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Exact Calculation of the Distributions of the Stopping Times of Two Types of Truncated SPRT for the Mean of the Exponential Distribution

Abstract

Truncated sequential test procedures are proposed for testing the mean time between failures of a system with exponential life distribution. The exact distributions of the stopping times for the sequential tests are derived by investigating boundary crossing times of homogeneous Poisson processes. The exact formulas for the expected values of the stopping variables and the survival functions are derived. Moreover, the operation characteristic functions are derived exactly for the proposed sequential tests.

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Correspondence to Shelemyahu Zacks.

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De, S.K., Zacks, S. Exact Calculation of the Distributions of the Stopping Times of Two Types of Truncated SPRT for the Mean of the Exponential Distribution. Methodol Comput Appl Probab 17, 915–927 (2015). https://doi.org/10.1007/s11009-014-9435-2

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  • DOI: https://doi.org/10.1007/s11009-014-9435-2

Keywords

  • Linear boundaries
  • Operating characteristic
  • Poisson process
  • Sequential testing
  • Stopping time
  • Survival function

Mathematics Subject Classification (2010)

  • 60G10
  • 60G51
  • 62L10
  • 62M02