Browsing by Author "Cheng, Ya Ching"

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Estimating process yield based on S-pk for multiple samples
(2007-01-01)
Pearn, W. L.
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Cheng, Ya Ching
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工業工程與管理學系
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Department of Industrial Engineering and Management
Boyles ( 1994) proposed a process measurement called S-pk, which provides an exact measure on the process yield for normal processes. Lee et al. ( 2002) considered an asymptotic distribution for the natural estimator of Spk under a single sample. In this paper, we extend the results for the case of multiple samples. We first compare the yield index S-pk with the most commonly used index, C-pk, and review some results of S-pk under a single sample. Next, we derive the sampling distribution for the estimator (S) over cap'(pk) of S-pk under multiple samples and find that for the same S-pk, the variance of (S) over cap'(pk) would be largest when the process mean is on the centre of specification limits. We calculate the lower bounds for various commonly used quality requirements under the situation with the largest variance of (S) over cap'(pk) for assurance purposes. To assess the normally approximated distribution of (S) over cap'(pk), we simulate with 10 000 replications to generate 10 000 estimates of (S) over cap'(pk), calculate their lower bounds, compare with the real (preset) S-pk and check the actual type I error. We also compute how many sample sizes are required for the normal approximation to converge to S-pk within a designated accuracy. Then, we present a real-world application of the one-cell rechargeable Li-ion battery packs, to illustrate how we apply the lower bounds to actual data collected from factories.
Procedure of the convolution method for estimating production yield with sample size information
(2010)
Pearn, W. L.
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Hung, Hui Nien
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Cheng, Ya Ching
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Lin, Gu Hong
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統計學研究所
The yield index S(pk) proposed by Boyles (1994. Process capability with asymmetric tolerances. Communications in Statistics - Simulation and Computation, 23 (1), 615-643) provides an exact measure on the production yield of normal processes. Lee et al. (Lee, J.C., Hung, H.N., Pearn, W. L. and Kueng, T. L., 2002. On the distribution of the estimated process yield index Spk. Quality and Reliability Engineering International, 18 (2), 111-116) considered a normal approximation for estimating Spk. In this paper, we consider a convolution approximation for estimating Spk, and compare with the normal approximation. The comparison results show that the convolution method does provide a more accurate estimation to Spk as well as the production yield than the normal approximation. An efficient step-by-step procedure based on the convolution method is developed to illustrate how to estimate the production yield. Also investigated is the accuracy of the convolution method which provides useful information about sample size required for designated power levels, and for convergence.