Question

In: Statistics and Probability

To determine if their 2.00 inch washers are properly adjusted, Duncan & Hall Inc. has decided...

To determine if their 2.00 inch washers are properly adjusted, Duncan & Hall Inc. has decided to use an x‾-Chart which uses the range to estimate the variability in the sample.

Table:

Period

obs1

obs2

obs3

obs4

obs5

Sample Mean

Sample Range

1

1.96

2.05

1.97

1.97

2

1.99

0.09

2

2

2.05

1.95

2

2.05

2.01

0.1

3

2.04

1.96

1.96

1.97

1.96

1.978

0.08

4

1.97

2

1.98

1.99

1.99

1.986

0.03

5

1.97

2.05

1.98

2.04

2.05

2.018

0.08

6

2.03

2.05

2.01

1.96

1.96

2.002

0.09

7

2.02

1.98

2.03

1.96

2.01

2

0.07

8

1.99

1.99

2.01

1.98

1.97

1.988

0.04

9

2

2.03

1.99

1.95

1.97

1.988

0.08

10

1.95

1.99

1.98

1.96

2

1.976

0.05

11

2.03

1.98

1.96

2.02

2.04

2.006

0.08

Step 5 of 7:

Use the following sample data, taken from the next time period, to determine if the process is "In Control" or "Out of Control".
Observations: 2,1.98,1.93,1.95,1.96
Sample Mean: 1.964

Solutions

Expert Solution

Period obs1 obs2 obs3 obs4 obs5 Sample Mean Sample Range
1 1.96 2.05 1.97 1.97 2 1.99 0.09
2 2 2.05 1.95 2 2.05 2.01 0.1
3 2.04 1.96 1.96 1.97 1.96 1.978 0.08
4 1.97 2 1.98 1.99 1.99 1.986 0.03
5 1.97 2.05 1.98 2.04 2.05 2.018 0.08
6 2.03 2.05 2.01 1.96 1.96 2.002 0.09
7 2.02 1.98 2.03 1.96 2.01 2 0.07
8 1.99 1.99 2.01 1.98 1.97 1.988 0.04
9 2 2.03 1.99 1.95 1.97 1.988 0.08
10 1.95 1.99 1.98 1.96 2 1.976 0.05
11 2.03 1.98 1.96 2.02 2.04 2.006 0.08
total 21.942 0.79
average 1.995 0.072

from above :

sample mean x̅ = 1.995
average range R̅ = 0.072
sample size n   = 5
for sample size n=5, criitcal value of constant A2= 0.577
control line (CL) = x̅= 1.995
upper control limit =x̅+3*A2R̅ = 2.037
lower control limit =x̅-3*A2R̅ = 1.953

as 1.964 falls between upper and lower control limit ; therefore process is "In Control"

orchestra answered 3 years ago
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