Question

A rum producer monitors the position of its label on the bottle by sampling four 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

μ = 1.6 inches.

Past experience indicates that the distance varies with

σ = 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

Answer 1

a)

sample mean x̅ =			1.6
population std deviation σ =			0.15
sample size n   =			4
control line (CL) = x̅=			1.6
upper control limit =x̅+3*σ/√n =			1.825
lower control limit =x̅+3*σ/√n =			1.375

from above:

CL =1.6

LCL=1.375

UCL=1.825

b)

for sample size n=4, criitcal value of constant C4 =					0.9213
for sample size n=, criitcal value of constant B6 =					2.088
for sample size n=, criitcal value of constant B5 =					0

CL = c₄*σ =0.1382

LCL =B₅*σ =0.0000

UCL =B₆*σ =0.3132