9 Copyright 2012 Health Administration Press
Books (available online)
Barry, R. 2003. Nan: A Six Sigma Mystery. Milwaukee, WI: ASQ
Quality Press.
George, M. L. 2003. Lean Six Sigma for Service: How to Use Lean
Speed and Six Sigma Quality
to Improve Services and Transactions. New York: McGraw-Hill.
Pyzdek, T. 2003. The Six Sigma Handbook: The Complete Guide for
Greenbelts, Blackbelts, and
Managers at All Levels, Revised and Expanded Edition. New York:
McGraw-Hill.
Tennant, G. 2001. Six Sigma: SPC and TQM in Manufacturing and
Services. London: Ashgate
Publishing.
Books (links to sources referenced in Chapter 8)
Berwick, D. M., A. B. Godfrey, and J. Roessner. 2002. Curing
Healthcare: New Strategies for
Quality Improvement. San Francisco: Jossey-Bass.
http://books.google.com/books?vid=ISBN0873896122&id=wLqbfn85eMoC&pg=RA1-PA1-IA2&lpg=RA1-PA1-IA2&dq=Nan:+A+Six+Sigma+Mystery.&sig=vLVvCj5HCp8DH4kMvEg7WtbJsughttp://books.google.com/books?hl=en&lr=&id=PpS931Oc5V8C&oi=fnd&pg=PR1&sig=supoaboCxBdTUK0xbVZKRex4D9k&dq=six+sigma+healthcare&prev=http://scholar.google.com/scholar%3Fq%3Dsix%2Bsigma%2Bhealthcare%26start%3D10%26hl%3Den%26lr%3D%26sa%3DNhttp://books.google.com/books?hl=en&lr=&id=PpS931Oc5V8C&oi=fnd&pg=PR1&sig=supoaboCxBdTUK0xbVZKRex4D9k&dq=six+sigma+healthcare&prev=http://scholar.google.com/scholar%3Fq%3Dsix%2Bsigma%2Bhealthcare%26start%3D10%26hl%3Den%26lr%3D%26sa%3DNhttp://books.google.com/books?hl=en&lr=&id=ly7iBGNVGe8C&oi=fnd&pg=PR13&sig=7jQjO_K3ho8G_xMwIDCpdvrXurg&dq=six+sigma&prev=http://scholar.google.com/scholar%3Fq%3Dsix%2Bsigma%26start%3D10%26hl%3Den%26lr%3D%26sa%3DN#PPA5,M1http://books.google.com/books?hl=en&lr=&id=ly7iBGNVGe8C&oi=fnd&pg=PR13&sig=7jQjO_K3ho8G_xMwIDCpdvrXurg&dq=six+sigma&prev=http://scholar.google.com/scholar%3Fq%3Dsix%2Bsigma%26start%3D10%26hl%3Den%26lr%3D%26sa%3DN#PPA5,M1http://books.google.com/books?hl=en&lr=&id=O6276jidG3IC&oi=fnd&pg=PA1&sig=eD_VuIt1vYdM-nYSXKVRHTCtwt0&dq=six+sigma+healthcare&prev=http://scholar.google.com/scholar%3Fq%3Dsix%2Bsigma%2Bhealthcare%26start%3D10%26hl%3Den%26lr%3D%26sa%3DNhttp://www.amazon.com/Curing-Health-Care-Strategies-Improvement/dp/0787964522/sr=8-1/qid=1163597743/ref=sr_1_1/104-4261184-7360724?ie=UTF8&s=bookshttp://www.amazon.com/Curing-Health-Care-Strategies-Improvement/dp/0787964522/sr=8-1/qid=1163597743/ref=sr_1_1/104-4261184-7360724?ie=UTF8&s=books
Instructions
Notes on using the QFD (Quality Function Deployment or House of
Quality) template:
All turquoise cells are to be entered by the user. Other values
are automatically calculated, and do not need to be altered.
Cells with red marks in the upper right corner have comments,
let the mouse hover over these cells to read the comments to
further explain the contents of a cell.
This spreadsheet is locked/protected in order to keep the cells
with equations from being changed. If a cell need to be altered,
the spreadsheet first needs to be unlocked/unprotected. Do this by
selecting the workbook you wish to unlock, click on "Tools",
highlight "Protection", and select "Unprotect Sheet". The sheet
will then be unlocked so alterations can be made.
Begin with the Customer and Design Requirement worksheet. 1.
Input a name for your House of Quality 2. Input each customer
requirement, an importance rating for that requirement, an
evaluation of how well your current process/product meets that
requirement, and an evaluation of how well the competition meets
that requirement.This information should be gathered from the
customer and is often referred to as the Voice of the Customer
(VOC). 3. Input the technical requirements of the process/product.
These are measureable technical requirements related to the
customer requirements. Units for each requirement should be input
along with an evaluation of the current process/product and the
competition.
Next, go to the HOQ 1A worksheet. 4. Input the strength of the
relationship between each customer requirement and each technical
requirement (1=weak, 3=medium, 5=strong) in the center of the HOQ.
5. Input the direction of the relationship among technical
requirements in the roof of the HOQ.
Finally, go to the HOQ 1B worksheet. 6. Input the desired target
specification values.
The final House of Quality can be found on the HOQ 1Final
worksheet.
Often this first House of Quality is followed by other matrices.
For products, the product target values are translated into parts
targets, process targets and production settings. For processes,
the process target values are translated into functional
requirements, design requirements and key process variables. We
have included the process type in this workbook.
Customer and Tech Requirement
House of Quality for ________
Competitive Evaluations (1-5)
Customer Requirement #Customer RequirementsRelative Importance
(1-5)Our Product/ServiceCompetitor ACompetitor B
1Customer requirement5511
2Customer requirement5411
3Customer requirement5311
4Customer requirement5111
5Customer requirement5111
6Customer requirement5111
7Customer requirement111
Technical Requirement #Customer Requirement #Technical
RequirementsMeasurement UnitOur Product/ServiceCompetitor
ACompetitor B
1Technical requirementMeasurement Unit532
2Technical requirementMeasurement Unit532
3Technical requirementMeasurement Unit532
4Technical requirementMeasurement Unit111
5Technical requirementMeasurement Unit111
6Technical requirementMeasurement Unit111
7Technical requirementMeasurement Unit111
8Technical requirementMeasurement Unit111
9Technical requirementMeasurement Unit111
10Technical requirementMeasurement Unit111
11Technical requirementMeasurement Unit111
12Technical requirementMeasurement Unit111
13Technical requirementMeasurement Unit111
14Technical requirementMeasurement Unit111
15Technical requirementMeasurement Unit111
16Technical requirementMeasurement Unit111
17Technical requirementMeasurement Unit111
HOQ 1A
House of Quality for ________
+Positive or Reinforcing Relationship
-Negative or Tradeoff Relationship
Relative Importance or Weight
Design RequirementsTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirement
Our Service/ProductCompeting Service/Product ACompeting
Service/Product B
Customer RequirementsX manufacturerY manufacturer
Customer requirement5511
Customer requirement5411
Customer requirement5311
Customer requirement5111
Customer requirement5111
Customer requirement5111
Customer requirement0111
calculations00000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000
Importance Weighting00000000000000000
Measurement UnitsMeasurement UnitMeasurement UnitMeasurement
UnitMeasurement UnitMeasurement UnitMeasurement UnitMeasurement
UnitMeasurement UnitMeasurement UnitMeasurement UnitMeasurement
UnitMeasurement UnitMeasurement UnitMeasurement UnitMeasurement
UnitMeasurement UnitMeasurement Unit
Our Value55511111111111111
Competitor A33311111111111111
Competitor B22211111111111111
Target Specification Values
From the customer and design requirements worksheet
From customer and design requirements worksheet
From customer and design requirements worksheet
From customer and design requirements worksheet
The triangular roof of the house of quality is used to indicate
where technical requirements trade-off or reinforce each other.
