability Trust 1988 

References

Bhat, U. N. and Lal, R. (1988) Control charts for Markov dependent production processes. Tech. Rep. # SMU/DS/TR/213, Department of Statistical Science, SMU, Dallas, Texas 75275, USA.Google Scholar
Bhat, U. N., Lal, R., and Karunaratne, M. (1987) A sequential inspection plane for Markov dependent production processes. Tech. Rep. # SMU/DS/TR/209 (Rev.), Department of Statistical Science, SMU, Dallas, Texas 75275, USA.Google Scholar
Gabriel, K. R. (1959) The distribution of the number of successes in a sequence of dependent trials. Biometrika 46, 454–460.Google Scholar
Kemeny, J. G. and Snell, J. L. (1960) Finite Markov Chains. Van Nostrand, New York.Google Scholar