ch. 8 quality template 2006

8/8/2019 Ch. 8 Quality Template 2006

http://slidepdf.com/reader/full/ch-8-quality-template-2006 1/26

Notes on using the quality control template:

All values in blue cells are to be entered by the user, lighter blue cells can be entered but will be calculatedautomatically calculated, and do not need to be altered. Each quality control model has a sample value setproceeding with your own data.

Cells with red marks in the upper right corner have comments, let the mouse hover over these cells to readcontrol model.

This spreadsheet is locked/protected in order to keep the cells with equations from being changed. If a mofirst needs to be unlocked/unprotected. Do this by selecting the workbook you wish to unlock, click on "ToolSheet". The sheet will then be unlocked so alterations can be made.

Equations for models will be given when available.



if not entered, all other values areentered, make sure to clear all values before

the comments to further explain the quality

el does need to be altered, the spreadsheetls", highlight "Protection", and select "Unprotect



Mean Control Chart (σ known)

σ UCL #DIV/0!

z LCL #DIV/0!

Mean #DIV/0!

Sample Mean UCL Mean LCL

1 #DIV/0! #DIV/0! #DIV/0!

2 #DIV/0! #DIV/0! #DIV/0!

3 #DIV/0! #DIV/0! #DIV/0!

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8 #DIV/0! #DIV/0! #DIV/0!9 #DIV/0! #DIV/0! #DIV/0!

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12 #DIV/0! #DIV/0! #DIV/0!

13 #DIV/0! #DIV/0! #DIV/0!

14 #DIV/0! #DIV/0! #DIV/0!

15 #DIV/0! #DIV/0! #DIV/0!

16 #DIV/0! #DIV/0! #DIV/0!

17 #DIV/0! #DIV/0! #DIV/0!

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31 #DIV/0! #DIV/0! #DIV/0!

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36 #DIV/0! #DIV/0! #DIV/0!

37 #DIV/0! #DIV/0! #DIV/0!

38 #DIV/0! #DIV/0! #DIV/0!

39 #DIV/0! #DIV/0! #DIV/0!

40 #DIV/0! #DIV/0! #DIV/0!

n = number of observations/sample

0 5 10

0

2

4

6

8

10

12

Mean

Column B

M e a n

The Mean Control Chart (sigma k (n) for each sample versus periodobservations and the upper and loor σ is known. A sample mean o(would only happen 3 times out of variation that should be investigat

Equations:UCL = Upper Control LimitLCL = Lower Control Limit

μ = Mean of population or

z = Number of standard errr σ = Standard deviation of p

n = Number of observation

UCL= μz*σ

n

LCL= μ− z ∗σ

n



#DIV/0! #DIV/0! #DIV/0!



15 20 25 30 35 40

ontrol Chart (σ known)

olumn C Column D Column E

Period

own)plots the mean of a set number of observationsnumber on the same chart as the overall mean of allwer control limits based on 3 sigma. In this case sigmautside the upper or lower control limits is very unusual1000) and indicates assignable or non-random

ed and the cause eliminated or corrected.

verall mean

ors for confidence level=3 for 99. 7% confidenceopulation

per sample



Mean Control Chart (σ unknown)

Overall Mean #DIV/0!

Average Range 1.5

UCL #N/A

LCL #N/A

Sample Mean Range UCL Mean LCL

1 1.38 #DIV/0! #DIV/0! #DIV/0!

2 1.06 #DIV/0! #DIV/0! #DIV/0!

3 1 #DIV/0! #DIV/0! #DIV/0!

4 2.21 #DIV/0! #DIV/0! #DIV/0!

5 1.46 #DIV/0! #DIV/0! #DIV/0!

6 1.62 #DIV/0! #DIV/0! #DIV/0!

7 1.03 #DIV/0! #DIV/0! #DIV/0!8 2.09 #DIV/0! #DIV/0! #DIV/0!

9 0.77 #DIV/0! #DIV/0! #DIV/0!

10 1.01 #DIV/0! #DIV/0! #DIV/0!

11 1.1 #DIV/0! #DIV/0! #DIV/0!

12 2.49 #DIV/0! #DIV/0! #DIV/0!

13 1.68 #DIV/0! #DIV/0! #DIV/0!

14 2.29 #DIV/0! #DIV/0! #DIV/0!

15 1.34 #DIV/0! #DIV/0! #DIV/0!

16 #DIV/0! #DIV/0! #DIV/0!

17 #DIV/0! #DIV/0! #DIV/0!

