QUALITY CONTROL T2i 



ject and some of the results obtained through the appHcation of the 

 chart have also been presented. ^ In general the detection of the 

 existence of assignable causes of variation leads to their elimination at 

 a minimum of cost. 



As a basis for this chart we start with the conception of a constant 

 system of causes as being one such that the probability of a unit of 

 product having the quality X within the range X to A' + dX is inde- 

 pendent of time. For convenience in the present discussion we may 

 represent this probability dP as a function / of the quality X and m 

 parameters. Thus 



dP = /(A^ Xi, Xo, • • • \n?)dX. (1) 



The present paper presents different ways of specifying the constant 

 system of causes and of detecting lack of control upon the basis of the 

 different specifications principally by setting sampling limits on the 

 parameters. In this way it is shown that the best control can be 

 secured when all of the parameters together with the function /in Eq. 1 

 are specified. We shall assume, in what follows, one set of specifica- 

 tions after another for the constant system of causes and then show 

 for each set how sampling limits may be established. Nomograms are 

 presented to make the determination of the limits possible without the 

 use of even a slide rule. We shall start with the simplest specification, 

 usually referred to as Type I, which has found extensive use. 



Type I often gives a satisfactory basis of control although it makes 

 use, as we shall see, of only a fraction of the information given by the 

 data used in connection with Specification Type V, which is the ideal 

 set wherever the manufacturer is warranted economically in trying to 

 secure the highest degree of control. The choice of specification to be 

 adopted in a given case depends entirely upon the economic advantage 

 attainable through the detection and elimination of assignable causes 

 of variation. In particular the use of Type V specification in the initial 

 stages of the development of the manufacturing process is almost al- 

 ways warranted, because it materially assists in arriving at a controlled 

 process with a minimum of labor. 



Specification Type I: The probability of the production of a defective 

 piece of apparatus shall be p' .^ 



To set limits in this case is very simple indeed, particularly if we 

 choose the probability P associated with the limits to exceed .9. It 



-Jones, R. L., "Quality of Telephone Materials," Bell Telephone Quarterly, Vol. 

 6, pp. 32-46, January 1927. 



^ The primed notation is used throughout to denote parameters of the universe as 

 contrasted with the estimates of these determined from the sample. 



