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The following samples were collected when monitoring a process using already est

ID: 427545 • Letter: T

Question

The following samples were collected when monitoring a process using already established x-bar and R control charts. The LCL and UCL for the x-bar chart are 15.38 and 15.65, respectively. Enter the number of the sample that is out of control or 0 if no sample is out of control. (Note: do not enter any text, just 0, 1, 2, 3, or 4.)


HINT: use the central limit theorem

Sample 1 15.431 15.651 15.405 15.654 Sample 2 15.734 15.791 15.663 15.683 Sample 3 15.580 15.552 15.561 15.537 Sample 4 15.625 15.394 15.512 15.646

Explanation / Answer

The average of data for sample 1

= ( 15.431 + 15.651 + 15.405 + 15.654 ) / 4 = 15.535

The average of data for sample 2

= ( 15.734 + 15.791 + 15.663 + 15.683 ) / 4 = 15.717

The average of data for sample 3

= ( 15.580 + 15.552 + 15.561 + 15.537 ) /4 = 15.557

The average of data for sample 4

= ( 15.625 + 15.394 + 15.512 + 15.646 ) /4 = 15.544

All the data on “average” as derived above i.e. 15.535 , 15.717 , 15.557 and 15.544 are NOT within the range defined by LCL and UCL of X bar chart i.e. 15.38 – 15.65 . The average of sample 2 which is 15.717 is outside such control limit since it is greater than UCL .

Therefore , we can conclude that SAMPLE 2 is out of control .