Does improving one requirement result in a decrease (-) of an
increase (+) in another requirement? This information can help the
design team by making explicit where tradeoffs are needed.
From the customer and design requirements worksheet.
Calculated on this worksheet
From the customer and design requirements worksheet.
From the customer and design requirements worksheet.
From the customer and design requirements worksheet.
From the customer and design requirements worksheet.
Input the strength of the relationship between each customer
requirement and each technical requirement.
1 = weak, 3=medium, 5=strong.
HOQ 1A
Our Service/Product
Competing Service/Product A
Competing Service/Product B
HOQ 1B
House of Quality for ________
0
00
000
0000
00000
+Positive or Reinforcing Relationship
000000
-Negative or Tradeoff Relationship
0000000
00000000
000000000
0000000000
00000000000
Relative Importance or Weight000000000000
0000000000000
00000000000000
000000000000000
0000000000000000
Design RequirementsTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirement
Our Service/ProductCompeting Service/Product ACompeting
Service/Product B
Customer RequirementsX manufacturerY manufacturer
Customer requirement500000000000000000511
Customer requirement500000000000000000411
Customer requirement500000000000000000311
Customer requirement500000000000000000111
Customer requirement500000000000000000111
Customer requirement500000000000000000111
Customer requirement000000000000000000111
Importance Weighting00000000000000000
Relative Importance Weighting00000000000000000
Measurement UnitsMeasurement UnitMeasurement UnitMeasurement
UnitMeasurement UnitMeasurement UnitMeasurement UnitMeasurement
UnitMeasurement UnitMeasurement UnitMeasurement UnitMeasurement
UnitMeasurement UnitMeasurement UnitMeasurement UnitMeasurement
UnitMeasurement UnitMeasurement Unit
Our Value55511111111111111
Competitor A33311111111111111
Competitor B22211111111111111
Target Specification Values
Our Value
Competitor A
Competitor B
Target Specification Values
From the customer and design requirements worksheet
From customer and design requirements worksheet
From customer and design requirements worksheet
From customer and design requirements worksheet
From HOQ template-1
From the customer and design requirements worksheet.
From HOQ template-1 worksheet.
From the customer and design requirements worksheet.
From the customer and design requirements worksheet.
From the customer and design requirements worksheet.
From the customer and design requirements worksheet.
From HOQ template -1
HOQ 1B
Our Service/Product
Competing Service/Product A
Competing Service/Product B
HOQ 1Final
House of Quality for ________
0
00
000
0000
00000
+Positive or Reinforcing Relationship
000000
-Negative or Tradeoff Relationship
0000000
00000000
000000000
0000000000
00000000000
Relative Importance or Weight000000000000
0000000000000
00000000000000
000000000000000
0000000000000000
Technical RequirementsTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirementTechnical requirementTechnical requirementTechnical
requirement
Our Service/ProductCompeting Service/Product ACompeting
Service/Product B
Customer RequirementsX manufacturerY manufacturer
Customer requirement500000000000000000511
Customer requirement500000000000000000411
Customer requirement500000000000000000311
Customer requirement500000000000000000111
Customer requirement500000000000000000111
Customer requirement500000000000000000111
Customer requirement000000000000000000111
Importance Weighting00000000000000000
Relative Importance Weighting00000000000000000
Measurement UnitsMeasurement UnitMeasurement UnitMeasurement
UnitMeasurement UnitMeasurement UnitMeasurement UnitMeasurement
UnitMeasurement UnitMeasurement UnitMeasurement UnitMeasurement
UnitMeasurement UnitMeasurement UnitMeasurement UnitMeasurement
UnitMeasurement UnitMeasurement Unit
Our Value55511111111111111
Competitor A33311111111111111
Competitor B22211111111111111
Target Specification Values00000000000000000
Our Value
Competitor A
Competitor B
Target Specification Values
From HOQ template-1 worksheet.
From the customer and design requirements worksheet
From customer and design requirements worksheet
From customer and design requirements worksheet
From customer and design requirements worksheet
From HOQ template-1
From the customer and design requirements worksheet.
From HOQ template-1 worksheet.
From the customer and design requirements worksheet.
From the customer and design requirements worksheet.
From the customer and design requirements worksheet.
From the customer and design requirements worksheet.
From HOQ template -1
HOQ 1Final
Our Service/Product
Competing Service/Product A
Competing Service/Product B
Matrix 2
Matrix 2
Functional Requirements
Technical RequirementsRelative WeightFunctional
RequirementFunctional RequirementFunctional RequirementFunctional
RequirementFunctional RequirementFunctional RequirementFunctional
RequirementFunctional RequirementFunctional RequirementFunctional
RequirementTotal
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Technical requirement00
Total0000000000
Relative Weight (Priority)0000000000
Our Value
Competitor A
Competitor B
Target Specification Values
From HOQ template-2 worksheet
From HOQ template-1 worksheet.
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
Matrix 3
Matrix 3
Design Requirements
Functional RequirementsRelative WeightDesign RequirementDesign
RequirementDesign RequirementDesign RequirementDesign
RequirementDesign RequirementDesign RequirementDesign
RequirementDesign RequirementDesign RequirementTotal
Functional Requirement00.00
Functional Requirement00.00
Functional Requirement00.00
Functional Requirement00.00
Functional Requirement00.00
Functional Requirement00.00
Functional Requirement00.00
Functional Requirement00.00
Functional Requirement00.00
Functional Requirement00.00
Total0000000000
Relative Weight (Priority)0000000000
From Matrix 2
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
Matrix 4
Matrix 4
Key Process Variables
Design RequirementsRelative WeightKey Process VariableKey
Process VariableKey Process VariableKey Process VariableKey Process
VariableKey Process VariableKey Process VariableKey Process
VariableKey Process VariableKey Process VariableTotal
Design Requirement00.00
Design Requirement00.00
Design Requirement00.00
Design Requirement00.00
Design Requirement00.00
Design Requirement00.00
Design Requirement00.00
Design Requirement00.00
Design Requirement00.00
Design Requirement00.00
Total0000000000
Relative Weight (Priority)0000000000
From Matrix 3
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
From HOQ 1 Final
Instructions
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 calculated if not entered,
all other values are automatically calculated, and do not need to
be altered. Each quality control model has a sample value set
entered, make sure to clear all values before proceeding with your
own data.
Cells with red marks in the upper right corner have comments,
let the mouse hover over these cells to read the comments to
further explain the quality control model.
This spreadsheet is locked/protected in order to keep the cells
with equations from being changed. If a model does need to be
altered, the spreadsheet first needs to be unlocked/unprotected. Do
this by selecting the workbook you wish to unlock, click on
"Tools", highlight "Protection", and select "Unprotect Sheet". The
sheet will then be unlocked so alterations can be made.
Equations for models will be given when available.
