QI Measurement
Module 7: SPC, p Charts, and XmR Charts
Brant Oliver, PhD, NP, MS, MPH Adjunct Assistant Professor 1
Mini-Modules • Module 1: Microsoft Excel Basic Training • Module 2: Defining Measures • Module 3: Data Collection Plan • Module 4: Data Display • Module 5: Balanced Measurement • Module 6: Variation and Run Charts • Module 7: SPC, p Charts, XmR Charts
SPC Mini-Module Competencies
Videos and Quick-‐ Reference Materials
Textbook Readings
Templates & Worksheets
Applied Learning AcAviAes
1. XmR Charts 2. p Charts 3. Data types 4. Appropriate SPC chart selec;on 5. Sta;s;cal control and when to transi;on to audi;ng.
1 . How to use the XmR Template (video) 2. How to use the p Chart Template (video) 3. Chart selec;on (algorithm) 4. SPC 1 page book (Harrison)
Team Handbook: Control Charts and Types of Varia;on, p. 4-‐24. Quality by Design: Control Charts, pp. 350-‐360.
1. XmR Template 2. XmR Example 3. p Chart Template 4. p Chart example
SPC exercises with data set
Types of Variation Common Cause
Special Cause
Variation caused by chance causes, by random variation in the system, resulting from many small factors.
Variation caused by special
circumstances or assignable cause not inherent to the system.
Example: Variation in work
commute due to traffic lights,
pedestrian traffic, parking issues.
Example: Variation in work commute impacted by flat tyre, road closure, heavy frost/ice.
Statistically significant 4
Addressing Variation
Special Cause Variation (Unpredictable)
Common Cause Variation (Predictable)
Identify the Cause: If Positive: “Maximize, optimize, replicate, or standardize.” If Negative: “Minimize or eliminate”
Reduce Variation (Increase Precision): Make the process even more reliable. Sub-Optimal Average Performance: Redesign process to get a better result. 5
SPC Control Limits
Mean (Avg.)
Measured Value (“x”)
Time-ordered Observations (1 n) Anatomy of a SPC Chart…
SPC UCL X XX XXX XXXX XXXXX XXXXX XXXX XXX XX X
_ X
LCL Example of a relationship between a normal distribution and a XmR chart. N.B. – XmR charts do not require a normal distribution for validity.
The Signals
17
8
SPC XmR vs. p Charts: What type of data do I have?
Attribute or Nominal
Measurement or Variable
P chart
XmR chart
XmR Chart Upper Control Limit of X: X bar + (2.66 * R bar)
160
120
X bar
100 80 60
Lower Control Limit of X: X bar - (2.66 * R bar)
40 20 0 1
Moving Range (mR)
Fast Blood Glucose
140
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Control Limit of R: (3.27 * R bar)
60 40 20
R bar
0 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 10 28 29 30 31
10
p Chart
Interpretation
“In Statistical Control” = No Special Cause (Common Cause Variation) § 8 points on same side of central line (SHIFT).* § 6 consecutive increases or decreases (7 points) without a change in direction (TREND).*
§ Any point outside of the control limits.
* Same as for Run Charts
N.B. – Do not count runs for SPC charts
Exercise
PortCF Data -- Example #1 Average Maximum BMI
13
Apply the Algorithm What type of data do I have?
Attribute or Nominal
P chart
14
Quarter 2007-1 2007-2 2007-3 2007-4 2008-1 2008-2 2008-3 2008-4 2009-1 2009-2 2009-3 2009-4 2010-1 2010-2 2010-3 2010-4 2011-1 2011-2 2011-3 2011-4
Avg Of Max BMI 23.81 24.57 23.98 24.41 24.13 24.08 24.08 24.16 24.72 24.22 24.83 24.67 25.67 26.14 26.11 24.56 25.75 26.10 24.93 29.40
Measurement or Variable
XmR chart
15"
2007-1"
15 2011-4"
2011-3"
2011-2"
2011-1"
2010-4"
2010-3"
2010-2"
2010-1"
2009-4"
2009-3"
2009-2"
2009-1"
2008-4"
2008-3"
2008-2"
2008-1"
2007-4"
2007-3"
2007-2"
Avg of Maximum BMI"
Question
How many special cause signals are there in this XmR chart? CF Center 1!
31"
29"
1. 2. 3. 4.
27"
25"
23"
21"
19"
17"
One Two Three Four
15"
16
Analysis Trends = 0 Shifts = 1 Points outside limits = 1 2011-4"
2011-3"
2011-2"
2011-1"
2010-4"
2010-3"
2010-2"
2010-1"
2009-4"
2009-3"
2009-2"
2009-1"
2008-4"
2008-3"
2008-2"
2008-1"
2007-4"
2007-3"
2007-2"
2007-1"
Avg of Maximum BMI"
Answer
There are TWO special cause signals. CF Center 1!
31"
29"
27"
25"
23"
21"
19"
17"
Exercise
PortCF Data -- Example #2 Exercise as Part of ACT
17
SPC Chart Selection Decision What type of data do I have?
Attribute or Nominal
P chart
18
Quarter 2007-1 2007-2 2007-3 2007-4 2008-1 2008-2 2008-3 2008-4 2009-1 2009-2 2009-3 2009-4 2010-1 2010-2 2010-3 2010-4 2011-1 2011-2 2011-3
Opportunities 79 95 76 100 111 103 101 49 119 88 80 86 145 108 129 138 138 132 92
Events 18 27 23 32 31 38 29 14 37 30 19 17 24 13 19 28 49 54 42
Measurement or Variable
XmR chart
Percent Incorporating Exercise 0%
19 2007-1 2007-2 2007-3 2007-4 2008-1 2008-2 2008-3 2008-4 2009-1 2009-2 2009-3 2009-4 2010-1 2010-2 2010-3 2010-4 2011-1 2011-2 2011-3
Question
How many special cause signals are there? CF Center 3
50%
45%
40%
35%
30%
25%
1. 2. 3. 4.
20%
15%
10%
5%
Quarter
One Three Five Seven
Answer There are FIVE special cause signals. CF Center 3 50%
40% Percent Analysis
35% 30%
Average LCLp
25%
UCLp 1. Shifts =1 2. Trends = 0 3. Points Outside Limits = 4
20% 15% 10%
2011-3
2011-2
2011-1
2010-4
2010-3
2010-2
2010-1
2009-4
2009-3
2009-2
2009-1
2008-4
2008-3
2008-2
2008-1
2007-4
2007-3
0%
2007-2
5% 2007-1
Percent Incorporating Exercise
45%
Quarter
20
20
Review: Variation
Special Cause Variation (Unpredictable)
Common Cause Variation (Predictable)
Identify the Cause: If Positive: “Maximize, optimize, replicate, or standardize.” If Negative: “Minimize or eliminate”
Reduce Variation (Increase Precision): Make the process even more reliable. Sub-Optimal Average Performance: Redesign process to get a better result. 21
SPC Mini-Module
Applied Exercises Create and interpret p Charts and XmR Charts using data from your seQng or the data set provided.
QI Measurement
Done! You have completed the QI Measurement Mini-Modules!
Brant Oliver, PhD, NP, MS, MPH Adjunct Assistant Professor 23