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An asymptotically efficient test for the bundle strength of filaments

Published online by Cambridge University Press:  14 July 2016

Pranab Kumar Sen
Pranab Kumar Sen*
Affiliation:
University of North Carolina, Chapel Hill
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Abstract

Based on a Wiener process approximation, a sequential test for the bundle strength of filaments is proposed and studied here. Asymptotic expressions for the OC and ASN functions are derived, and it is shown that asymptotically the test is more efficient than the usual fixed sample size procedure based on the asymptotic normality of the standarized form of the bundle strength of filaments, studied earlier by Daniels (1945), and Sen, Bhattacharyya and Suh (1973).

Keywords

ASYMPTOTIC RELATIVE EFFICIENCYAVERAGE SAMPLE NUMBERALMOST SURE CONVERGENCEBUNDLE STRENGTH OF FILAMENTSOC FUNCTIONSEQUENTIAL TESTWIENER PROCESS APPROXIMATION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 3 , September 1973 , pp. 586 - 596
Copyright
Copyright © Applied Probability Trust 1973 

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Footnotes

Research sponsored by the Aerospace Research Laboratories, Air Force systems Command, U. S. Air Force, Contract F33615-71-C-1927.

References

[1] Bahadur, R. R. (1966) A note on quantiles in large samples. Ann. Math. Statist. 37, 577–580Google Scholar
[2] Bhattacharyya, B. B., Suh, M. W. and Grandage, A. H. E. (1970) On the distribution and moments of the strength of a bundle of filaments. J. Appl. Prob. 7, 712–720.Google Scholar
[3] Chow, Y. S. and Robbins, H. (1965) On the asymptotic theory of fixed width sequential confidence intervals for the mean. Ann. Math. Statist. 36, 457–462.Google Scholar
[4] Daniels, H. A. (1945) The statistical theory of the strength of bundles of threads. Proc. Roy. Soc. A 183, 405–435.Google Scholar
[5] Dvoretzky, A., Kiefer, J. and Wolfowitz, J. (1953) Sequential decision problems for processes with continuous time parameter. Testing hypotheses. Ann. Math. Statist. 24, 254–264.10.1214/aoms/1177729031Google Scholar
[6] Hoeffding, W. (1963) Probability inequalities for sums of bounded random variables J. Amer. Statist. Ass. 58, 13–30.Google Scholar
[7] Sen, P. K. (1973) On the fixed size confidence bands for the bundle strength of filaments. Ann. Statist. 1, 526–537.Google Scholar
[8] Sen, P. K., Bhattacharyya, B. B. and Suh, M. W. (1973) Limiting behavior of the extremum of certain sample functions. Ann. Statist. 1, 297–311.Google Scholar
[9] Strassen, V. (1967) Almost sure behavior of sample sums of independent random variables and martingales. Proc. 5th. Berkeley Symp. Math. Statist. Prob. 2, 315–343Google Scholar
[10] Wald, A. (1947) Sequential Analysis. John Wiley, New YorkGoogle Scholar