18 #DIV/0! #DIV/0! #DIV/0!


21 #DIV/0! #DIV/0! #DIV/0!

22 #DIV/0! #DIV/0! #DIV/0!

23 #DIV/0! #DIV/0! #DIV/0!

24 #DIV/0! #DIV/0! #DIV/0!

25 #DIV/0! #DIV/0! #DIV/0!

26 #DIV/0! #DIV/0! #DIV/0!

27 #DIV/0! #DIV/0! #DIV/0!

28 #DIV/0! #DIV/0! #DIV/0!

29 #DIV/0! #DIV/0! #DIV/0!

30 #DIV/0! #DIV/0! #DIV/0!


33 #DIV/0! #DIV/0! #DIV/0!

34 #DIV/0! #DIV/0! #DIV/0!

35 #DIV/0! #DIV/0! #DIV/0!

36 #DIV/0! #DIV/0! #DIV/0!

37 #DIV/0! #DIV/0! #DIV/0!

38 #DIV/0! #DIV/0! #DIV/0!

39 #DIV/0! #DIV/0! #DIV/0!

n = number of observations/sample

0 5

0

2

4

6

8

10

12

M

Colum

M e a n

The Mean Control Chexcept that the controlrather than the standathat sigma is unknowcalculate. The averagdeviation of the populmultiplying the averagThe tabulated factorsmean values, the ranAs in the previous chalimits is very unusual

Equation:UCL = Upper ControlLCL = Lower Control

X = A verage o f

A 2 = Factor for

R= A verage o f r

U C L= X A2∗ R

L C L= X − A2∗ R



40 #DIV/0! #DIV/0! #DIV/0!

n value A2 factor

2 1.883 1.02

4 0.73

5 0.58

6 0.48

7 0.42

8 0.37

9 0.34

10 0.31

11 0.29

12 0.27

13 0.25

14 0.2415 0.22

16 0.21

17 0.2

18 0.19

19 0.19

20 0.18



10 15 20 25 30 35 40

ean Control Chart (σ unknown)

n B Column D Column E Column F

Period

rt (sigma unknown) is similar to the previous chart,l limits are based on the range found in each sample,rd deviation of the population. The assumption here isfor the population and/or the range is easier torange of all samples is related to the standard

tion and upper and lower control limits are found bye range by a tabulated factor rather than the z value.begin on A54 of this sheet. In addition to the samplee of these values for each sample must be entered.rt, a sample mean outside the upper or lower controlnd indicates assignable or non-random variation.

Limitimit

ample m eans , overa l l m ean , o r popu l

3 s igma conf idence leve lstart ing a t A 54ange values



Range Control Chart

n Average Range #DIV/0!

UCL #N/A

LCL #N/A

Sample Range UCL Mean LCL

1 #DIV/0! #DIV/0! #DIV/0!

2 #DIV/0! #DIV/0! #DIV/0!

3 #DIV/0! #DIV/0! #DIV/0!

4 #DIV/0! #DIV/0! #DIV/0!

5 #DIV/0! #DIV/0! #DIV/0!

6 #DIV/0! #DIV/0! #DIV/0!

7 #DIV/0! #DIV/0! #DIV/0!

8 #DIV/0! #DIV/0! #DIV/0!


11 #DIV/0! #DIV/0! #DIV/0!

12 #DIV/0! #DIV/0! #DIV/0!

13 #DIV/0! #DIV/0! #DIV/0!

14 #DIV/0! #DIV/0! #DIV/0!

15 #DIV/0! #DIV/0! #DIV/0!

16 #DIV/0! #DIV/0! #DIV/0!

17 #DIV/0! #DIV/0! #DIV/0!

18 #DIV/0! #DIV/0! #DIV/0!

19 #DIV/0! #DIV/0! #DIV/0!

20 #DIV/0! #DIV/0! #DIV/0!


23 #DIV/0! #DIV/0! #DIV/0!

24 #DIV/0! #DIV/0! #DIV/0!

25 #DIV/0! #DIV/0! #DIV/0!

26 #DIV/0! #DIV/0! #DIV/0!

27 #DIV/0! #DIV/0! #DIV/0!

28 #DIV/0! #DIV/0! #DIV/0!

29 #DIV/0! #DIV/0! #DIV/0!

30 #DIV/0! #DIV/0! #DIV/0!

31 #DIV/0! #DIV/0! #DIV/0!

32 #DIV/0! #DIV/0! #DIV/0!


35 #DIV/0! #DIV/0! #DIV/0!

36 #DIV/0! #DIV/0! #DIV/0!