Mean Chart ( known)
Mean Control Chart ( known)
UCL0
zLCL0
n = number of observations/ sampleMean0
SampleMeanUCLMeanLCL
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
19000
20000
21000
22000
23000
24000
25000
26000
27000
28000
29000
30000
31000
32000
33000
34000
35000
36000
37000
38000
39000
40000
000
Mean Chart ( known)
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
Sample Means
UCL
Mean
LCL
Period
Mean
Mean Control Chart ( known)
Mean Chart ( unknown)
Mean Control Chart ( unknown)
n = number of observations/ sampleOverall Mean0
Average Range1.502
UCL0
LCL0
SampleMeanRangeUCLMeanLCL
11.38000
21.06000
31000
42.21000
51.46000
61.62000
71.03000
82.09000
90.77000
101.01000
111.1000
122.49000
131.68000
142.29000
151.34000
16000
17000
18000
19000
20000
21000
22000
23000
24000
25000
26000
27000
28000
29000
30000
31000
32000
33000
34000
35000
36000
37000
38000
39000
40000
n valueA2 factor
21.88
31.02
40.73
50.58
60.48
70.42
80.37
90.34
100.31
110.29
120.27
130.25
140.24
150.22
160.21
170.2
180.19
190.19
200.18
The Mean Control Chart (sigma known)plots the mean of a set
number of observations (n) for each sample versus period number on
the same chart as the overall mean of all observations and the
upper and lower control limits based on 3 sigma. In this case sigma
or s is known. A sample mean outside the upper or lower control
limits is very unusual (would only happen 3 times out of 1000) and
indicates assignable or non-random variation that should be
investigated and the cause eliminated or corrected.
Equations:UCL = Upper Control LimitLCL = Lower Control Limit
Number of standard deviations for a specific confidence level
(typically z = 3)
Sample size (number of observations per sample)
Sigma, standard deviation of the population
Upper Control Limit
Lower Control Limit
Average of sample means, population mean or overall mean
The average of the observations in each sample
Mean Chart ( unknown)
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
Sample Means
UCL
Mean
LCL
Period
Mean
Mean Control Chart ( unknown)
Range Chart
Range Control Chart
nAverage Range0
UCL0
LCL0
SampleRangeUCLMeanLCL
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
19000
20000
21000
22000
23000
24000
25000
26000
27000
28000
29000
30000
31000
32000
33000
34000
35000
36000
37000
38000
39000
40000
LCLUCL
n valueD3 factorD4 factor
203.27
302.57
402.28
502.11
602
70.081.92
80.141.86
90.181.82
100.221.78
110.261.74
120.281.72
130.311.69
140.331.67
150.351.65
160.361.64
170.381.62
180.391.61
190.41.6
200.411.59
The Mean Control Chart (sigma unknown) is similar to the
previous chart, except that the control limits are based on the
range found in each sample, rather than the standard deviation of
the population. The assumption here is that sigma is unknown for
the population and/or the range is easier to calculate. The average
range of all samples is related to the standard deviation of the
population and upper and lower control limits are found by
multiplying the average range by a tabulated factor rather than the
z value. The tabulated factors begin on A54 of this sheet. In
addition to the sample mean values, the range of these values for
each sample must be entered.As in the previous chart, a sample mean
outside the upper or lower control limits is very unusual and
indicates assignable or non-random variation.
Equation:UCL = Upper Control LimitLCL = Lower Control Limit
Sample size (number of observations per sample)
Average of mean values, population mean, or overall mean
Average of range values
Upper Control Limit
Lower Control Limit
The difference between the maximum and minimum values from the
observations taken for each sample
The average of the observations in each sample
Range Chart
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
19000
20000
21000
22000
23000
24000
25000
26000
27000
28000
29000
30000
31000
32000
33000
34000
35000
36000
37000
38000
39000
40000
Sample Ranges
UCL
Mean
LCL
Period
Mean
Range Control Chart
p Chart
p Chart
nAverage p0
0
zUCL0
0LCL0
0
SamplepUCLMeanLCL
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
19000
20000
21000
22000
23000
24000
25000
26000
27000
28000
29000
30000
31000
32000
33000
34000
35000
36000
37000
38000
39000
40000
The Range Control Chart plots the ranges of the samples on the
same chart as the mean of the ranges and the upper and lower
control limit for the range. The range is a measure of variability
within the samples and sample ranges outside the control limits
indicate that the variablility in the sample is very unusual and
should be investigated for assingnable causes. The upper and lower
control limits for the range are calculated using tabulated
factors. These factors are on this sheet, starting at A54.
Equation:UCL = Upper Control LimitLCL = Lower Control Limit
Average of range values
Upper Control Limit
Lower Control Limit
Sample size (number of observations per sample)
The difference between the maximum and minimum values from the
observations taken for each sample
p Chart
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
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20000
21000
22000
23000
24000
25000
26000
27000
28000
29000
30000
31000
32000
33000
34000
35000
36000
37000
38000
39000
40000
Sample p's
UCL
Mean
LCL
Period
Mean
p Chart
c Chart
c Chart
z3Average c0
UCL0
LCL0
SamplecUCLMeanLCL
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
19000
20000
21000
22000
23000
24000
25000
26000
27000
28000
29000
30000
31000
32000
33000
34000
35000
36000
37000
38000
39000
40000
The p Chart plots values which are a proportions (typically,
proportion of defects.) This chart is similar to both the Mean
Chart with s known and unknown, except it is used when the data is
proportional rather than absolute. It is based on the normal
approximation to the binomial distribution. A sample mean
proportion outside the upper or lower control limits is very
unusual (would only happen 3 times out of 1000) and indicates
assignable or non-random variation that should be investigated and
the cause eliminated or corrected.
Equation:UCL = Upper Control LimitLCL = Lower Control Limit
Average of proportions
Standard error of the proportions
Upper Control Limit
Lower Control Limit
Sample size (number of observations per sample)
Proportion (of defects), all values must be less than 1.
Number of standard deviations for a specific confidence level
(typically z = 3)
c Chart
Sample p's
UCL
Mean
LCL
Period
Mean
c Chart
Process Capability
Process Capability
StandardMachineSpecification
MachineDeviationCapabilityWidthCp
A00
B00
C00
D00
E00
Non centered
ProcessStandardLowerUpper
MachineMeanDeviationSpecificationRatioSpecificationRatioCpk
A000
B000
C000
D000
E000
The c Chart is essentially the same as the p Chart. However, In
this chart, we plot the number of defectives (per batch, per day,
per machine, per 100 feet of pipe, etc.) and the control limits in
this chart are computed based on the Poisson distribution
(distribution of rare events).
Equation:UCL = Upper Control LimitLCL = Lower Control Limit
Defects per unit
Average defects per unit
Upper Control Limit
Lower Control Limit
Number of standard deviations for a specific confidence level
(typically z = 3)
Process Capability
Capability Index
Process Capability is a measure of how capable the process is,
assuming the process is centered. A Cp of greater than or equal to
1 means the process is capable, while less than 1 means it is not
capable and needs to be "fixed" or changed in order to produce the
product. A capable process, with a Cp of 1, will only produce 3
defects per 1000 opportunities. A Cp of 1 means that the CLs and
the SLs are the same. Six sigma has a Cp of 1.5, a very capable
process. The process will only produce 3.4 defects per million
opportunities (DPMO) on one tail.
Equation:Machine Capability = Standard Deviation * 6Capability =
Specification Width / Machine Capability
For a non centered process (the mean of the process and the
center of the specifications are not the same), the Capability
Index (Cpk) needs to be calculated. As above, Cpk of greater than
or equal to 1 means the process is capable, while less than 1 means
it is not capable and needs to be "fixed" in order to produce the
product. Note that if the process is centered Cp=Cpk. If the
process is not centered, it is possible to get a Cp of greater than
1 and a Cpk of less than 1. Cpk is basically an adjustment for Cp
when the process is not centered to get the right answer. Six sigma
quality implies a Cpk of 1.5, a very capable process.
