18 BELL SYSTEM TECHNICAL JOURNAL 



Where a steady supply of product is offered for acceptance on a lot-by-lot 

 basis, the use of these sampling procedures and tables, together with con- 

 tinuing control chart analyses of the inspection results obtained therefrom, 

 have been found to provide a balanced and economical inspection program. 



Acknowledgment 



Work underlying the development and application of these tables has 

 been contributed by many individuals in the Bell Telephone Laboratories 

 and the Western Electric Company, The authors here express their in- 

 debtedness to these associates, particularly to those in the Western Electric 

 Company who cooperated in the early development of the technical features 

 of the plans and worked out shop procedures for use in their application. 

 The laborious work of computing and preparing the tables in their final 

 form was carried out by Miss Mary N. Torrey and Miss Ruth A. Bender — 

 we wish to express our appeciation to them for their efforts to make 

 the tables as free from error as possible. 



REFERENCES 



1. W. A. Shewhart, "Economic Control of Quality of Manufactured Product," (New 



York: D. Van Nostrand Co., 1931). 



2. E. S. Pearson, "The Application of Statistical Methods to Industrial Standardisation 



and Quality Control" (British Standards Institution, London, 1935). 

 3 H. F. Dodge and H. G. Romig, "A Method of Samphng Inspection," The Bell System 

 Technical Journal, Vol. VIII, October 1929, pp. 613-631. 



4. H. F. Dodge, "Acceptance-Rejection Requirements in Specifications," Proc.A.S.T.M. 



Vol. 34, Part II, 1934, pp. 877-890. 



5. G. Udney Yule and M. G. Kendall, "An Introduction to the Theory of Statistics," 



(11th Ed.; London: Charles Griffin & Co., 1937). 



6. W. A. Shewhart, "Statistical Method from the Viewpoint of Quality Control," 



(The Graduate School, U. S. Dept. of Agriculture, Washington, 1939). 



7. A.S.T.M. Manual on Presentation of Data, Supplement B (Philadelphia: A.S.T.M., 



1940). 



8. Karl Pearson, "Tables for Statisticians and Biometricians," (London: Cambridge 



University Press, 1914), Table LI. 



9. G. A. Campbell, "ProbabiHty Curves Showing Poisson's Exponential Summation," 



The Bell System Technical Journal, Vol. II, January 1923, pp. 95-113. 

 10. Frances Thorndike, "Apphcations of Poisson's ProbabiUty Summation," The Bell 

 System Technical Journal, Vol. V, October 1926, pp. 604-624. 



MATHEMATICAL APPENDIX 



Fundamental Probability Formulas 



The mathematical probabilities used in the solutions are based on equations 

 corresponding to one or the other of the following two sets of conditions: 



(a) Sampling from a finite universe. 



(b) Sampling from an infinite universe. 



In relations involving the determination of the Consumer's Risk, the sample 

 is considered as a sample from a lot of a finite number of pieces and probabilities 

 are correspondingly based on (a). For all other relations in the solutions — in- 

 volving the determination of the Producer's Risk, the determination of the 

 average number of pieces inspected per lot, etc. — the sample is considered as a 



