THE L3 SYSTEM — QUALITY CONTROL REQUIREMENTS 953 

 3.1 CONTROL CHART METHOD 



The control chart method is intended for appUcation where production 

 comprises a reasonably steady succession of individual units or small 

 groups of units from a common source; so that units or groups, as pro- 

 duced, may be kept in the order of their production and control chart 

 techniques applied to test results. Under this method control charts are 

 maintained for averages and ranges of samples of 5. 



At the outset it is necessary to demonstrate an adequate degree of 

 control of the product in order to be considered eligible for application 

 of this method. Once eligibility has been established, a second and some- 

 what more lenient set of conditions is used to judge whether this eligi- 

 bility is maintained. For convenience of reference these two sets of 

 conditions are designated (a) Criterion I, for establishing eligibility (or 

 for reestabhshing it), and (b) Criterion II, for maintaining eligibility. 



The control charts used in this section are an adaptation of the well- 

 known Shewhart control charts for sample averages, X, and sample 

 ranges, R, for "control with respect to a given standard." Two modifica- 

 tions of the techniques customarily used in applying the control chart 

 for X have been introduced: (a) a central band rather than a central 

 line has been provided, and (b) a non-parametric requirement has been 

 imposed on seven successive sample averages to limit the excursions of 

 the product average from the nominal value. These modifications are 

 related to the two acceptable distributions referred to in Fig. 2 and 

 reproduced as dotted lines in Fig. 3. 



The PA limits of Fig. 3 are the desired minimum and maximum values 

 of the process average, and are the averages of the two acceptable dis- 

 tributions. As indicated in Fig. 2, the PA limits for the process average 

 give the boundaries of the band, N db J-^o-", where o-" is the standard 

 deviation of the two acceptable distributions. 



To determine control limits of the control charts for X and R, con- 

 sideration is given to the sampling distributions of averages of samples 

 of 5 drawn from such acceptable distributions, as shown in Fig. 3, as 

 well as to the sampling distribution of ranges of samples of 5 from these 

 distributions. 



The A5 limits of Fig. 3 (limits to be met by the average of a sample 

 of 5) are 3-sigma control limits for averages of 5, given by 



N M yy + 3 



W)' 



The R5 limit (limit to be met by the range of a sample of 5) is the 



