Main Article Content

Abstract

The performance of step-wise group screening with unequal a-priori probabilities in terms of the expected number of runs and the expected maximum number of incorrect decisions is considered. A method of obtaining optimal step-wise designs with unequal a-priori probabilities is presented for the case in which the direction of each defective factor is assumed to be known a -priori and observations are subject to error. An appropriate cost function is introduced and the value of the group size which minimizes the expected total cost is obtained.

 

 

Keywords

Step-Wise Designs Group-Factors Initial Step Subsequent Steps Expected Number of Runs Incorrect Decisions Cost Function.

Article Details

References

  1. DORFMAN, R. 1943. The de1ection of defective members of large populations, Annals of Mathematical Statistics, 14: 438 -440.
  2. LI, C.H. 1962. A sequential method for screening experimental variables. Jour. Arner Statistical Assoc. 57: 455-477.
  3. MANENE, M.M. 1985. Further investigations of group screening designs: Step-wise designs; Ph.D. thesis submitted to University of Nairobi.
  4. MANENE, M.M. 1997. On Two Type Step-wise group screening designs, Proc of fifth scientific con£. Of Eastern. Central and Southern Africa Network of I. B.S., 57 –62.
  5. ODHIAMBO, J.W. and MANENE, M.M. 1987. Step-wise Group Screening Designs with Errors in Observations. Comm. In Statistics Theor. Meth. 16(1 0): 3095-3115.
  6. ODHIAMBO, J.W. and PATEL, M.S. 1986. On Multistage Group Screening Designs. Comm. in Statistics Theor. Meth. 15(5): 1627-1645.
  7. OTTIENO, J.A.M. and PATEL M.S. 1984. Two Stage Group Screening Designs with Unequal A-priori Probabilities. Comm in Statistics Theor. Meth. 13(6): 761-779.
  8. PATEL, M.S. 1962. Group Screening with more than Two Stages; Technometrics, 4: 209-217.
  9. PATEL, M.S. and MANENE, M.M. 1987. Step-Wise Group Screening with Equal Prior Probabilities and no errors in Observations, Comm. In Statistics Simula_and Comguta, 16(3): 817-833.
  10. PLACKET, R.L. and BURMAN, J.P 1946. The Design of Optimum Multifactor Experiments. Biometrika, 33: 305-325.
  11. STERRET, A. 1957. On the Detection of Defective Members of Large Populations, Annals of Mathematical Statistics. 28: 1033-1036.
  12. WATSON, G.S. 1961. A study of the Group Screening Method, Technometrics, 3: 371-388.