o r g a n i z a t i o n known as the American Society for Quality Control. T h i s organizat i o n proposes t o continue the development of t h e s e techniques. T h e s e q u e n t i a l techniques as published oy C o l u m b i a University P r e s s late in 1945 w e r e developed b y t h e Statistical R e s e a r c h G r o u p of Columbia University for t h e Applied M a t h e m a t i c s P a n e l of N D R C . D e v e l o p m e n t preceded publication b y about t w o years, b u t except for r e s t r i c t e d distribution t o w a r industries, t h e A r m y , N a v y , and Air Forces, no publicity w a s given t o these classics i n statistical d e v e l o p m e n t , because t h e techniques d e s c r i b e d were considered so efficient in a n a l y z i n g statistical d a t a t h a t publication would h a v e violated the War Secrets Act in t h e j u d g m e n t of O S R D . T h e s e restrict i o n s h a v e since been removed. T h e development of the "Sequential A n a l y s i s of Statistical D a t a : Applicat i o n s " w a s based on t h e theoretical work of A. W a l d , "Sequential Analysis of Statistical D a t a : Theor} 7 ", a report s u b m i t t e d by t h e Statistical Research G r o u p of C o l u m b i a University to the Applied M a t h e m a t i c s Panel, N D R C , i n September 1943. A u t h o r s h i p of the "Applications" is a s c r i b e d to t h e group as a whole; however, H . A. F r e e m a n prepared t h e first (res t r i c t e d ) edition, and he shared t h e planning a n d preparation of the second with M . A. Girshick a n d W. Allen Wallis, with t h e cooperation of K e n n e t h J . Arnold, M i l t o n F r e i d m a n , Edward P a u l s o n , and others. T h e s e q u e n t i a l techniques a r e of particular interest t o research and developm e n t w o r k e r s ; all are designed t o extract t h e m a x i m u m of information from a given a m o u n t of d a t a , a n d t h e y differ from those p r e v i o u s l y described in that n o fixed number of s a m p l e s or m e a s u r e m e n t s are pred e t e r m i n e d ; instead, for a given degree of a s s u r a n c e (or probability) a n d for a pred e t e r m i n e d risk t h a t a wrong conclusion (or decision) m a y be reached, the sampling or m e a s u r i n g is continued until o n e of two decisions is reached, namely (1) to reject t h e lot (or hypothesis) or (2) accept the lot (or h y p o t h e s i s ) . As long as sampling or m e a s u r i n g is not decisive in this respect, w i t h the assurance required, these o p e r a t i o n s are continued. T h u s , doubtful cases receive t h e most a t t e n t i o n a n d / o r t e s t i n g ; clear-cut cases of acceptance (or r e j e c t i o n ) of t h e lot (or hypothesis) are q u i c k l y a n d efficiently disposed of. If t h e a s s u r a n c e required is only 60 chances in 100, s a m p l i n g a n d / o r testing m a y be r e l a t i v e l y simple; if on the o t h e r hand, a s s u r a n c e t o 99 chances in 100 i s desired t h e e x p e r i m e n t m a y be so expensive as to require modification with respect t o assura ^e desired, or m o n e y available. Summary
of
Jofen D. Fevry T h e Eli Xilly and Company A w a r d in Biological Chemistry w a s presented to J o h n D . jFerry, assistant professor of chemistry a t the University of Wisconsin, at thie ACS m e e t i n g i n Chicago. T h e award, $1,000 a n d a bronze m e d a l , was given, for "versatile a n d incisive studies on t h e chemistry of large molecules". H i s studies on the properties of large protein molecules a n d their gels contributed to the understanding of such processes a s gelation of gelatin and clotting of blood and led t o production during the war of fibrinogen plastic and fibrin sponges, tubes, a n d films t h a t are finding important use in n e u r o - and general surgery. Canadian, born, F e r r y received t h e B.S. (1932) and P h . D . (1935) degrees at Stanford interrupted by a two-year interval at the National I n s t i t u t e for Medical Research in London. Going t o H a r v a r d t h e next year a s instructor in biochemistry, he was research associate and junior fellow until 1941 w h e n he went to the Oceanographic I n s t i t u t e at Woods Hole, Mass., a s associate chemist wMle continuing h i s work on proteins of blood plasma a t H a r v a r d Medical Scbool. H e went t o Wisconsin in February of this year,
