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Burn-in and mixed populations

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Henry W. Block ,
Jie Mi  and
Thomas H. Savits
Henry W. Block*
Affiliation:
University of Pittsburgh
Jie Mi*
Affiliation:
Florida International University
Thomas H. Savits*
Affiliation:
University of Pittsburgh
*
∗ Postal address: Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
∗∗ Postal address: Department of Statistics, Florida International University, Tamiami Trail, Miami, FL 33199, USA.
∗ Postal address: Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
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Abstract

Burn-in is a procedure used for eliminating weak components in a mixed population. In this paper we focus on general mixed populations. Three types of results are established. First, it is shown that any mixed population displays a type of monotonicity property which is appropriate for burn-in. Second, it is shown that if, asymptotically, components have constant failure rates, then the mixed population will also asymptotically have a constant failure rate and this will correspond to the rate of the strongest subpopulation of the mixture. Finally, it is shown for a reasonable cost function, that if one mixture distribution dominates another in a strong sense, the resulting mixture of the dominant distribution will have larger optimal burn-in time.

Keywords

BATHTUB FAILURE RATERR2EXPONENTIAL FAMILYCOST FUNCTION

MSC classification

Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 3 , September 1993 , pp. 692 - 702
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Research supported by NSA Grant No. RO909237 and NSF Grant No. DMS-9203444.

References

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Karlin, S. and Rinott, Y. (1980) Classes of orderings of measures and related correlation inequalities. J. Multivariate Anal. 10, 499–516.Google Scholar
Mi, Jie (1991) Optimal Burn-in. Ph.D. Dissertation. University of Pittsburgh, Department of Mathematics and Statistics.Google Scholar