I / E C
Statistical Design
Locating Important Sources of Variation A multistage process can be sampled to determine which stages contribute most variability in the product by W. S. Connor, The Research Triangle Institute
V ^ N E O F T H E most useful func tions of statistics is to identify im p o r t a n t sources of variation in a production process. A process m a y be divided into a n u m b e r of subprocesses a n d these, in t u r n , m a y be divided. I t is then possible to distinguish several stages, or hier archies, in the process. For example, a material m a y be obtained from a n u m b e r of suppliers, in a sequence of shipments, from each of which several batches of p r o d u c t are manufactured. The p r o d u c t m a y h a v e numerous vari able characteristics, for each of which it is desired to determine the i m p o r t a n t sources of variation. V a r iation in product m a d e from m a t e rial from different suppliers is the sum of four components of variance : . . . a m o n g suppliers . . . a m o n g shipments from t h e same supplier . . . a m o n g batches from t h e same shipment . . . a m o n g samples from t h e same batch By a p p r o p r i a t e l y s a m p l i n g the batches, it is possible to estimate these four c o m p o n e n t s of v a r i a n c e . If t h e p r o d u c t is discrete items, like tires or bolts, a sample consists of a n u m b e r of these items; b u t if the p r o d u c t is a bulk material, like cement or oil, a sample consists of several portions of the material. I n either case, a b a t c h c a n b e thought of as composed of disjointed parts, some of which are taken into the sample. A n example will be discussed to illustrate some of the concepts a n d techniques. I t is concerned with the wool content of p a r t wool blankets. Sources of variability are colors, batches, looms, a n d pieces, which m a y be identified with sup pliers, shipments, batches, a n d sam ples, respectively.
Variability of Wool Content
m a n y batches of each color, a n d each b a t c h was supplied to m a n y looms. A sample was taken which consisted of 16 pieces, eight for each color, four for each batch, a n d two for each loom. T h e batches, looms, a n d pieces were selected randomly. Observations, in per cent wool,
A study was u n d e r t a k e n to d e termine the i m p o r t a n t sources of variation in t h e wool content of nominally 1 0 % wool blankets. T h e r e were only two colors being manufactured—green a n d yellow—
Table 1.
