John Michael Croft

Part 3:

4) Figure 4.1 below shows an NP Chart for number of defects each day. Day 1-20, sample sizes were 30. Subsequently, new equipment was installed and the sample sizes were increased to 40 per day.

a. No out of control signals or run rule violations appear below. The process appears to be in statistical control to monitor performance going forward.

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8

6

4

2

0

Sample

Sam

ple

Cou

nt

__NP=4.4

UCL=10.34

LCL=0

Figure 4.1: NP Chart for Equipment Final Inspections

Tests performed with unequal sample sizes

b. Figure 4.2 below shows a standardized Z-chart for the above for comparison purposes. Again, no OOC signals or run rule violations occur.

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1.5

0.0

-1.5

-3.0

Observation

Stan

dard

ized

Dat

a

0

UCL=3

LCL=-3

30 40

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3

2

1

0

Observation

Mov

ing

Ran

ge

__MR=1.128

UCL=3.686

LCL=0

30 40

Figure 4.2: Standardized Z-MR Chart

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John Michael Croft

c. Figure 4.3 below shows an NP Chart by stages (old and new equipment). Again no OOC signals or run rule violations occur. Notice the newer equipment has a wider variance due to lack of use suggesting it may need to be monitored and calibrated to reduce the variance of defects per day.

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6

4

2

0

Sample

Sam

ple

Cou

nt

__NP=5.45

UCL=11.96

LCL=0

Old New

Figure 4.3: NP Chart by Stage

5) Below are a series of evaluations on the X5 variable assuming the first 30 subgroups as a baseline with very good control of the process.

a. Figure 5.1 below shows an IMR chart of the first 30 subgroups to estimate the mean and standard deviation.

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65

60

55

50

Observation

Indi

vidu

al V

alue

_X=60.21

UCL=72.62

LCL=47.81

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8

4

0

Observation

Mov

ing

Ran

ge

__MR=4.66

UCL=15.24

LCL=0

Figure 5.1: IM-R of Subgroups 1-30

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John Michael Croft

Process Mean=60.21

ProcessStandard Deviation= 4.661.128

=4.13

b. Figure 5.2 below attempts to monitor the remaining subgroups based on the parameter estimates from the first 30 subgroups using an IMR chart. Notice several OOC and run rule violations in the MR chart that need to be addressed prior to making meaningful decisions based on the I chart. However, the I chart displays one OOC and 2 run rule violations.

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70

60

50

Observation

Indi

vidu

al V

alue

_X=60.21

UCL=72.6

LCL=47.82

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10

5

0

Observation

Mov

ing

Ran

ge

__MR=4.66

UCL=15.22

LCL=0

5

5

1

11

2

2

1

1

Figure 5.2: IM-R all Subgroups

c. Figure 5.3 simulates the above again, but with a EWMA chart. Again, notice several OOC points beyond the UCL suggesting the process is unstable and needs to be calibrated to remove the unwanted variability.

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John Michael Croft

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63

62

61

60

59

58

57

Sample

EWM

A

__X=60.21

UCL=63.052

LCL=57.368

Figure 5.3: EWMA Chart

d. Figure 5.4 below simulates the above again but with a CUSUM Chart. Again we notice several OOC signals toward the end of the process suggesting the need to refine and reduce variability.

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30

20

10

0

-10

-20

Sample

Cum

ulat

ive

Sum

0

UCL=20.65

LCL=-20.65

Figure 5.4 CUSUM Chart

e. To summarize the above results:

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John Michael Croft

i. Subgroups 1-30 represent a stab process with a mean, 60.21 and standard deviation, 4.13.

ii. Figures 5.2 – 5.4 all suggest assignable cause variation or possible mean shifts while monitoring subgroups 31-60.

iii. Figure 5.2 suggest an OOC signal at subgroup 46 and run rule violations at 48 and 50.

iv. Figure 5.3 show several OOC signals within the cluster of subgroups 45 – 54 suggesting the process lost control between 31 and 43.

v. Figure 5.4 show several OOC signals from 46 – 57. vi. Recommend eliminating assignable cause variation and closely

monitoring to reduce variability within the process. 6) Below are several charts evaluating two parameters, separately and together, monitoring

process performance in a multivariate setting. a. Figures 6.1 and 6.2 below show X6A and X6B to be independently in statistical

control with no OOC signals or run rule violations.

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35

30

25

20

Observation

Indi

vidu

al V

alue

_X=29.65

UCL=42.38

LCL=16.93

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4

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Observation

Mov

ing

Ran

ge

__MR=4.78

UCL=15.63

LCL=0

Figure 6.1: IM-R X6A

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John Michael Croft

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22.5

20.0

17.5

15.0

Observation

Indi

vidu

al V

alue

_X=20.16

UCL=26.50

LCL=13.82

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4

2

0

Observation

Mov

ing

Ran

ge

__MR=2.384

UCL=7.790

LCL=0

Figure 6.2: IM-R X6B

b. Figure 6.3 performs a multivariate T^2 Chart considering both variables together. Subgroup 30 appears to be OOC as it exceeds the UCL on the T^2n chart. This appears consistent with the spike in the Generalized Variance.

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5

0

Sample

Tsqu

ared

Median=2.25

UCL=14.31

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1.2

0.8

0.4

0.0

Sample

Gen

eral

ized

Var

ianc

e

|S|=0.442

UCL=1.443

LCL=0

Figure 6.3: Multivariate Chart

c. Considering the interaction of the two effect together allows for OOC signals to be detected where univariate charts might not.

File:document.docx Page 6 of 6 John Michael Croft