Quality Control Management

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By Eric H. Glendinning

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We do not believe that we shall ever see the die showing three and one-half points. 5. 9 2 ) 38 DlSCRErE VARLABLES, OK AITRIBUTES For a binomial distribution, X is the sum of X , , . . , and so ri independent variables X,, E ( X ) = E ( X , ) + E ( X , ) 3- * . = np . 3) The following properties of expectations are easily verified. If a is some constant. E ( u X )= u E ( X ) . Y. 4) This is merely a matter of change of scale. If X has been measured in yards and if Y is the corresponding measurement in feet, then Y = 3 X , and so E(Y)=3E(X).

Fishhone diagram. the graph. Is there a pattern? Do the points tend to lie on a line, showing that scores in the two subjects are highly correlated, or do they fall into the shotgun pattern that suggests independence? Again, one could use stratification, using one symbol for engineers and another for arts students. Would that suggest a pattern? A cause-and-effect diagram looks like the diagram that students in English grammar classes used to draw to analyze sentences. Suppose, for example, that we are concerned about the number of defective items being produced.

In a set of 80 observations, we should expect X = 2 to occur (6/16)(80) = 30 times. The random variable X is said to have a binomial distribution. This topic is developed further in the next two sections. 1. A fair coin is tossed five times. What are the probabilities that X = 0, X = 3, and X = S? ) = 10 ways. cl Hcnce, Y ( 3 ) = 10/32. 7. UNEQUAL PROBABILITIES The binomial distribution was introduced in the previous section from the coin tossing model. 5. That is a special case of a more general model.

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