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Explicit solution of an optimal stopping problem: the burn-in of conditionally exponential components
Published online by Cambridge University Press: 14 July 2016
Abstract
We consider the problem of the optimal duration of a burn-in experiment for n identical units with conditionally exponential life-times of unknown parameter Λ. The problem is formulated as an optimal stopping problem for a suitably defined two-dimensional continuous-time Markov process. By exploiting monotonicity properties of the statistical model and of the costs we prove that the optimal stopping region is monotone (according to an appropriate definition) and derive a set of equations that uniquely determine it and that can be easily solved recursively. The optimal stopping region varies monotonically with the costs. For the class of problems corresponding to a prior distribution on Λ of type gamma it is shown how the optimal stopping region varies with respect to the prior distribution and with respect to n.
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- Copyright © Applied Probability Trust 1997
Footnotes
This research was supported by CNR project ‘Statistica Bayesiana e simulazione in affidabilita' e modellistica biologica' and by MURST project ‘Processi aleatori e modelli stocastici-teoria e applicazioni alle scienze ad all'industria'.
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