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 ]
Normal Distribution
Normal Distribution
Mean =20
Std Dev =2
x =29
z =4.5
P(x) =0.0000034008
Cumulative P(X)NormXZP(X)X
0.0115.3473060001-2.32634699990.013326098229
0.0215.8925049621-2.0537475190.024209137129
0.0316.2384146997-1.88079265010.03402103729
0.0416.498628866-1.7506855670.04308692529
0.0516.7102930487-1.64485347570.05156783329
0.0616.8904526186-1.55477369070.059561473729
0.0717.0484174344-1.47579128280.067133932129
0.0817.1898561931-1.40507190340.074333077329
0.0917.3184891762-1.34075541190.081195272729
0.117.4368961213-1.28155193930.087749123929
0.1117.5469430777-1.22652846110.094017744229
0.1217.6500258375-1.17498708130.100020207929
0.1317.7472172912-1.12639135440.105772527729
0.1417.8393610074-1.08031949630.111288336429
0.1517.9271330527-1.03643347360.116579377529
0.1618.0110842035-0.99445789820.121655868629
0.1718.0916695917-0.95416520420.126526775129
0.1818.1692700358-0.91536498210.131200021429
0.1918.2442077172-0.87789614140.13568265629
0.218.3167579163-0.84162104190.139980982829
0.2118.3871579444-0.80642102780.144100666529
0.2218.4556140436-0.77219297820.148046818929
0.2318.5223067859-0.7388466070.151824069229
0.2418.5873953505-0.70630232480.155436622829
0.2518.6510209487-0.67448952570.158888310429
0.2618.7133095941-0.6433452030.162182629129
0.2718.7743743638-0.61281281810.165322777529
0.2818.8343172603-0.58284136980.16831168629
0.2918.8932307558-0.55338462210.171152041929
0.318.951199084-0.5244004580.173846312129
0.3119.0082993271-0.49585033640.17639676229
0.3219.0646023376-0.46769883120.178805472129
0.3319.120173524-0.4399132380.18107435329
0.3419.1750735252-0.41246323740.183205157529
0.3519.2293587927-0.38532060360.185199492429
0.3619.2830820967-0.35845895160.187058827929
0.3719.3362929671-0.33185351650.188784506429
0.3819.3890380819-0.3054809590.190377750129
0.3919.4413616104-0.27931919480.191839667729
0.419.4933055178-0.25334724110.1931712629
0.4119.5449098382-0.22754508090.194373425629
0.4219.5962129206-0.20189353970.195446965129
0.4319.6472516522-0.17637417390.19639258529
0.4419.6980616617-0.15096916910.197210901129
0.4519.7486775074-0.12566124630.197902441729
0.4619.7991328512-0.10043357440.198467649829
0.4719.8494606225-0.07526968880.198906885329
0.4819.8996931722-0.05015341390.199220426529
0.4919.9498624204-0.02506878980.199408471829
0.520.00000000110.00000000050.199471140229
0.5120.05013757960.02506878980.199408471829
0.5220.10030682780.05015341390.199220426529
0.5320.15053937750.07526968880.198906885329
0.5420.20086714880.10043357440.198467649829
0.5520.25132249260.12566124630.197902441729
0.5620.30193833830.15096916910.197210901129
0.5720.35274834780.17637417390.19639258529
0.5820.40378707940.20189353970.195446965129
0.5920.45509016180.22754508090.194373425629
0.620.50669448220.25334724110.1931712629
0.6120.55863838960.27931919480.191839667729
0.6220.61096191810.3054809590.190377750129
0.6320.66370703290.33185351650.188784506429
0.6420.71691790330.35845895160.187058827929
0.6520.77064120730.38532060360.185199492429
0.6620.82492647480.41246323740.183205157529
0.6720.8798264760.4399132380.18107435329
0.6820.93539766240.46769883120.178805472129
0.6920.99170067290.49585033640.17639676229
0.721.0488009160.5244004580.173846312129
0.7121.10676924420.55338462210.171152041929
0.7221.16568273970.58284136980.16831168629
0.7321.22562563620.61281281810.165322777529
0.7421.28669040590.6433452030.162182629129
0.7521.34897905130.67448952570.158888310429
0.7621.41260464950.70630232480.155436622829
0.7721.47769321410.7388466070.151824069229
0.7821.54438595640.77219297820.148046818929
0.7921.61284205560.80642102780.144100666529
0.821.68324208370.84162104190.139980982829
0.8121.75579228280.87789614140.13568265629
0.8221.83072996420.91536498210.131200021429
0.8321.90833040830.95416520420.126526775129
0.8421.98891579650.99445789820.121655868629
0.8522.07286694731.03643347360.116579377529
0.8622.16063899261.08031949630.111288336429
0.8722.25278270881.12639135440.105772527729
0.8822.34997416251.17498708130.100020207929
0.8922.45305692231.22652846110.094017744229
0.922.56310387871.28155193930.087749123929
0.9122.68151082381.34075541190.081195272729
0.9222.81014380691.40507190340.074333077329
0.9322.95158256561.47579128280.067133932129
0.9423.10954738141.55477369070.059561473729
0.9523.28970695131.64485347570.05156783329
0.9623.5013711341.7506855670.04308692529
0.9723.76158530031.88079265010.03402103729
0.9824.10749503792.0537475190.024209137129
0.9924.65269399992.32634699990.013326098229
Normal Distribution
Normal
X
Normal Distribution
n
)
(z
LCL
n
)
*
(z
UCL
sample
per
ns
observatio
of
Number
n
population
of
deviation
Standard
confidence
99.7%
for
3
level
confidence
for
errrors
standard
of
Number
z
mean
overall
or
population
of
Mean
*
-
=
+
=
=
=
=
=
=
n
)(z
LCL
n
)*(z
UCL
sample per nsobservatio of Number n
population of deviation Standard
confidence 99.7% for 3 level confidence for errrors standard of
Number z
mean overall or population of Mean
*
R
A
X
LCL
R
A
X
UCL
values
range
of
Average
=
R
A54)
at
(starting
level
confidence
sigma
3
for
Factor
=
A2
mean
population
or
mean,
overall
means,
sample
of
Average
=
X
2
2
*
*
-
=
+
=
RAXLCL
RAXUCL
values range of Average=R
A54)at (starting level confidence sigma 3 for Factor = A2
mean population or mean, overall means, sample of Average=X
2
2
*
*
R
*
D
UCL
R
*
D
LCL
A54)
at
(starting
for UCL
Factor
=
D4
A54)
at
(starting
LCL
for
Factor
=
D3
ranges
sample
of
Average
=
R
4
3
=
=
R*DUCL
R*DLCL
A54)at (starting for UCLFactor = D4
A54)at (starting LCLfor Factor = D3
ranges sample of Average = R
4
3
c
z
c
LCL
c
z
c
UCL
3)
(usually
level
Confidence
=
z
unit
per
defects
of
number
Average
=
c
-
=
+
=
czcLCL
czcUCL
3)(usually level Confidence = z
unit per defects of number Average= c
p
p
p
p
*
z
p
LCL
*
z
p
UCL
n
)
p
(1
*
p
confidence
99.7%
for
3
level
confidence
for
errrors
standard
of
Number
=
z
ns/sample
observatio
of
Number
=
n
s
proportion
sample
of
Average
=
p
proportion
of
error
Standard
=
-
=
+
=
-
=
=
p
p
p
p
*zpLCL
*zpUCL
n
)p(1*p
confidence 99.7% for 3 level confidence for errrors standard of
Number = z
ns/sampleobservatio of Number = n
sproportion sample of Average= p
proportion of error Standard =
MBD000863BB.unknown
MBD0001552C.unknown
MBD00041595.unknown
MBD00052840.unknown
MBD0003B55B.unknown
Chapter 8
Quality Management: Focus on Six Sigma
Quality Management: Focus on Six Sigma
Defining quality
Cost of quality
Quality programs
Six Sigma
DMAIC process
Seven basic quality tools
Statistical process control (SPC)
Benchmarking
Quality function deployment (QFD)
Taguchi methods
Mistake proofing (poka-yoke)
Copyright 2012 Health Administration Press
Defining Quality
Organizations perspective
Performance (design) quality
Conformance (design) quality
Customer perspective
Garvins eight dimensions
Parasuraman, Zeithaml, and Berrys five dimensions
Institute of Medicine
Quality assurance program
Copyright 2012 Health Administration Press
Cost of (Poor) Quality
External failurecosts associated with failure after the customer
receives the product or service
Internal failurecosts associated with failure before the
customer receives the product or service
