972 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1953 



conditions. The curve which can be used to represent the observed 

 frequency distribution of data obtained under controlled conditions may, 

 for most practical purposes, be illustrated by the shape shown in Fig. 1. 

 The characteristics of this curve are mathematically represented by the 

 average X (arithmetic mean) and the standard deviation a (the root- 

 mean-square deviation of individual values from their average X). 



The control chart techniques as originally developed by Walter A. 

 Shewhart^ of Bell Telephone Laboratories provide economical methods 

 for measuring and evaluating the characteristics of such distributions. In 

 practice they are useful in obtaining an estimate of the capabilities of 

 manufacturing processes, sometimes referred to as the "natural toler- 

 ances" of the process and in maintaining control at that quality level. 

 In general, a process having a controlled distribution with an average X 



Fig. 1 — The ideal frequency distribution for observations obtained under con- 

 trolled conditions. 



and a standard deviation a will result in practically all of the individual 

 units of product falling within the band X zt Sa. 



Conventional quality control techniques are used by both the design 

 and manufacturing engineers. The design engineer, in order to specify 

 tolerances compatible with the design needs and the capabilities of ec- 

 onomical commercial manufacture, applies the techniques to a reason- 

 able number of preproduction models or possibly to a limited quantity 

 of initial regular production. The manufacturing engineer in turn uses 

 the techniques for determining the capabilities of existing or new manu- 

 facturing facilities in order to select the most effective facilities and 

 methods. The techniques are also effective tools for locating and elim- 

 inating assignable causes of manufacturing variations, while their con- 

 tinued use as a regular part of the manufacturing process provides an 

 excellent contribution to effective quality control. In these applications 

 there usually exists a substantial margin between the =b3o- variation 

 around the nominal value and the specification limits. This is illustrated 



