That we cannot make all pieces of a given kind of product identically alike is accepted as a general truth. It follows that the qualities of pieces of the same kind of product differ among themselves, or, in other words, the quality of product must be expected to vary. The causes of this variability are, in general, unknown.The present paper presents a scientific basis for determining when we have gone as far as it is economically feasible to go in eliminating these unknown or chance causes of variability in the quality of a product. When this state has been reached, the product is said to be COl/trolled because it is then possible to set up limits within which the quality may be expected to remain in the future. By securing control, we attain the five economic advantages discussed in Part II r.I I "TRODUCTIO" What is the Problem of Control?W H AT is the problem involved in the control of quality of manu, factured product? To answer this question, let us put ourselves in the position of a manufacturer turning out millions of the same kind of thing every year. Whether it be lead pencils, chewing gum, bars of soap, telephones or automobiles, the problem is much the same. He sets up a standard for the quality of his product and then tries to make all pieces of product conform with this standard. Here his troubles begin. For him standard quality is a bull's-eye, but like a marksman shooting at such a target, he often misses. As is the case in everything we do, unknown or chance causes exert their influence. The problem then is: how much may the quality of a product vary and yet be controlled? In other words, how much variation should we leave to chance?To make a thing the way we want to make it is one popular conception of control. We have been trying to do this for a good many years and we see the fruition of this effort in the marvelous industrial development around us. \Ve have accepted the idea of applying scientific principles but now a change is coming about in the principles themselves which necessitates a new concept of control.A few years ago we were inclined to look forward to the time when a manufacturer would be able to do just what he wanted to do. We shared the enthusiasm of Pope when he said" All chance is but direction thou canst not see," and we looked forward to the time when we would see that direction. I n other words, emphasis was laid 011 the exactness

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Synopsis: Whenever we measure any physical quantity we customarily obtain as many different values as there are observations. From a consideration of these measurements we must determine the most probable value; we must find out how much an observation may be expected to vary from this most probable value; and we must learn as much as possible of the reasons why it varies in the particular way that it does. In other words, the real value of physical measurements lies in the fact that from them it is possible to determine something of the nature of the results to be expected if the series of observations is repeated. The best use can be made of the data if we can find from them the most probable frequency or occurrence of any observed magnitude of the physical quantity or, in other words, the most probable law of distribution. It is customary practice in connection with physical and engineering measurements to assume that the arithmetic mean of the observations is the most probable value and that the frequency of occurrence of deviations from this mean is in accord with the Gaussian or normal law of error which lies at the foundation of the theory of errors. In most of those cases where the observed distributions of deviations have been compared with the theoretical ones based on the assumption of this law, it has been found highly improbable that the groups of observations could have arisen from systems of causes consistent with the normal law. Furthermore, even upon an a priori basis the normal law is a very limited case of a more generalized one. Therefore, in order to find the probability of the occurrence of a deviation of a given magnitude, it is necessary in most instances to find the theoretical distribution which is more probable than that given by the normal law. The present paper deals with the application of elementary statistical methods for finding this best frequency distribution of the deviations. In other words, the present paper points out some of the limitations of the theory of errors, based upon the normal law, in the analysis of physical and engineering data; it suggests methods for overcoming these difficulties by basing the analysis upon a more generalized law of error; it reviews the methods for finding the best theoretical distribution and closes with a discussion of the magnitude of the advantages to be gained by either the physicist or the engineer from an application of the methods reviewed herein.

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