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CONTROL CHARTS FOR MUTIVARIATE, CORRELATED OBSERVATIONS

NCJ Number
60687
Author(s)
F B ALT; S J DEUTSCH; J W WALKER
Date Published
1977
Length
10 pages
Annotation
QUALITY CONTROL CHARTS FOR THE MEANS OF POPULATIONS HAVING ONE AND MULTIPLE QUALITY CHARACTERISTICS ARE DISCUSSED, WITH ATTENTION GIVEN TO THE ASSUMPTION THAT THE SAMPLES BEHAVE RANDOMLY.
Abstract
THE GENERAL MULTIVARIATE STATISTICAL QUALITY CONTROL PROBLEM INVOLVES A REPETITIVE PROCESS WHERE EACH ITEM IS CHARACTERIZED BY A DETERMINED NUMBER OF QUALITY CHARACTERISTICS WHICH ARE RANDOM VARIABLES BECAUSE OF THE CHANCE CAUSES INHERENT IN THE PROCESS. WHEN THE SCENARIO IS A REPETITIVE MANUFACTURING OPERATION, MULTIPLE MEASUREMENTS WILL BE MADE ON A SAMPLE OF THE SUCCESSIVELY MANUFACTURED ITEMS. INTEREST IS USUALLY CENTERED ON THE POPULATION MEAN QUALITY VECTOR. WHEN CHANGES IN THE PROCESS CAUSE QUALITY CHARACTERISTICS TO SHIFT FROM THEIR NOMINAL VALUE, THUS AFFECTING THE MEAN VECTOR, THESE CHANGES MUST BE DETECTED TO ASSURE A UNIFORM QUALITY PRODUCT. QUALITY CONTROL CHARTS ARE DEVELOPED TO ACHIEVE THIS DETECTION. IN INDEPENDENT OBSERVATIONS OF SAMPLES WHERE ONLY ONE QUALITY CHARACTERISTIC IS INVOLVED AND STANDARD VALUES ARE SPECIFIED FOR THE POPULATION MEAN AND VARIANCE, SHEWHART CONTROL CHARTS CAN BE DEVELOPED FOR THE MEAN, WITH A CENTRAL LINE AND UPPER AND LOWER CONTROL LIMITS. IT IS CONVENIENT TO USE AUTOREGRESSIVE MOVING AVERAGE MODELS FOR INVESTIGATING THE SPECIFIC NATURE OF DEPENDENCE AMONG THE OBSERVATIONS IN A SAMPLE. QUALITY CONTROL CHARTS FOR THE MEAN OF A POPULATION WITH MULTIPLE QUALITY CHARACTERISTICS CAN BE DEVELOPED, BASED ON THE ASSUMPTIONS OF PROCESS NORMALITY AND INDEPENDENCE OF THE SAMPLE ELEMENTS. THE EFFECT UPON THE DECISION RULE OF DEPARTURES FROM THESE LATTER ASSUMPTIONS ARE DETERMINED THROUGH AN EXAMINATION OF CORRELATED OBSERVATIONS AND THE DETERMINATION OF OUT OF CONTROL CHARACTERISTICS. MATHEMATICAL EQUATIONS AND REFERENCES ARE PROVIDED. (RCB)

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