37 #DIV/0! #DIV/0! #DIV/0!

38 #DIV/0! #DIV/0! #DIV/0!

39 #DIV/0! #DIV/0! #DIV/0!

40 #DIV/0! #DIV/0! #DIV/0!

0 5 10

0

2

4

6

8

10

12

Column B

M e a n

The Range Control Chart plots t

mean of the ranges and the uppmeasure of variability within theindicate that the variablility in theassingnable causes. The upper using tabulated factors. These fa

Equation:UCL = Upper Control LimitLCL = Lower Control Limit

R = Average of sample r D3 = Factor for LCL sta

D4 = Factor for UCL stLCL= D3∗ R

UCL= D4∗ R



LCL UCL

n value D3 factor D4 factor

2 0 3.27

3 0 2.57

4 0 2.285 0 2.11

6 0 2

7 0.08 1.92

8 0.14 1.86

9 0.18 1.82

10 0.22 1.78

11 0.26 1.74

12 0.28 1.72

13 0.31 1.69

14 0.33 1.67

15 0.35 1.65

16 0.36 1.6417 0.38 1.62

18 0.39 1.61

19 0.4 1.6

20 0.41 1.59



15 20 25 30 35 40

Range Control Chart

Column C Column D Column E

Period

e ranges of the samples on the same chart as the

r and lower control limit for the range. The range is aamples and sample ranges outside the control limitssample is very unusual and should be investigated for nd lower control limits for the range are calculatedctors are on this sheet, starting at A54.

ngesting at A54

rting at A54



p Chart

n Average p #DIV/0!

σ #DIV/0!

z UCL #DIV/0!

LCL #DIV/0!

Sample p UCL Mean LCL

1 #DIV/0! #DIV/0! #DIV/0!

2 #DIV/0! #DIV/0! #DIV/0!

3 #DIV/0! #DIV/0! #DIV/0!

4 #DIV/0! #DIV/0! #DIV/0!

5 #DIV/0! #DIV/0! #DIV/0!

6 #DIV/0! #DIV/0! #DIV/0!

7 #DIV/0! #DIV/0! #DIV/0!

8 #DIV/0! #DIV/0! #DIV/0!


11 #DIV/0! #DIV/0! #DIV/0!

12 #DIV/0! #DIV/0! #DIV/0!

13 #DIV/0! #DIV/0! #DIV/0!

14 #DIV/0! #DIV/0! #DIV/0!

15 #DIV/0! #DIV/0! #DIV/0!

16 #DIV/0! #DIV/0! #DIV/0!

17 #DIV/0! #DIV/0! #DIV/0!

18 #DIV/0! #DIV/0! #DIV/0!

19 #DIV/0! #DIV/0! #DIV/0!

20 #DIV/0! #DIV/0! #DIV/0!


23 #DIV/0! #DIV/0! #DIV/0!

24 #DIV/0! #DIV/0! #DIV/0!

25 #DIV/0! #DIV/0! #DIV/0!

26 #DIV/0! #DIV/0! #DIV/0!

27 #DIV/0! #DIV/0! #DIV/0!

28 #DIV/0! #DIV/0! #DIV/0!

29 #DIV/0! #DIV/0! #DIV/0!

30 #DIV/0! #DIV/0! #DIV/0!

31 #DIV/0! #DIV/0! #DIV/0!

32 #DIV/0! #DIV/0! #DIV/0!


35 #DIV/0! #DIV/0! #DIV/0!

36 #DIV/0! #DIV/0! #DIV/0!

37 #DIV/0! #DIV/0! #DIV/0!

38 #DIV/0! #DIV/0! #DIV/0!

39 #DIV/0! #DIV/0! #DIV/0!

40 #DIV/0! #DIV/0! #DIV/0!

0 5 10

0

2

4

6

8

10

12

Column B

M e a n

The p Chart plots values which a

chart is similar to both the Meanwhen the data is proportional ratapproximation to the binomial disor lower control limits is very unuindicates assignable or non-randeliminated or corrected.


σ p

= S tandard er ror of propo

p = A verage of sample pron = N umb er of observat ions

z = Num ber of s tandard er r

σ p=

p∗1− p

n

U C L= pz*σ p

L C L= p−z*σ p



c Chart

z 3 Average c #DIV/0!

UCL #DIV/0!

LCL #DIV/0!

Sample c UCL Mean LCL

1 #DIV/0! #DIV/0! #DIV/0!

2 #DIV/0! #DIV/0! #DIV/0!