Appraisalcosts associated with inspecting and evaluating the
quality of supplies and/or final product/service
Preventioncosts incurred to eliminate or minimize appraisal and
failure costs
Copyright 2012 Health Administration Press
Quality Programs
ISO 9000
Baldrige criteria
Six Sigma
Copyright 2012 Health Administration Press
ISO 9000
International standards concerned with ensuring that
organizations maintain consistently high levels of quality
Five sections:
Quality management system
Management responsibility
Resource management
Measurement, analysis, and improvement
Product realization
Copyright 2012 Health Administration Press
Baldrige Award
Established to recognize organizations for their achievements in
quality and to raise awareness about the importance of quality
Seven categories:
Leadership
Strategic planning
Customer and market
focus
Measurement, analysis, and knowledge management
Human resources focus
Process management
Results
Copyright 2012 Health Administration Press
Six Sigma
Philosophy
Eliminate defects through prevention and process improvement
Methodology
Team-based approach to process improvement using the DMAIC
cycle
Set of tools
Quantitative and qualitative statistically based tools
Goal
3.4 defects per million opportunities (DPMO)
Copyright 2012 Health Administration Press
Successful Six Sigma
Top-management support
Use of quantitative measures
Culture and Leadership
Extensive training
DMAIC approach
Team-based projects
Impact on organizations financials
Copyright 2012 Health Administration Press
Six Sigma Infrastructure
Copyright 2012 Health Administration Press
DMAIC Process
Define
Measure
Analyze
Improve
Control
Copyright 2012 Health Administration Press
DMAIC Process: Define
Project team chooses a project on the basis of the businesss
strategic objectives and the needs or requirements of the customers
of the process
Characteristics of good projects:
Save or make money for the organization
Produce measurable process outcomes
Relate clearly to organizational strategy
Are supported by the organization
Copyright 2012 Health Administration Press
DMAIC Process: Measure
Copyright 2012 Health Administration Press
DMAIC Process
Analyze
Analyze collected data to determine the root causes
Improve
Identify, evaluate, and implement the improvement solutions
Control
Put controls in place to ensure process improvement gains are
maintained
Copyright 2012 Health Administration Press
Seven Basic Quality Tools
Flow Chart
Copyright 2012 Health Administration Press
Statistical Process Control (SPC)
SPC is a statistics-based methodology for determining when a
process is moving out of control.
All processes have variation in output.
Some of the variation is inherent in the process (common).
Some of the variation is due to assignable (special) causes.
SPC is aimed at discovering variation due to assignable causes
and correcting those causes.
Copyright 2012 Health Administration Press
Statistical Process Control (SPC)
Copyright 2012 Health Administration Press
SPC: Out-of-Control Situations
Copyright 2012 Health Administration Press
Statistical Process Control (SPC)
50% of patients wait more than 30 minutes
10% of patients wait more than 30 minutes
Copyright 2012 Health Administration Press
Process Capability
A measure of how well the process can produce output that meets
desired standards or specifications
Compares process specifications (set by the customer or
management) to control limits (the natural or common variability in
the process)
Copyright 2012 Health Administration Press
Process Capability
Cp and Cpk
Copyright 2012 Health Administration Press
Process Capability
Cp and Cpk
Copyright 2012 Health Administration Press
Process Capability
Cp and Cpk
Copyright 2012 Health Administration Press
Rolled Throughput Yield
Step 2
95/100 error-free products
Step 3
95/100 error-free products
Step 4
95/100 error-free products
Step 1
95/100 error-free products
Proportions
Actual
Copyright 2012 Health Administration Press
Quality Function Deployment (QFD): House of Quality
Correlation
matrix
Design
requirements
Customer
requirements
Competitive
assessment
Relationship
matrix
Specifications
or
target values
Importance
Importance weight
Importance
Importance weight
Copyright 2012 Health Administration Press
QFD Example
Customer needs
Goal: Develop a system to ensure that diabetes patients receive
preventive exams
Copyright 2012 Health Administration Press
Knowledge that it is time for an office visit
Knowledge of why follow-up is needed
Convenient to schedule
Known appointment length
Appointment on time
QFD Example
Technical responses
On-time appointment
Appointment length range
Time to schedule
Information on need
Subsequent notification
Initial notification
Copyright 2012 Health Administration Press
Time knowledge
Why knowledge
Convenient
Appointment length
Appointment time
QFD Example
Importance:
Patient desire
Cost
Competitive
advantage
On-time appointment
Appointment length range
Time to schedule
Information on need
Subsequent notification
Initial notification
Copyright 2012 Health Administration Press
Time knowledge5
Why knowledge3
Convenient4
Appointment length3
Appointment time4
QFD Example
On-time appointment
Appointment length range
Time to schedule
Information on need
Subsequent notification
Initial notification
Relationships:
Strong = 5
Medium = 3
Weak = 1
Copyright 2012 Health Administration Press
Time knowledge5
Why knowledge3
Convenient4
Appointment length3
Appointment time4
QFD Example
On-time appointment
Appointment length range
Time to schedule
Information on need
Subsequent notification
Initial notification
Replace icons with numbers
Relationships:
Strong = 5
Medium = 3
Weak = 1
Copyright 2012 Health Administration Press
Time knowledge553
Why knowledge35
Convenient43
Appointment length353
Appointment time435
QFD Example
On-time appointment
Appointment length range
Time to schedule
Information on need
Subsequent notification
Initial notification
Multiply by importance and sum
Copyright 2012 Health Administration Press
Time knowledge553
Why knowledge35
Convenient45
Appointment length353
Appointment time435
251515202729
QFD Example
On-time appointment
Appointment length range
Time to schedule
Information on need
Subsequent notification
Initial notification
Technical correlations
Relationships:
+ = Strong positive
= Strong negative
+
+
Copyright 2012 Health Administration Press
Time knowledge553
Why knowledge35
Convenient45
Appointment length353
Appointment time435
251515202729
QFD Example
On-time appointment
Appointment length range
Time to schedule
Information on need
Subsequent notification
Initial notification
Target:
100 diabetics/month; 85% compliance
Copyright 2012 Health Administration Press
Time knowledge553
Why knowledge35
Convenient45
Appointment length353
Appointment time435
251515202729
QFD Example: Outcome
To: Dan McLaughlin
From: Southview Clinic
Dear Dan,
You had an appointment with Dr. Adams about six months ago, and
it is now time for another visit. We need to check your blood
pressure, do some blood tests, and adjust your prescriptions if
needed. We would like to review these preventive procedures in
advance, so please see www.southview.com/prev22.