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when t h e result of t h e test is a decision between two methods or products (double dichotomies, winch means "two-part" problems). T h e objective here is to decide whether process A is superior t o B or vice versa, on t h e basis of observations of pairs of data, or results of tests which result favorably (or unfavorably) for one of the processes. Those tests which result in both pairs giving favorable (or unfavorable) results are discarded; t h e test (to the degree of assurance required) is continued until a decision is reached. Sec. 4. T h e application of these techniques when the quality being tested is measured, a n d when t h e question is whether a s t a n d a r d is exceeded or fallen short of, is discussed. Sec. 5. Cases when the quality being tested is measured, and when the question is whether t h e lot differs from a standard are covered. Sec. 6. T h e variability of a quality about its average is analyzed. In this type of problem variability m a y be of more interest t h a n average performance; for instance, the variability of piston ring life in a given motor m a y b e desired in a very narrow range t o minimize t h e cost of tearing down the m o t o r for replacement, even though average life is sacrificed to some extent. Sec. 7. Some properties a n d principles of sequential analysis, as average sample size required as compared to other plans, effects of t r u n c a t i o n (termination before all conditions are met) a n d formulas used in Sec. 2, 3, 4, 5, a n d 6, are described. T h e development of statistical techniques is not a completed project by any means; A S T M h a s reorganized t h e committee responsible for preparation of the ASTM m a n u a l u n d e r the chairmanship of H a r o l d F . Dodge, who served so ably in p r e p a r a t i o n of t h e original manual and the ASA standards. T h i s committee will continue development work along quality control and related lines. A I E E has organized a joint committee with the American Statistical Association for this same purpose, and A S M E lias been active in education of inspection and engineering personnel in statistical procedures for years past. T h e techniques of application to a n y given industry will always require refinement a n d a d a p t a t i o n ; and tins can probably be best accomplished by the education of the engineer in use of the tools of t h e statistician r a t h e r t h a n by the invasion of t h e engineering field by statisticians.
T¥MC C o r e f •• • .
Report
T h e r e p o r t is divided into s e v e n sections s e p a r a t e l y b o u n d for convenience in using, a n d a v e r y brief description of t h e s e follows : V O L U M E
Sec. 1. T h i s section is devoted to an introduction to t h e general sequential procedures b y way of a foreword; t h e statistical aspects of inspection a r e developed and this discussion, with minor, modifications, is applicable to experimentation also. The tovo kinds of errors involved in estimating lot quality, t h e quantities which must be dealt with in sampling inspection, and the statistician's contribution to standard and sequential inspection is discussed. This is followed by an exposition of t h e sequential t e s t , a n d its chief merit—namely (as compared to standard inspection plans), a 5 0 % savings in inspection (or testing) labor—is usually possible, w i t h no sacrifice i n efficiency The numerical measures used are defined,, and t h e terminology changes necessary to a d o p t the discussion to experimentation are developed. Sec. 2. T h e application of sequential procedure when the result of a single observation is a classification as good or bad and when t h e result of such observation is acceptance o r rejection is developed. This section was widely used during t h e war for the formulation of inspection plans for acceptance testing of t h e millions of p a r t s required for planes, tanks, guns, ammunition, a n d the like in several thousand war plants; it m a y fairly be said t h a t enough manpower was not available t o have performed 100% inspection of such p a r t s . By t h i s means a tremendous saving i n inspection, with little or no loss in efficiency was unquestionably made. Sec. 3 . Develops t h e sequential procedure when the result of a single observation is a classification as good or b a d , and
Bib liograp hy (1) ASTM "Manual on Presentation of Data", American Society for Testing Materials, 260 South Broad St., Philadelphia 2, Pa. (2) American War Standards Zl. 1—1941, Z1.2 — 1941, Z1.3 — 1942, American Standards Association, 70 East 45th St.. New York 17, N.Y. (3) Sequential Analysis of Statistical Data: Applications, New York, Columbia University Press, 1945. (4) Shewhart, Walter A., "Economic Control of Qualitj^ of Manufactured Product", NVw York, D . Van Nostrand Co. 1931. (5) Simon, Leslie E., "An Engineers Manual of Statistical Methods", New York, John Wiley and Sons, Inc., 1941. 2775