3 #DIV/0! #DIV/0! #DIV/0!

4 #DIV/0! #DIV/0! #DIV/0!

5 #DIV/0! #DIV/0! #DIV/0!

6 #DIV/0! #DIV/0! #DIV/0!

7 #DIV/0! #DIV/0! #DIV/0!

8 #DIV/0! #DIV/0! #DIV/0!


11 #DIV/0! #DIV/0! #DIV/0!

12 #DIV/0! #DIV/0! #DIV/0!

13 #DIV/0! #DIV/0! #DIV/0!

14 #DIV/0! #DIV/0! #DIV/0!

15 #DIV/0! #DIV/0! #DIV/0!

16 #DIV/0! #DIV/0! #DIV/0!

17 #DIV/0! #DIV/0! #DIV/0!

18 #DIV/0! #DIV/0! #DIV/0!

19 #DIV/0! #DIV/0! #DIV/0!

20 #DIV/0! #DIV/0! #DIV/0!


23 #DIV/0! #DIV/0! #DIV/0!

24 #DIV/0! #DIV/0! #DIV/0!

25 #DIV/0! #DIV/0! #DIV/0!

26 #DIV/0! #DIV/0! #DIV/0!

27 #DIV/0! #DIV/0! #DIV/0!

28 #DIV/0! #DIV/0! #DIV/0!

29 #DIV/0! #DIV/0! #DIV/0!

30 #DIV/0! #DIV/0! #DIV/0!

31 #DIV/0! #DIV/0! #DIV/0!

32 #DIV/0! #DIV/0! #DIV/0!


35 #DIV/0! #DIV/0! #DIV/0!

36 #DIV/0! #DIV/0! #DIV/0!

37 #DIV/0! #DIV/0! #DIV/0!

38 #DIV/0! #DIV/0! #DIV/0!

39 #DIV/0! #DIV/0! #DIV/0!

40 #DIV/0! #DIV/0! #DIV/0!

0 5 10

0

0.2

0.4

0.6

0.8

1

Column B

M e a n

The c Chart is essentially the sa

number of defectives (per batch,control limits in this chart are comrare events).


c = Average number of de

z = Confidence level usuall

UCL=c z ⋅ c

LCL=c− z ⋅ c



15 20 25 30 35 40

c Chart

Column C Column D Column E

Period

e as the p Chart. However, In this chart, we plot the

per day, per machine, per 100 feet of pipe, etc.) and theputed based on the Poisson distribution (distribution of

ects per u

y 3



Process Capability

Standard Machine Specification

Machine Deviation Capability Width Cp

A

B

CD

E

Non centered

Process Standard Lower Upper

Machine Mean Deviation Specification Ratio Specification

A

B

C

D

E

Process Ca process is ccapable, whchanged inwill only proCLs and the

process. Th(DPMO) on

Equation:Machine CaCapability =

For a non centered process (the mean of the process and the center of the specifications are not t(Cpk) needs to be calculated. As above, Cpk of greater than or equal to 1 means the process is cit is not capable and needs to be "fixed" in order to produce the product. Note that if the process isprocess is not centered, it is possible to get a Cp of greater than 1 and a Cpk of less than 1. Cpk iswhen the process is not centered to get the right answer. Six sigma quality implies a Cpk of 1.5, a

Equation:Lower Ratio = (Process Mean - Lower Specification) / (3 * Standard Deviation)Upper Ratio = (Upper Specification - Process Mean) / (3 * Standard Deviation)

Cpk = Min[ Lower Ratio or Upper Ratio ]



Ratio Cpk

ability is a measure of how capable the process is, assuming theentered. A Cp of greater than or equal to 1 means the process isile less than 1 means it is not capable and needs to be "fixed" or rder to produce the product. A capable process, with a Cp of 1,uce 3 defects per 1000 opportunities. A Cp of 1 means that theSLs are the same. Six sigma has a Cp of 1.5, a very capable

process will only produce 3.4 defects per million opportunitiesone tail.

pability = Standard Deviation * 6Specification Width / Machine Capability

e same), the Capability Index pable, while less than 1 meanscentered Cp=Cpk. If thebasically an adjustment for Cpvery capable process.