We have two openings available next week, on Tuesday at 8:30 am
and Thursday at 2:30, to see Dr. Adams. Click on one of these days
to make the appointment, or e-mail us with dates and times that
work for you.
We appreciate you continuing your care with us, and Dr. Adams
looks forward to seeing you.
Copyright 2012 Health Administration Press
Taguchi Methods
Taguchi loss function
A quality product is a product that causes a minimal loss
(expressed in $) to society during its entire life.
Design of Experiments (DOE)
Design for Six Sigma (DFSS)
Copyright 2012 Health Administration Press
Benchmarking
Process of identifying, understanding, and adapting outstanding
practices and processes to improve organizational performance
Steps in benchmarking:
Determine what to benchmark
Determine how to measure it
Gather information and data
Implement the best practice
in the organization
Copyright 2012 Health Administration Press
Mistake Proofing (Poka-Yoke)
A mechanism that either:
Prevents a mistake from being made
Makes the mistake immediately obvious
Eliminates errors
Copyright 2012 Health Administration Press
Riverview Generic Drug Project: Prescription Process
Copyright 2012 Health Administration Press
Riverview Generic Drug Project: Drug Type and Availability
Microsoft Excel screen shots reprinted with permission from
Microsoft Corporation.
Copyright 2012 Health Administration Press
Riverview Generic Drug Project
Microsoft Excel screen shots reprinted with permission from
Microsoft Corporation.
Copyright 2012 Health Administration Press
DMAIC Process
Seven Quality Control Tools
Copyright 2012 Health Administration Press
DMAIC Process: Other Tools
Copyright 2012 Health Administration Press
DMAIC Process: Other Tools
Copyright 2012 Health Administration Press
Copyright 2012 Health Administration Press
End of Chapter 8
OPERATIONS HEALTHCARE
MANAGEMENTs e c o n d e d i t i o n
D a n i e l B . M c L a u g h l i n a n d
J o h n R . O l s o n
6
6
6
6
6
6
20
25
30
35
40
051015202530
Day
Mean Wait Time (minutes)
+/- 1
s
+/- 2
s
+/- 3
s
Out of
Control
Sample
Observation
_
X=0
UCL=3
LCL=-3
8orMoreSamplesAbove(orBelow)Mean
Observation
_
X=0
LCL=-3
UCL=3
6orMoreSamplesIncreasing(orDecreasing)
Observation
_
X=0
UCL=3
LCL=-3
OneSampleMoreThan+/-3StandardErrorsfromMean
Observation
_
X=0
UCL=3
LCL=-3
14orMoreSamplesOscillating
One Sample More Than +/ -3 Standard
Errors from Mean
14 or More Samples Oscillating
8 or More Samples Above (or Below)
Mean
6 or More Samples Increasing (or
Decreasing)
Observation
_
X=0
UCL=3
LCL=-3
8orMoreSamplesAbove(orBelow)Mean
Observation
_
X=0
LCL=-3
UCL=3
6orMoreSamplesIncreasing(orDecreasing)
Observation
_
X=0
UCL=3
LCL=-3
OneSampleMoreThan+/-3StandardErrorsfromMean
Observation
_
X=0
UCL=3
LCL=-3
14orMoreSamplesOscillating
One Sample More Than +/ -3 Standard
Errors from Mean
14 or More Samples Oscillating
8 or More Samples Above (or Below)
Mean
6 or More Samples Increasing (or
Decreasing)
Current Wait Time
15
20
25
30
35
40
45
Wait Time (minutes)
Wait Time Goal
15
20
25
30
35
40
45
Wait Time (minutes)
-
-
=
-
-
=
-
=
-
=
s
x
USL
or
s
LSL
x
C
x
USL
or
LSL
x
C
s
LSL
USL
C
LSL
USL
C
pk
pk
p
p
3
3
min
by
estimated
is
and
3
3
min
6
by
estimated
is
and
6
s
s
s
-7-6-5-4-3-2-101234567
1.5
s
shift
LSL
USL
3.4
DPM
O
Taguchi Loss Function
Y ($)
LSLTarget
USL
Loss
2
2
2
$
whereLoss
kTYk
Best
Worst
Range
of
values
Your
organization
Best
Worst
Range
of
values
Range
of
values
Your
organization
Your
organization
Patient
needs
drug
Clinician
prescribes
drug
Information
on drugs
Type of
drug
Drug
efficacy
End
Drug
efficacy
End
Generic
Drug
works
Non-Generic
Drug
works
Drug
doesnt
work
Drug doesnt work
65%35%
15%
20%
Generic
Non-Generic,
Generic
Available
Non-Generic,
Generic Not
Available
Tools and Techniques
Define
Measure
Analyze
Improve
Control
Cause-and-Effect Diagram x
Run Chart xx
Check Sheet
Histogram xx
Pareto Chart xxx
Scatter Diagram xx
Flowchart xx
TAT Data
ObservationObservation
1234512345
DayDay
14441805125161444353276
22832584218175284556315
35483595046182820677669
45753631552192523352123
53050626842204674241047
64240504973213354624027
72617504791226455621472
85439398228235349724961
94662536457241516183578
10497134424325649514770
115364123543263621514057
127543435064272458198816
137419525559287566342771
149140661573296042205960
155932594971305228853967
RV CS Data column
DayProportion of patients who were unsatisfied
10.17
20.13
30.15
40.22
50.16
60.13
70.17
80.17
90.11
100.16
110.15
120.17
130.17
140.12
150.15
160.14
170.13
180.15
190.15
200.22
210.19
220.15
230.12
240.16
250.18
260.14
270.17
280.18
290.19
300.14
310.19
320.10
330.17
340.15
350.17
360.15
370.15
380.15
390.14
400.19
RV CS Data
DayProportion of patients who were unsatisfiedDayProportion of
patients who were unsatisfiedDayProportion of patients who were
unsatisfied
10.17150.15280.18
20.13160.14290.19
30.15170.13300.14
40.22180.15310.19
50.16190.15320.10
60.13200.22330.17
70.17210.19340.15
80.17220.15350.17
90.11230.12360.15
100.16240.16370.15
110.15250.18380.15
120.17260.14390.14
130.17270.17400.19
140.12
Notes
This workbook contains all the information for the Riverview
Clinic SPC Example in Chapter 7 Healthcare Operations Management
and utilizes the Excel Quality Control template.
The RV Wait Times contains the data both with and without the
out-of-control observation.
Mean Chart (sigma known and unknown) and Range Chart are the
initial control charts with the out-of-control point included.
(Note that the sigma known and unknown charts are essentially the
same.
Mean Chart (sigma known and unknown)(2) and Range Chart (2) are
the control charts with the out-of-control point removed.
The ND charts illustrate the proportion of patients that will
experience various wait times given the system mean and s.d.
The Process Capability worksheet (Machine A) illustrates the Cp
and Cpk with the current system. Note that although the Cp implies
that the process is capable, the process is not centered on the
specification limits and, therefore, the correct measure is Cpk.
The Cpk shows that the process is not capable. Machine B-E
illustrate process capabilites for the other scenarios discussed in
the text.
The remaining worksheets are for the text illustrations and
powerpoint slides.
