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=
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*A_{2}R̅ = | 95.783 | ||||
lower control limit (LCL) =x̅-3*A_{2}R̅ = | 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)=D_{4}R̅ = | 1.406 | ||||
lower control limit(LCL) =D_{3}R̅ = | 0.000 |
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