Question

The following are quality control data for a manufacturing process at Kensport Chemical Company. The data show the temperature in degrees centigrade at five points in time during a manufacturing cycle.

Sample	x	R
1	95.72	1.0
2	95.24	0.9
3	95.18	0.9
4	95.42	0.4
5	95.46	0.5
6	95.32	1.1
7	95.40	1.0
8	95.44	0.3
9	95.08	0.2
10	95.50	0.6
11	95.80	0.6
12	95.22	0.2
13	95.60	1.3
14	95.22	0.5
15	95.04	0.8
16	95.72	1.1
17	94.82	0.6
18	95.46	0.5
19	95.60	0.4
20	95.74	0.6

The company is interested in using control charts to monitor the temperature of its manufacturing process. Compute the upper and lower control limits for the R chart. (Round your answers to three decimal places.)

UCL=___

LCL=___

Construct the R chart.

12

3 4

Compute the upper and lower control limits for the x chart. (Round your answers to three decimal places.)

UCL=___

LCL=___

Construct the x chart.

12

3 4

What conclusions can be made about the quality of the process?

The R chart indicates that the process variability is  in control/out of control .  - No samples fall/One sample falls/Two samples fall/More than two samples fall...outside the R chart control limits. The x chart indicates that the process mean is  in control/out of control .  No samples fall/One sample falls/Two samples fall/More than two samples fall....outside the x chart control limits.

Answer 1

for R Chart:

average range R̅ =			0.675
sample size n   =			4
for sample size n=4, criitcal value of constant D3=					0
for sample size n=4, criitcal value of constant D4=					2.282
control line (CL) = R̅=			0.675
upper control limit (UCL)=D4R̅ =			1.540
lower control limit(LCL) =D3R̅ =			0.000

for the x chart.:

sample mean x̅ =			95.399
average range R̅ =			0.6750
sample size n   =			4
for sample size n=4, criitcal value of constant A2=					0.729
control line (CL) = x̅=			95.399
upper control limit =x̅+3*A2R̅ =			95.891
lower control limit =x̅-3*A2R̅ =			94.907

The R chart indicates that the process variability is  in control

No samples fall outside the R chart control limits. The x chart indicates that the process mean is  in control No samples fall outside the   x chart control limits.