RV Wait Times
Riverview Clinic Wait TimeRiverview Clinic Wait Time (Remove
Outlier)
Observations of Wait Times (minutes)Sample MeanSample
RangeObservations of Wait Times (minutes)Sample MeanSample
Range
ObservationObservation
Day123456Day123456
129292231293128.509129292231293128.509
224294026363030.8316224294026363030.8316
328332526283328.838328332526283328.838
426313830232829.3315426313830232829.3315
536292429263229.3312536292429263229.3312
626273225302928.177626273225302928.177
722333031373431.1715722333031373431.1715
840292629323031.0014840292629323031.0014
932322134282929.3313932322134282929.3313
1034263527312629.8391034263527312629.839
1135302930312730.3381135302930312730.338
1231393232303132.5091231393232303132.509
1336243029312629.33121336243029312629.3312
1425232931252326.0081425232931252326.008
1538433735383237.17111635293025283029.5010
1635293025283029.50101726292033302827.6713
1726292033302827.67131822292630362828.5014
1822292630362828.50141933333437283032.509
1933333437283032.5092026263434253630.1711
2026263434253630.1711
Standard Deviation =4.13Overall Mean =29.62
Standard Deviation =4.42Overall Mean =30.00
Instructions
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 calculated if not entered,
all other values are automatically calculated, and do not need to
be altered. Each quality control model has a sample value set
entered, make sure to clear all values before proceeding with your
own data.
Cells with red marks in the upper right corner have comments,
let the mouse hover over these cells to read the comments to
further explain the quality control model.
This spreadsheet is locked/protected in order to keep the cells
with equations from being changed. If a model does need to be
altered, the spreadsheet first needs to be unlocked/unprotected. Do
this by selecting the workbook you wish to unlock, click on
"Tools", highlight "Protection", and select "Unprotect Sheet". The
sheet will then be unlocked so alterations can be made.
Equations for models will be given when available.
Mean Chart ( known)
Mean Control Chart ( known)
4.42UCL35.4133723316
z3LCL24.5866276684
n = number of observations/ sample6Mean30
SampleMeanUCLMeanLCL
128.535.41337233163024.5866276684
230.833333333335.41337233163024.5866276684
328.833333333335.41337233163024.5866276684
429.333333333335.41337233163024.5866276684
529.333333333335.41337233163024.5866276684
628.166666666735.41337233163024.5866276684
731.166666666735.41337233163024.5866276684
83135.41337233163024.5866276684
929.333333333335.41337233163024.5866276684
1029.833333333335.41337233163024.5866276684
1130.333333333335.41337233163024.5866276684
1232.535.41337233163024.5866276684
1329.333333333335.41337233163024.5866276684
142635.41337233163024.5866276684
1537.166666666735.41337233163024.5866276684
1629.535.41337233163024.5866276684
1727.666666666735.41337233163024.5866276684
1828.535.41337233163024.5866276684
1932.535.41337233163024.5866276684
2030.166666666735.41337233163024.5866276684
2135.41337233163024.5866276684
2235.41337233163024.5866276684
2335.41337233163024.5866276684
2435.41337233163024.5866276684
2535.41337233163024.5866276684
2635.41337233163024.5866276684
2735.41337233163024.5866276684
2835.41337233163024.5866276684
2935.41337233163024.5866276684
3035.41337233163024.5866276684
3135.41337233163024.5866276684
3235.41337233163024.5866276684
3335.41337233163024.5866276684
3435.41337233163024.5866276684
3535.41337233163024.5866276684
3635.41337233163024.5866276684
3735.41337233163024.5866276684
3835.41337233163024.5866276684
3935.41337233163024.5866276684
4035.41337233163024.5866276684
35.41337233163024.5866276684
Mean Chart ( known)
Sample Means
UCL
Mean
LCL
Period
Mean
Mean Control Chart ( known)
Mean Chart ( unknown)
Mean Control Chart ( unknown)
n = number of observations/ sample6Overall Mean30
Average Range11.25
UCL35.4
LCL24.6
SampleMeanRangeUCLMeanLCL
128.5935.43024.6
230.83333333331435.43024.6
328.8333333333835.43024.6
429.33333333331535.43024.6
529.33333333331235.43024.6
628.1666666667835.43024.6
731.16666666671535.43024.6
8311435.43024.6
929.33333333331335.43024.6
1029.8333333333935.43024.6
1130.3333333333835.43024.6
1232.5935.43024.6
1329.33333333331235.43024.6
14261135.43024.6
1537.16666666671135.43024.6
1629.51035.43024.6
1727.66666666671335.43024.6
1828.51435.43024.6
1932.5935.43024.6
2030.16666666671135.43024.6
2135.43024.6
2235.43024.6
2335.43024.6
2435.43024.6
2535.43024.6
2635.43024.6
2735.43024.6
2835.43024.6
2935.43024.6
3035.43024.6
3135.43024.6
3235.43024.6
3335.43024.6
3435.43024.6
3535.43024.6
3635.43024.6
3735.43024.6
3835.43024.6
3935.43024.6
4035.43024.6
n valueA2 factor
21.88
31.02
40.73
50.58
60.48
70.42
80.37
90.34
100.31
110.29
120.27
130.25
140.24
150.22
160.21
170.2
180.19
190.19
200.18
The Mean Control Chart (sigma known)plots the mean of a set
number of observations (n) for each sample versus period number on
the same chart as the overall mean of all observations and the
upper and lower control limits based on 3 sigma. In this case sigma
or s is known. A sample mean outside the upper or lower control
limits is very unusual (would only happen 3 times out of 1000) and
indicates assignable or non-random variation that should be
investigated and the cause eliminated or corrected.
Equations:UCL = Upper Control LimitLCL = Lower Control Limit
Number of standard deviations for a specific confidence level
(typically z = 3)
Sample size (number of observations per sample)
Sigma, standard deviation of the population
Upper Control Limit
Lower Control Limit
Average of sample means, population mean or overall mean
The average of the observations in each sample
Mean Chart ( unknown)
Sample Means
UCL
Mean
LCL
Period
Mean
Mean Control Chart ( unknown)
Range Chart
Range Control Chart
n6Average Range11.15
UCL22.3
LCL0
SampleRangeUCLMeanLCL
1922.311.150
21622.311.150
3822.311.150
41522.311.150
51222.311.150
6722.311.150
71522.311.150
81422.311.150
91322.311.150
10922.311.150
11822.311.150
12922.311.150
131222.311.150
14822.311.150
151122.311.150
161022.311.150
171322.311.150
181422.311.150
19922.311.150
201122.311.150
2122.311.150
2222.311.150
2322.311.150
2422.311.150
2522.311.150
2622.311.150
2722.311.150
2822.311.150
2922.311.150
3022.311.150
3122.311.150
3222.311.150
3322.311.150
3422.311.150
3522.311.150
3622.311.150
3722.311.150
3822.311.150
3922.311.150
4022.311.150
LCLUCL
n valueD3 factorD4 factor
203.27
302.57
402.28
502.11
602
70.081.92
80.141.86
90.181.82
100.221.78
110.261.74
120.281.72
130.311.69
140.331.67
150.351.65
160.361.64
170.381.62
180.391.61
190.41.6
200.411.59
The Mean Control Chart (sigma unknown) is similar to the
previous chart, except that the control limits are based on the
range found in each sample, rather than the standard deviation of
the population. The assumption here is that sigma is unknown for
the population and/or the range is easier to calculate. The average
range of all samples is related to the standard deviation of the
population and upper and lower control limits are found by
multiplying the average range by a tabulated factor rather than the
z value. The tabulated factors begin on A54 of this sheet. In
addition to the sample mean values, the range of these values for
each sample must be entered.As in the previous chart, a sample mean
outside the upper or lower control limits is very unusual and
indicates assignable or non-random variation.
