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Conclusions 209
Table 13.7 C pk confidence limits: performance comparison of SB, PB, BCBP and AM.
n = 30 n = 50 n = 75
Cov. prob. Ave. width Cov. prob. Ave. width Cov. prob. Ave. width
μ = 50,σ = 2, k = 0.0476, C p = 1.750, C pk = 1.667, C pk = C pk1
SB 0.894 0.799 0.895 0.584 0.899 0.476
PB 0.841 0.785 0.856 0.579 0.875 0.474
BCBP 0.852 0.727 0.864 0.552 0.878 0.458
AM 0.885 0.717 0.879 0.552 0.882 0.450
μ = 52,σ = 2, k = 0.1429, C p = 1.750, C pk = 1.500, C pk = C pk1
SB 0.902 0.729 0.897 0.545 0.923 0.434
PB 0.842 0.715 0.858 0.540 0.894 0.432
BCBP 0.854 0.651 0.873 0.510 0.906 0.416
AM 0.877 0.645 0.890 0.497 0·899 0.405
μ = 50,σ = 3, k = 0.0476, C p = 1.167, C pk = 1.111, C pk = C pk1
SB 0.901 0.527 0.890 0.399 0.893 0.322
PB 0.883 0.519 0.880 0.396 0.890 0.321
BCBP 0.880 0.495 0.880 0.386 0.877 0.315
AM 0.889 0.478 0.887 0.368 0.886 0.300
μ = 52,σ = 3, k = 0.1429, C p = 1.167, C pk = 1.000, C = C
pk pk1
SB 0.900 0.506 0.904 0.378 0.909 0.306
PB 0.825 0.496 0.866 0.375 0.884 0.306
BCBP 0.841 0.457 0.875 0.356 0.888 0.295
AM 0.851 0.450 0.854 0.331 0.867 0.270
μ = 50,σ = 3.7, k = 0.0476, C p = 0.946, C pk = 0.901, C = C
pk pk1
SB 0.892 0.432 0.896 0.329 0.879 0.269
PB 0.875 0.425 0.887 0.327 0.880 0.268
BCBP 0.867 0.413 0.876 0.322 0.868 0.265
AM 0.869 0.387 0.878 0.299 0.874 0.243
μ = 52,σ = 3.7, k = 0.1429, C p = 0.946, C pk = 0.811, C pk = C pk1
SB 0.896 0.429 0.899 0.317 0.896 0.256
PB 0.849 0.423 0.862 0.315 0.867 0.256
BCBP 0.860 0.395 0.874 0.301 0.879 0.248
AM 0.845 0.349 0.863 0.269 0.865 0.219

C pk -values the AM attains coverages comparable with the SB method and yet has
the narrowest average widths.

13.8 CONCLUSIONS

We have proposed an approximate method to derive the confidence limits for C pk .
The method is easier to compute compared with other methods such as bootstrapping
and non-central t integration. A graphical method was used to show the relationship
between C p , p, and k. Based on the graphs, we derived the confidence limits of k