Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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ON THE LIMITING DISTRIBUTION FOR ESTIMATE OF PROCESS CAPABILITY INDEX

  • Park, Hyo-Il (Department of Statistics, Chong-ju University) ;
  • Cho, Joong-Jae (Department of Information Statistics, Chungbuk National University)
  • Published : 2007.12.31
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Abstract

In this paper, we provide a new proof to correct the asymptotic normality for the estimate $\hat{C}_{pmk}\;of\;C_{pmk}$, which is one of the well-known definitions of the process capability index. Also we comment briefly on the correction of the limiting distribution for $\hat{C}_{pmk}$ and on the use of re-sampling methods for the inference of $C_{pmk}$. Finally we discuss the concept of asymptotic unbiasedness.

Keywords

References

  1. BICKEL, P. J. AND DOKSUM, K. A. (1977). Mathematical Statisics: Basic Ideas and Selected Topics, Vol I, Holden-Day, San Francisco
  2. CHAN, L. K., XIONG, Z. AND ZHANG, D. (1990). 'On the asymptotic distribution of some process capability indices', Communications in Statistics-Theory and Methods, 19, 1118
  3. CHEN, S. M. AND Hsu, N. F. (1995). 'The asymptotic distribution of the process capability index $C_{pmk}$', Communications in Statistics-Theory and Methods, 24, 1279-1291 https://doi.org/10.1080/03610929508831553
  4. CHEN, S.-M. AND PEARN, W. L. (1997). 'The asymptotic distribution of the estimated process capability index $\tilde{C}_{pk}$ ', Communications in Statistics-Theory and Methods, 26, 2489-2497 https://doi.org/10.1080/03610929708832061
  5. EFRON, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans, CBMS-NSF, Regional Conference Series in Applied mathematics, SIAM, Philadelphia
  6. GOOD, P. (2000). Permutation Test: A Practical Guide to Resampling Methods for Testing Hypotheses, 2nd ed., Springer, New York
  7. SERFLING, R. J. (1980). Approximation Theorems of Mathematical Statistics, John Wiley & Sons, New York