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
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 .