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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

Methodology and Computing in Applied Probability volume 17, pages 915–927 (2015)Cite this article

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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References

  • Dvoretzkt A, Kiefer J, Wolfowitz J (1953) Sequential decision problems for processes with continuous time parameter. testing hypotheses. Ann Math Stat 24(2):254–264

    Article  Google Scholar 

  • Ghosh BK (1970) Sequential tests of statistical hypotheses. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Kao EPC (1997) An introduction to stochastic processes. Duxbury, New York

    Google Scholar 

  • Kemperman JHB (1963) A Weiner-Hopf type method for a general random walk with a two-sided boundary. Ann Math Stat 34(4):1168–1193

    Article  MathSciNet  MATH  Google Scholar 

  • Siegmund D (1985) Sequential analysis: tests and confidence intervals. Springer, New York

    Book  MATH  Google Scholar 

  • Woodroofe M (1982) Nonlinear renewal theory in sequential analysis. SIAM monograph

  • Xu Y (2012) First exit times of compound Poisson processes with parallel boundaries. Sequential Analysis: Tests and Confidence Intervals 31(2):135–144

    Article  MATH  Google Scholar 

  • Zacks S (1991) Distributions of stopping times for Poisson processes with linear boundaries. Communications in Statistics. Stochastic Models 7:233–242

    Article  MathSciNet  MATH  Google Scholar 

  • Zacks S (2009) Stage-wise adaptive designs. Wiley, New York

    Book  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, Odisha, 751005, India

    Shyamal K De

  2. Department of Mathematical Sciences, Binghamton University, 4400 Vestal parkway East, Binghamton, NY, 13902, USA

    Shelemyahu Zacks

Authors
  1. Shyamal K De
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  2. Shelemyahu Zacks
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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