Equation:UCL = Upper Control LimitLCL = Lower Control Limit
Sample size (number of observations per sample)
Average of mean values, population mean, or overall mean
Average of range values
Upper Control Limit
Lower Control Limit
The difference between the maximum and minimum values from the
observations taken for each sample
The average of the observations in each sample
Range Chart
Sample Ranges
UCL
Mean
LCL
Period
Mean
Range Control Chart
Mean Chart ( known) (2)
Mean Control Chart ( known)
4.13UCL34.6810033364
z3LCL24.5646106987
n = number of observations/ sample6Mean29.6228070175
SampleMeanUCLMeanLCL
128.534.681003336429.622807017524.5646106987
230.833333333334.681003336429.622807017524.5646106987
328.833333333334.681003336429.622807017524.5646106987
429.333333333334.681003336429.622807017524.5646106987
529.333333333334.681003336429.622807017524.5646106987
628.166666666734.681003336429.622807017524.5646106987
731.166666666734.681003336429.622807017524.5646106987
83134.681003336429.622807017524.5646106987
929.333333333334.681003336429.622807017524.5646106987
1029.833333333334.681003336429.622807017524.5646106987
1130.333333333334.681003336429.622807017524.5646106987
1232.534.681003336429.622807017524.5646106987
1329.333333333334.681003336429.622807017524.5646106987
142634.681003336429.622807017524.5646106987
1529.534.681003336429.622807017524.5646106987
1627.666666666734.681003336429.622807017524.5646106987
1728.534.681003336429.622807017524.5646106987
1832.534.681003336429.622807017524.5646106987
1930.166666666734.681003336429.622807017524.5646106987
2034.681003336429.622807017524.5646106987
2134.681003336429.622807017524.5646106987
2234.681003336429.622807017524.5646106987
2334.681003336429.622807017524.5646106987
2434.681003336429.622807017524.5646106987
2534.681003336429.622807017524.5646106987
2634.681003336429.622807017524.5646106987
2734.681003336429.622807017524.5646106987
2834.681003336429.622807017524.5646106987
2934.681003336429.622807017524.5646106987
3034.681003336429.622807017524.5646106987
3134.681003336429.622807017524.5646106987
3234.681003336429.622807017524.5646106987
3334.681003336429.622807017524.5646106987
3434.681003336429.622807017524.5646106987
3534.681003336429.622807017524.5646106987
3634.681003336429.622807017524.5646106987
3734.681003336429.622807017524.5646106987
3834.681003336429.622807017524.5646106987
3934.681003336429.622807017524.5646106987
4034.681003336429.622807017524.5646106987
34.681003336429.622807017524.5646106987
The Range Control Chart plots the ranges of the samples on the
same chart as the mean of the ranges and the upper and lower
control limit for the range. The range is a measure of variability
within the samples and sample ranges outside the control limits
indicate that the variablility in the sample is very unusual and
should be investigated for assingnable causes. The upper and lower
control limits for the range are calculated using tabulated
factors. These factors are on this sheet, starting at A54.
Equation:UCL = Upper Control LimitLCL = Lower Control Limit
Average of range values
Upper Control Limit
Lower Control Limit
Sample size (number of observations per sample)
The difference between the maximum and minimum values from the
observations taken for each sample
Mean Chart ( known) (2)
Sample Means
UCL
Mean
LCL
Period
Mean
Mean Control Chart ( known)
Mean Chart ( unknown) (2)
Mean Control Chart ( unknown)
n = number of observations/ sample6Overall Mean29.6228070175
Average Range11.2631578947
UCL35.029122807
LCL24.2164912281
SampleMeanRangeUCLMeanLCL
128.5935.02912280729.622807017524.2164912281
230.83333333331435.02912280729.622807017524.2164912281
328.8333333333835.02912280729.622807017524.2164912281
429.33333333331535.02912280729.622807017524.2164912281
529.33333333331235.02912280729.622807017524.2164912281
628.1666666667835.02912280729.622807017524.2164912281
731.16666666671535.02912280729.622807017524.2164912281
8311435.02912280729.622807017524.2164912281
929.33333333331335.02912280729.622807017524.2164912281
1029.8333333333935.02912280729.622807017524.2164912281
1130.3333333333835.02912280729.622807017524.2164912281
1232.5935.02912280729.622807017524.2164912281
1329.33333333331235.02912280729.622807017524.2164912281
14261135.02912280729.622807017524.2164912281
1529.51135.02912280729.622807017524.2164912281
1627.66666666671035.02912280729.622807017524.2164912281
1728.51335.02912280729.622807017524.2164912281
1832.51435.02912280729.622807017524.2164912281
1930.1666666667935.02912280729.622807017524.2164912281
2035.02912280729.622807017524.2164912281
2135.02912280729.622807017524.2164912281
2235.02912280729.622807017524.2164912281
2335.02912280729.622807017524.2164912281
2435.02912280729.622807017524.2164912281
2535.02912280729.622807017524.2164912281
2635.02912280729.622807017524.2164912281
2735.02912280729.622807017524.2164912281
2835.02912280729.622807017524.2164912281
2935.02912280729.622807017524.2164912281
3035.02912280729.622807017524.2164912281
3135.02912280729.622807017524.2164912281
3235.02912280729.622807017524.2164912281
3335.02912280729.622807017524.2164912281
3435.02912280729.622807017524.2164912281
3535.02912280729.622807017524.2164912281
3635.02912280729.622807017524.2164912281
3735.02912280729.622807017524.2164912281
3835.02912280729.622807017524.2164912281
3935.02912280729.622807017524.2164912281
4035.02912280729.622807017524.2164912281
n valueA2 factor
21.88
31.02
40.73
50.58
60.48
70.42
80.37
90.34
100.31
110.29
120.27
130.25
140.24
150.22
160.21
170.2
180.19
190.19
200.18
The Mean Control Chart (sigma known)plots the mean of a set
number of observations (n) for each sample versus period number on
the same chart as the overall mean of all observations and the
upper and lower control limits based on 3 sigma. In this case sigma
or s is known. A sample mean outside the upper or lower control
limits is very unusual (would only happen 3 times out of 1000) and
indicates assignable or non-random variation that should be
investigated and the cause eliminated or corrected.
Equations:UCL = Upper Control LimitLCL = Lower Control Limit
Number of standard deviations for a specific confidence level
(typically z = 3)
Sample size (number of observations per sample)
Sigma, standard deviation of the population
Upper Control Limit
Lower Control Limit
Average of sample means, population mean or overall mean
The average of the observations in each sample
Mean Chart ( unknown) (2)
Sample Means
UCL
Mean
LCL
Period
Mean
Mean Control Chart ( unknown)
Range Chart (2)
Range Control Chart
n6Average Range11.2631578947
UCL22.5263157895
LCL0
SampleRangeUCLMeanLCL
1922.526315789511.26315789470
21422.526315789511.26315789470
3822.526315789511.26315789470
41522.526315789511.26315789470
51222.526315789511.26315789470
6822.526315789511.26315789470
71522.526315789511.26315789470
81422.526315789511.26315789470
91322.526315789511.26315789470
10922.526315789511.26315789470
11822.526315789511.26315789470
12922.526315789511.2