8/10/2019 SPCHW LE2

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SPC HW

Professor Silverman

Sample # X1 X2 X3 X4 X5

1 12.44 12.14 12.2 12.25 12.32

2 12.16 12.16 12.18 12.35 12.36

3 12.18 12.18 12.18 12.01 12.23

4 12.1 11.78 12.36 12.06 12.06

5 12.2 11.96 12.3 12.33 12.38

6 11.88 12.24 12.04 12.29 12.12

7 11.96 12.4 12.24 12.10 12.30

8 12.52 11.86 12.52 12.09 12.03

9 12 11.94 12.16 12.15 12.22

10 12.08 12.14 11.76 12.03 12.38

11 12.3 11.86 11.72 12.37 12.29

12 11.92 11.86 12.18 12.16 12.0413 12.02 12.2 12.08 12.17 12.12

14 12.14 12.06 12.3 12.03 12.20

15 12.02 11.9 11.9 12.06 12.04

16 12.06 12.28 11.92 12.21 12.23

17 12.32 12.5 11.51 12.23 12.29

18 11.78 11.96 12.34 12.31 12.26

19 12.14 12.06 12.04 12.28 12.34

20 12.34 12.18 12.18 12.33 12.14

21 11.9 12.26 12.14 12.11 12.27

22 11.53 11.92 12.56 12.17 12.01

23 12.06 12.08 12.2 12.19 12.17

24 12.2 12.1 12.02 12.05 12.30

25 12.16 11.54 12.54 12.06 12.01

A bottle filli

specificatio

decided tosettled dow

in rows 1-1

1. Construc

the process

size, n, whic

chart factor

spreadshee

2. After co

to collect dshown in sa

calculate ne

process no

3. Calculat

not capable

8/10/2019 SPCHW LE2

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ng plant has been having trouble meeting the customer

s of 11.7 to 12.3 ounces of liquid in bottles. The company

onstruct statistical process control charts and after the processn collected 5 samples per day for 15 days resulting in the data

shown in the first box on the left.

t x-bar and r charts using the first 15 samples. Discuss whether

is in control or not. Be sure to correctly identify the sample

h is the number of observations in each sample. The control

s d2, D3 and D4 are provided in the SPC Control Chart Factors

t.

structing the two control charts above, the company continued

ta. Since they made no systemic changes, add the new data as

mples 16-25 to the two charts constructed above. Do not

w overall means or control limits. Discuss the quality of the

.

the capability index Cpk and discuss why the process is or is

of meeting the customer's needs.

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7

11

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26

33

37

41

45

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A B C D E F G H I J K L M N O P Q R S T U V

SPC HW Solution Specifications d2 D4 D3

Professor Silverman 11.7 - 12.3 2.326 2.11 0

Sample # X1 X2 X3 X4 X5 Xbar-bar Xbar UCLx LCLx Rbar R UCLr LCLr

1 12.44 12.14 12.2 12.25 12.32 12.137 12.270 12.36 11.92 0.380 0.300 0.8 0

2 12.16 12.16 12.18 12.35 12.36 12.137 12.243 12.36 11.92 0.380 0.204 0.8 0

3 12.18 12.18 12.18 12.01 12.23 12.137 12.155 12.36 11.92 0.380 0.216 0.8 0

4 12.1 11.78 12.36 12.06 12.06 12.137 12.071 12.36 11.92 0.380 0.580 0.8 0

5 12.2 11.96 12.3 12.33 12.38 12.137 12.232 12.36 11.92 0.380 0.416 0.8 0

6 11.88 12.24 12.04 12.29 12.12 12.137 12.113 12.36 11.92 0.380 0.405 0.8 07 11.96 12.4 12.24 12.10 12.30 12.137 12.200 12.36 11.92 0.380 0.440 0.8 0

8 12.52 11.86 12.52 12.09 12.03 12.137 12.205 12.36 11.92 0.380 0.660 0.8 0

9 12 11.94 12.16 12.15 12.22 12.137 1 2.095 12.36 11.92 0.380 0.285 0.8 0

10 12.08 12.14 11.76 12.03 12.38 12.137 12.078 12.36 11.92 0.380 0.622 0.8 0

11 12.3 11.86 11.72 12.37 12.29 12.137 12.107 12.36 11.92 0.380 0.650 0.8 0

12 11.92 11.86 12.18 12.16 12.04 12.137 12.032 12.36 11.92 0.380 0.320 0.8 0

13 12.02 12.2 12.08 12.17 12.12 12.137 12.118 12.36 11.92 0.380 0.180 0.8 0

14 12.14 12.06 12.3 12.03 12.20 12.137 12.146 12.36 11.92 0.380 0.266 0.8 0

15 12.02 11.9 11.9 12.06 12.04 12.137 11.985 12.36 11.92 0.380 0.161 0.8 0

16 12.06 12.28 11.92 12.21 12.23 12.137 12.139 12.36 11.92 0.380 0.360 0.8 0

17 12.32 12.5 11.51 12.23 12.29 12.137 12.170 12.36 11.92 0.380 0.990 0.8 0

18 11.78 11.96 12.34 12.31 12.26 12.137 12.130 12.36 11.92 0.380 0.560 0.8 0

19 12.14 12.06 12.04 12.28 12.34 12.137 12.172 12.36 11.92 0.380 0.302 0.8 0

20 12.34 12.18 12.18 12.33 12.14 12.137 12.234 12.36 11.92 0.380 0.197 0.8 0

21 11.9 12.26 12.14 12.11 12.27 12.137 12.137 12.36 11.92 0.380 0.373 0.8 0

22 11.53 11.92 12.56 12.17 12.01 12.137 12.039 12.36 11.92 0.380 1.030 0.8 0

23 12.06 12.08 12.2 12.19 12.17 12.137 12.140 12.36 11.92 0.380 0.140 0.8 0

24 12.2 12.1 12.02 12.05 12.30 12.137 12.134 12.36 11.92 0.380 0.283 0.8 0

25 12.16 11.54 12.54 12.06 12.01 12.137 12.062 12.36 11.92 0.380 1.000 0.8 0

75

Question 1

Question 2

11.700

11.800

11.900

12.000

12.100

12.200

12.300

12.400

X-bar with new data

Xbar-bar

Xbar

UCLx

LCLx

0.200

0.400

0.600

0.800

1.000

1.200

R with new data

Rbar

R

UCLr

LCLr

11.600

11.700

11.800

11.900

12.000

12.100

12.200

12.300

12.400

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

X-bar Base line data

Xbar-bar

Xbar

UCLx

LCLx

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

R Base line data

Rbar

R

UCLr

LCLr