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2 results

  • On a quickest detection problem with variable monitoring

  • D. W. Balmer
  • Journal:
    Journal of Applied Probability / Volume 13 / Issue 4 / December 1976
    Published online by Cambridge University Press:
    14 July 2016, pp. 760-767
    Print publication:
    December 1976

  • The problem of detecting the arrival of a ‘disorder' in a process observed through a monitoring facility which may operate in ‘slow’ or ‘fast’ mode, is formulated as an optimal stopping problem. It is shown that in all circumstances where there may exist an optimal policy specifying the mode of observation and the time of stopping there is a unique policy satisfying certain necessary conditions of optimality; the various circumstances and control policies are specified.

  • On a quickest detection problem with costly information

  • D. W. Balmer
  • Journal:
    Journal of Applied Probability / Volume 12 / Issue 1 / March 1975
    Published online by Cambridge University Press:
    14 July 2016, pp. 87-97
    Print publication:
    March 1975

  • Problems of detecting the arrival of a ‘disorder' are of central importance in quality control. One such problem is formulated as an optimal stopping problem in which information about the process to be stopped may be bought at any time. A control policy will involve a determination of times at which information should be bought and of the time at which the process should be stopped. It is shown that in all circumstances there is a unique policy satisfying necessary conditions for optimality; the various circumstances and control policies are specified.