Normal Distribution

Mean = 20

Std Dev = 2

x = 29

z = 4.5

P(<x) = 1

P(>x) = 0

NormX Z P(X) X

0.01 15.35 -2.33 0.01 29

0.02 15.89 -2.05 0.02 29

0.03 16.24 -1.88 0.03 29

0.04 16.5 -1.75 0.04 29

0.05 16.71 -1.64 0.05 29

0.06 16.89 -1.55 0.06 29

0.07 17.05 -1.48 0.07 29

0.08 17.19 -1.41 0.07 29

0.09 17.32 -1.34 0.08 29

0.1 17.44 -1.28 0.09 29

0.11 17.55 -1.23 0.09 29

0.12 17.65 -1.17 0.1 29

0.13 17.75 -1.13 0.11 29

0.14 17.84 -1.08 0.11 29

0.15 17.93 -1.04 0.12 29

0.16 18.01 -0.99 0.12 29

0.17 18.09 -0.95 0.13 29

0.18 18.17 -0.92 0.13 29

0.19 18.24 -0.88 0.14 29

0.2 18.32 -0.84 0.14 29

0.21 18.39 -0.81 0.14 29

0.22 18.46 -0.77 0.15 29

0.23 18.52 -0.74 0.15 29

0.24 18.59 -0.71 0.16 29

0.25 18.65 -0.67 0.16 29

0.26 18.71 -0.64 0.16 29

0.27 18.77 -0.61 0.17 29

CumulativeP(X)

14 16 18 20 22 24

Normal Distribution



0.28 18.83 -0.58 0.17 29

0.29 18.89 -0.55 0.17 29

0.3 18.95 -0.52 0.17 29

0.31 19.01 -0.5 0.18 29

0.32 19.06 -0.47 0.18 29

0.33 19.12 -0.44 0.18 29

0.34 19.18 -0.41 0.18 290.35 19.23 -0.39 0.19 29

0.36 19.28 -0.36 0.19 29

0.37 19.34 -0.33 0.19 29

0.38 19.39 -0.31 0.19 29

0.39 19.44 -0.28 0.19 29

0.4 19.49 -0.25 0.19 29

0.41 19.54 -0.23 0.19 29

0.42 19.6 -0.2 0.2 29

0.43 19.65 -0.18 0.2 29

0.44 19.7 -0.15 0.2 29

0.45 19.75 -0.13 0.2 29

0.46 19.8 -0.1 0.2 290.47 19.85 -0.08 0.2 29

0.48 19.9 -0.05 0.2 29

0.49 19.95 -0.03 0.2 29

0.5 20 0 0.2 29

0.51 20.05 0.03 0.2 29

0.52 20.1 0.05 0.2 29

0.53 20.15 0.08 0.2 29

0.54 20.2 0.1 0.2 29

0.55 20.25 0.13 0.2 29

0.56 20.3 0.15 0.2 29

0.57 20.35 0.18 0.2 29

0.58 20.4 0.2 0.2 290.59 20.46 0.23 0.19 29

0.6 20.51 0.25 0.19 29

0.61 20.56 0.28 0.19 29

0.62 20.61 0.31 0.19 29

0.63 20.66 0.33 0.19 29

0.64 20.72 0.36 0.19 29

0.65 20.77 0.39 0.19 29

0.66 20.82 0.41 0.18 29

0.67 20.88 0.44 0.18 29

0.68 20.94 0.47 0.18 29

0.69 20.99 0.5 0.18 29

0.7 21.05 0.52 0.17 290.71 21.11 0.55 0.17 29

0.72 21.17 0.58 0.17 29

0.73 21.23 0.61 0.17 29

0.74 21.29 0.64 0.16 29

0.75 21.35 0.67 0.16 29

0.76 21.41 0.71 0.16 29

0.77 21.48 0.74 0.15 29

0.78 21.54 0.77 0.15 29



0.79 21.61 0.81 0.14 29

0.8 21.68 0.84 0.14 29

0.81 21.76 0.88 0.14 29

0.82 21.83 0.92 0.13 29

0.83 21.91 0.95 0.13 29

0.84 21.99 0.99 0.12 29

0.85 22.07 1.04 0.12 290.86 22.16 1.08 0.11 29

0.87 22.25 1.13 0.11 29

0.88 22.35 1.17 0.1 29

0.89 22.45 1.23 0.09 29

0.9 22.56 1.28 0.09 29

0.91 22.68 1.34 0.08 29

0.92 22.81 1.41 0.07 29

0.93 22.95 1.48 0.07 29

0.94 23.11 1.55 0.06 29

0.95 23.29 1.64 0.05 29

0.96 23.5 1.75 0.04 29

0.97 23.76 1.88 0.03 290.98 24.11 2.05 0.02 29

0.99 24.65 2.33 0.01 29



26 28 30

ch. 8 quality template 2006

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