Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지

Better Bootstrap Confidence Intervals for Process Incapability Index $C_{pp}$

  • Cho, Joong-Jae (Department of Statistics, Chungbuk National University) ;
  • Han, Jeong-Hye (National Institute of Professional Administration Statistical Training Center) ;
  • Lee, In-Pyo (Department of International Commerce, Woosong University)
  • Published : 1999.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

Greenwich and Jahr-Schaffrath(1995) considered a new process incapability index(PII) $C_{pp}$, which modified the useful index $C^{\ast}_{pm}{$ for detecting assignable causes. The new index $C_{pp}$ provides an uncontaminated separation between information concerning the process accuracy and precision while this kind of information separation is not available with the $C^{\ast}_{pm}$ index. In this paper, we will study about the index $C_{pp}$ based on the bootstrap. First, we will prove the consistency of bootstrap deriving the bootstrap asymptotic distribution for our index $C_{pp}$. Moreover, with the consistency of bootstrap, we will construct six bootstrap confidence intervals and compare their performances. Some simulation results, comparison and analysis are provided. In particular, two STUD and ABC bootstrap methods perform significantly better.

Keywords

References

  1. Communications in Statistics:Theory and Methods v.19 no.1 On the Asymptotic Distributions of Some Process Capability Indices Chan, L. K.;Xiong, Z.;Zhang, D.
  2. Korean Journal of Applied Statistics v.12 no.1 Better Nonparametric Bootstrap Confidence Intervals for Process Capability Index $C_{pk}$ Cho, J. J.;Kim, J. S.;Park, B. S.
  3. Journal of the American Statistical Association v.82 Better Bootstrap Confidence Intervals (with discussion) Efron, B.
  4. Communications in Statistics : Simulation and Computation v.20 no.1 Bootstrap Confidence Interval Estimates of $C_{pk}$ Franklin, L. A.;Wasserman, G. S.
  5. Journal of Quality technology v.24 Bootstrap Lower Confidence Interval Limits for Capability Indices Franklin, L. A.;Wasserman, G. S.
  6. International Journal of Quality & Reliability Management v.12 no.4 A Process Incapability Index Greenwich, M.;Jahr-Schaffrath, B. L.
  7. Annals of Statistics v.16 Theoretical Comparison of Bootstrap Confidence Intervals Hall, P.
  8. Communications in Statistics : Simulation and Computation Bootstrap Confidence Limits for Wright's $C_s$ Han, J. H.;Cho, J. J.;Leem, C. S.
  9. Journal of the Korean Society for Quality Management v.23 no.4 Bootstrapping Some Process Capability Indices Kim, P. K.;Cho, J. J.
  10. ASQC Quality Congress Transactions Capability Indices : Process Performance Measures Marcucci, M. D.;Beazley, C. E.
  11. Approximation Theorems of Mathematical Statistics Serfling, R. J.