NCJ Number
60688
Date Published
1979
Length
8 pages
Annotation
THE SAMPLE SIZE AND QUALITY CONTROL CHART CONSTANT ARE DETERMINED FOR ONE QUALITY CHARACTERISTIC WHEN THE ELEMENTS OF THE SAMPLE ARE CORRELATED. ARE CORRELATED.
Abstract
ONE OF THE MOST INTERESTING EXTENSIONS OF THE SHEWHART QUALITY CONTROL CHART HAS BEEN THE DETERMINATION OF THE ECONOMIC PARAMETERS OF SAMPLE SIZE AND CONTROL CHART CONSTANT. E.S. PAGE DEVELOPED THE PROCEDURE FOR DETERMINING THESE PARAMETERS BY MINIMIZING THE AVERAGE RUN LENGTH OF AN OUT-OF-CONTROL PROCESS. PAGE'S SCHEME, THE SAMPLE SIZE AND THE CONTROL CHART CONSTANT ARE DETERMINED IN THE PRESENCE OF CORRELATION. THIS IS ACCOMPLISHED BY MINIMIZING THE AVERAGE RUN LENGTH OF AN OUT-OF-CONTROL PROCESS IS FIXED AND THE SIZE OF THE SHIFT THAT IS IMPORTANT TO DETECT IS ALSO FIXED. ONE RESULT IS THAT THE SAMPLE SIZE NEEDED TO DETECT A SHIFT OF GIVEN MAGNITUDE IS LARGER FOR UNCORRELATED OBSERVATIONS THAN FOR NEGATIVE FIRST-ORDER SERIAL CORRELATIONS. RESULTS WERE ALSO OBTAINED FOR SECOND-ORDER SERIAL CORRELATION. TABULAR DATA, MATHEMATICAL EQUATIONS, AND REFERENCES ARE PROVIDED. (RCB)