Exact computation for some sequential tests

References

• Anderson , T.W. 1960 . A modification of the sequential probability ratio test to reduce the sample size . Ann. Math. Statist. , 31 : 165 – 197 .
   Google Scholar
• Aitchison , J. and Dunsmore , I.R. 1975 . Statistical Prediction Analysis , Cambridge University Press .
   Google Scholar
• Armitage , P. 1957 . Restricted sequential procedures . Biometrika , 44 : 9 – 26 .
   Web of Science ®Google Scholar
• Bancroft , G.A and Dunsmore , I.R. 1978 . Predictive sequential life testing . Biometrika , 65 : 609 – 613 .
   Google Scholar
• Barlow , R.E. and Campo , R. 1975 . “ Total Time on Test Processes and Applications to Failure Data Analysis ” . In Reliability and fault Tree Analysis , Edited by: Barlow , R.E. , Fussell , J. and Singpurwalla , N.D. 451 – 481 . Philadelphia, PA : SIAM .
   Google Scholar
• Barnett , V.D. 1972 . A Bayes sequential life test . Technometrics , 14 : 453 – 467 .
   Google Scholar
• Berger , J.O. and Sun , D. 1993 . Bayesian analysis for the poly-Weibull distribution . J. Amer. Statist. Assoc. , 88 : 1412 – 1418 .
   Web of Science ®Google Scholar
• Brown , L.D. , Cohen , A. and Samuel , Cahn E. 1983 . A sharp necessary condition for admissibility of sequential tests — necessary and sufficient conditions for admissibility of SPRT's . Ann. Statist. , 11 : 640 – 653 .
   Google Scholar
• Brown , L.D. , Cohen , A. and Strawderman , W.E. 1980 . Complete classes for sequential tests of hypotheses . Ann. Statist. , 8 : 377 – 398 .
   Web of Science ®Google Scholar
• Dvoretsky , A , Kiefer , J and Wolfowitz , J . 1953 . Sequential decision problems for processes with continuous time parameters . Ann. Math. Statist. , 24 : 254 – 264 . Correction in Ann. Math. Statist. 30, 1265.
   Google Scholar
• Epstein , B. and Sobel , M. 1955 . Sequential life tests in the exponential case . Ann. Math. Statist. , 26 : 82 – 93 .
   Google Scholar
• Hoel , D.G. 1968 . Closed sequential tests of an exponential parameter . Biometrika , 55 : 387 – 391 .
   Web of Science ®Google Scholar
• Jewel , W.S. 1977 . “ Bayesian life testing using the total Q on test ” . In The Theory and Applications of Reliability, with Emphasis on Bayesian and Nonparametric Methods , Edited by: Tsokos , C.P. and Shimi , I.N. 49 – 66 . New York : Academic Press, Inc. .
   Google Scholar
• Kemperman J.H.B. The General One-Dimensional Random Walk with Absorbing Barriers with Applications to Sequential Analysis Excelsior, 's-Gravenhage Netherlands 1950
   Google Scholar
• Klefsjö , B. 1991 . TTT-plotting — a tool for both theoretical and practical problems . J. of Statist. Plan. and Inference , 29 : 99 – 110 .
   Google Scholar
• Ghosh , B.K. 1970 . “ Sequential Tests of Statistical Hypotheses ” . Reading : Addison-Wesley . Mass
   Google Scholar
• Martz , H.F. and Waller , R.A. 1982 . Bayesian Reliability Analysis , New York : John Wiley Sons .
   Google Scholar
• Noe , M. 1972 . The calculation of distributions of two-sided kolmogorov Smirnov type statistics . Ann. Statist. , 9 : 58 – 64 .
   Google Scholar
• Raghavachari , M. 1965 . Operating characteristic and expected sample size of a sequential probability ratio test for the simple exponential distribution . calcutta Statist. Assoc. Bull. , 14 : 65 – 73 .
   Google Scholar
• Schafer , R.E. 1969 . “ Bayesian Reliability Demonstration, Phase I—Data for the A Priori Distribution ” . In RADC-TR-69-389 , Rome, NY : Rome Air Development Center .
   Google Scholar
• Schafer , R.E. and Singpurwalla , N.D. 1970 . A sequential Bayes procedure for reliability demonstration . Naval Research Logistics Quarterly , 17 : 55 – 67 .
   Google Scholar
• Schneiderman , M.A. and Armitage , P. 1962 . A family of closed sequential procedure . Biometrika , 49 : 41 – 56 .
   Web of Science ®Google Scholar
• Shobel , M. 1953 . An essentially complete class of decision functions for certain standard sequential problems . Ann. Math. Statist. , 24 : 319 – 337 .
   Google Scholar
• Soland , R.M. 1968 . Bayesian analysis of the weibull process with unknown scale parameter and its application to acceptance sampling . IEEE Transactions on Reliability , R-17 : 84 – 90 .
   Web of Science ®Google Scholar
• Steck , G.P. 1971 . Bayesian sequential estimation . Ann. Math. Statist. , 42 : 1 – 11 .
   Google Scholar
• Sun , D. 1994 . Integrable expansions for posterior distributions for a two-parameter exponential family . Ann. Statist. , 22 : 1808 – 1830 .
   Google Scholar
• Sun , D. and Berger , J.O. 1993 . “ Recent development in Bayesian sequential reliability demonstration tests ” . In Advances in Reliability , Edited by: Basu , A. 379 – 393 . Amsterdam : North-Holland .
   Google Scholar
• Sun , D. and Berger , J.O. 1994 . Bayseian sequential reliability for Weibull and related distributions . Ann. Inst. Statist. Math. , 46 : 221 – 249 .
   Web of Science ®Google Scholar
• Wald , A. 1947 . Sequential Analysis , New York : John Wiley Sons .
   Google Scholar
• Wald , A. and Wolfowitz , J. 1948 . Optimum character of sequential probability ratio Tests . Ann. Math. Statist. , 19 : 326 – 339 .
   Google Scholar
• Wijsman , W.A. 1991 . “ Stopping times: termination, moments, distribution ” . In Handbook of Sequential Analysis , Edited by: Ghosh , B.K. and Sen , P.K. 67 – 121 . Marcel Dekker, Inc. .
   Google Scholar
• Ye , K. 1993 . Reference priors when the stopping rule depends on the parameter of interest . J. Amer. Statist. Assoc. , 88 : 360 – 363 .
   Web of Science ®Google Scholar