Question

A speaker manufacturer molds Kevlar woofer surrounds for use in 6.5” woofers. Samples of 7 woofer surrounds are randomly sampled each five minutes, measured, and the average and range for each sample is computed. The following data represent the summary statistics for the most recent 14 samples.

Sample    Mean    Range

1 6.49” 0.05”

2 6.47” 0.03”

3 6.49” 0.07”

4 6.51” 0.02”

5 6.50” 0.06”

6    6.46” 0.08”

7    6.47”    0.03”

8    6.52” 0.04”

9 6.51”    0.07”

10 6.48” 0.03”

11    6.49” 0.05”

12 6.50”    0.03”

13 6.52” 0.04”

14    6.46”    0.03”

What is the CL for the R-chart?

What is the UCL for the R-chart?

What is the LCL for the R-chart?

Does this process appear to be in statistical control? Why or why not?

What is the CL for the ¯x-chart?

What is the UCL for the ¯x-chart?

What is the LCL for the ¯x-chart

Does this process appear to be in statistical control? Why or why not?

Answer 1

Answers related to Range chart

R= Max- Min
0.05
0.03
0.07
0.02
0.06
0.08
0.03
0.04
0.07
0.03
0.05
0.03
0.04
0.03

0.0450
R-bar
control limits for Range, z=3
UCL=R-bar+ z*STD			0.101
CL= R-bar			0.045
LCL=R-bar- z*STD	0 if negative	-0.011	0.000
Standerd deviation= STD=		STDEV(select all range values)	0.0187
The process is in control: As we can see that NO sample is beyond control limits in charts

Answers related to Xbar chart

X-bar= average of sample	UCL	CL	LCL
6.490	6.552	6.491	6.429
6.470	6.552	6.491	6.429
6.490	6.552	6.491	6.429
6.510	6.552	6.491	6.429
6.500	6.552	6.491	6.429
6.460	6.552	6.491	6.429
6.470	6.552	6.491	6.429
6.520	6.552	6.491	6.429
6.510	6.552	6.491	6.429
6.480	6.552	6.491	6.429
6.490	6.552	6.491	6.429
6.500	6.552	6.491	6.429
6.520	6.552	6.491	6.429
6.460	6.552	6.491	6.429
6.4907	Average of all mean's
X-bar-bar
control limits for x-bar, z=3
UCL= Xbar-bar+ z*STD			6.552
CL= X-bar-bar			6.491
LCL= Xbarbar- z*STD			6.429
Standard deviation= STD=		STDEV(select all X-bar values)	0.0206

Yes, the process is in control. Because all the points lie within its control limits. And all the points of X-bar lies in X-bar control limits