A rum producer monitors the position of its label on the bottle by sampling thre
ID: 3324579 • Letter: A
Question
A rum producer monitors the position of its label on the bottle by sampling three bottles from each batch. One quantity measured is the distance from the bottom of the bottle neck to the top of the label. The process mean should be = 1.6 inches. Past experience indicates that the distance varies with = 0.15 inch.
(a) The mean distance x for each batch sample is plotted on an x control chart. Calculate the center line and control limits for this chart. (Round your answers to three decimal places.)
CL = in
LCL = in
UCL = in
(b) The sample standard deviation s for each batch's sample is plotted on an s control chart. What are the center line and control limits for this chart? (Round your answers to four decimal places.)
CL = in
LCL = in
UCL = in
Explanation / Answer
Solution:- Given that values = 1.6 inches. , = 0.15 inch. n = 3
a) CL = 1.6 in
LCL = 1.6 - 3*0.15/sqrt(3) = 1.340
UCL = 1.6 + 3*0.15/sqrt(3) = 1.860
b) the center line and control limits for this chart
By using Chart Standard deviation n = 3.
CL = C4 = 0.8862*0.15 = 0.13293
LCL = B5 = 0*0.15 = 0
UCL = B6 = 2.276*0.15 = 0.3414
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