ESTIMATING THE DISTRIBUTIONS OF MANUFACTURED DIMENSIONS WITH THE BETA PROBABILITY DENSITY-FUNCTION

As mentioned by the author [Ph.D. Dissertation, University of New South Wales, 1989] the percentage of scrap and rework in the manufacturing cost function has been shown to be a function of the shape and variability of the distribution of the manufactured dimensions and of the allocated manufactured tolerances. Therefore questions pertaining to the choice of specific distributions and the determination of the parameters are of interest. This paper presents a method of statistical data analysis to represent the distribution of manufactured dimensions from observational data with a beta probability density function. Instead of using the four moments, a simpler method has been developed which estimates the two bounds first, then estimates the shape exponents using the first and second moments and these four parameters can be improved continuously until some predetermined accuracy is obtained. The use of the distributions of dimensions produced by manufacturing processes is to estimate process capabilities and the probabilities of selected tolerances being achieved by a process or a given set of manufacturing conditions.