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Sequential tolerance control (STC) is a tolerance control methodology used in discrete parts manufacturing. Recently, an adaptive sphere-fitting method for STC (ASF–STC) was developed to account for potential skewness in manufacturing operations' distributions, a factor not considered in conventional STC. ASF–STC offers significant improvements over conventional STC when such skewness exists. The direction of skewness of an operations' distribution is a necessary input to ASF–STC. Thus, a novel approach to determining the skewness of a distribution for small sample sizes is presented here. ASF–STC has an additional requirement of distribution information for each operation. The beta distribution is an ideal candidate here, as it is very flexible in shape. The literature on four-parameter beta estimation is very limited, and their performance for small sample sizes is poor. STC was designed for low-volume production, thus the estimation for small sample sizes is necessary here. This study presents a heuristic, based on the method of moments estimates for a beta distribution, that estimates the four parameters for a beta distribution with small sample size. Several computational results are provided to compare this heuristic to the best-known procedure, with the heuristic found to perform better for the test problems considered. Copyright © 2002 John Wiley & Sons, Ltd. |
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