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	0.7
4	95.42	0.4
5	95.46	0.5
6	95.32	1.1
7	95.40	0.9
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	0.6
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.

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

UCL=

LCL=

Answer 1

1)for xbar chart":

sample mean x̅ =			95.399
average range R̅ =			0.6650
sample size n   =			5
for sample size n=5, criitcal value of constant A2=					0.577
control line (CL) = x̅=			95.399
upper control limit (UCL)=x̅+3*A2R̅ =			95.783
lower control limit (LCL) =x̅-3*A2R̅ =			95.015

2)

for R chart:

average range R̅ =			0.665
sample size n   =			5
for sample size n=5, criitcal value of constant D3=					0
for sample size n=5, criitcal value of constant D4=					2.115
control line (CL) = R̅=			0.665
upper control limit (UCL)=D4R̅ =			1.406
lower control limit(LCL) =D3R̅ =			0.000