Ozcan: Chapter 12
Quality Assurance and Quality Control
Part 2
Dr. Joan Burtner,
Certified Quality Engineer
Associate Professor of
Industrial Engineering and
Industrial Management
Topics
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Part 1
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Quality in Healthcare
Quality Experts
Quality Certification
TQM & CQI
Six-Sigma
Part 2
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Monitoring Quality through Control Charts
 Control Charts for Attributes
 Control Charts for Variables
Process improvement
Methods for Generating New Ideas
Tools for Investigation
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
2
Fall 2009
2
Quality Measurement and Control Techniques
Process Variability 1
In the delivery of health care, there are many occasions when an
error can happen in the tasks performed by various clinical staff.
Often the same task may not even be performed the same way for
all patients, though minor alterations within defined limits can be
acceptable.
When provider performance falls beyond acceptable limits, the
errors that occur require investigation and correction.
In order to detect noteworthy variations in process, or tendencies
that may cause unacceptable levels of errors, healthcare
managers must monitor the processes for quality, using various
charts.
The intent of the monitoring is to distinguish between random
and non-random variation.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
3
3
Quality Measurement and Control Techniques
Process Variability 2
The common variations in process variability that are
caused by natural incidences are in general not repetitive,
but various minor factors due to chance and are called
random variation.
If the cause of variation is systematic, not natural, and the
source of the variation is identifiable, the process variation
is called non-random variation.
In healthcare, non-random variation may occur by not
following procedures, using defective materials, fatigue,
carelessness, or not having appropriate training or
orientation to the work situation, among many reasons.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
4
4
Control Limits, Random and Nonrandom Sample Observations
Upper
Control
Limit
(UCL)
Non-random
Non-random
99.7%
+3σ
Process
Mean
Lower
Control
Limit
(LCL)
-3σ
1
2
3
4
5
6
7
8
9
10
11
12
Sample number
5
Source: Ozcan Figure 12.4 (Modified for Three Sigma Limits)
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
5
Control Charts Overview
Attributes
c-chart
Variables
p-chart
Mean-Charts
σ Method
ISE 491 Dr. Joan Burtner
Range-Charts
X-bar Charts
6
Range Method
Ozcan Chapter 12 Part 2
Fall 2009
6
Control Charts for Attributes
When process characteristics can be counted,
attribute-based control charts are the appropriate
way to display the monitoring process.
If the number of occurrences per unit of measure
can be counted, or there can be a count of the
number of bad occurrences but not of nonoccurrences, then a c-chart is the appropriate tool
to display monitoring.
Counting also can occur for a process with only two
outcomes, good or bad (defective); in such cases
p-chart is the appropriate control chart because it is
based on the binomial distribution.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
7
7
Control Charts for Attributes: c-Chart
UCL  c  z c
LCL  c  z c
8
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
8
Control Charts for Attributes: c-Chart Example
Source: Quantitatve Methods
in Health Care Management
Months
The number of infections from
the Intensive Care Unit (ICU)
at the ABC Medical Center
over a period of 24 months is
obtained. These numbers are
the counts of stool assay
positive for toxin, segregated
by month. The patient
population and other external
factors such as change in
provider have been stable.
Infections in ICU
Year 1
Year 2
January
3
4
February
4
3
March
3
6
April
4
3
May
3
4
June
4
3
July
5
5
August
3
6
September
4
3
October
3
3
November
7
6
December
4
3
Total
47
49
9
The nurse manager who serves on the quality team wants to
discover whether the infections are in control within 95.5%
confidence limits.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
9
Control Charts for Attributes: c-Chart Example Solution
If we consider each month as a sample of bad quality outcomes,
for 24 samples we have a total of 96 quality defects (infections),
and the average would be: c = 96/24 = 4.0.
Since the z-value for 95.5% confidence level is equal to 2, using
formulas we obtain:
UCL  c  z c  4  2 4  4  2 * 2  8.
LCL  c  z c  4  2 4  4  2 * 2  0.
10
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
10
ABC Medical Center Infection Control Monitoring
Infections per month
UCL=8
c 4
LCL=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
Sample number
The resulting control chart based on 2 sigma limits indicates that
the process is “in-control”. Typically, the control chart will include
lines connecting the samples.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
11
11
Control Charts for Attributes: p-Chart
The proportion of defects in a process can be monitored
using a p-chart that has binomial distribution as its
theoretical base. The center of the p-chart represents the
average for defects and LCL and UCL are calculated as:
UCL  p  z
p (1 p )
n
LCL  p  z
p (1 p )
n
12
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
12
Source: Quantitatve Methods in Health Care Management
Control Charts for Attributes: p-Chart
The indicator Family Satisfaction,
which is part of the National Hospice
and Palliative Care Organization’s
survey, reflects the percentage of
respondents who would not
recommend the hospice services to
others. The following data are from
Holistic Care Corporation’s
completed surveys from 200
families each month during a year,
showing the number of respondents
each month who expressed
dissatisfaction with the
organization’s services.
Months
Dissatisfied
Patient
Families
Percent
Dissatisfied
January
12
0.060
February
14
0.070
March
16
0.080
April
14
0.070
May
25
0.125
June
14
0.070
July
15
0.075
August
16
0.080
September
14
0.070
October
14
0.070
November
24
0.120
December
14
0.070
Total
192
0.080
13
The manager in charge of quality wishes to construct a control chart for this data within
95.5% confidence intervals.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
13
Control Charts for Attributes: p-Chart
Solution:
First, we need to estimate the proportion mean,
p
Total number of quality infractions
192
192
= -------------------------------------------- = ----------- = ------- = .08
Total number of observations
12(200)
2400
Since the z value for the 95.5% confidence level is equal to
2.0, using formulas we obtain:
UCL  .08  2
.08(1.08)
200
 0.118.
LCL  .08  2
.08(1.08)
200
 0.042.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
14
Fall 2009
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Proportion of Families Dissatisfied
Holistic Care Corporation’s Quality Monitoring
UCL=0.118
p  .08
LCL=0.042
1
2
3
4
5
6
7
8
9
10
11
12
Sample number
The resulting control chart based on 2 sigma limits indicates that the process is not “in-control”.
Since we are measuring dissatisfaction, points above the UCL are cause for concern.
Typically, the control chart will include lines connecting the samples.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
15
15
Control Charts for Variables
Mean Charts - Standard Deviation Approach.
In general the population standard deviation is unknown, and so the average of sample means (x )
and the standard deviation of sample distribution σ
are used to construct the confidence limits as:
UCL  x  z x
.
LCL  x  z x
where σ x  s / n
16
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
16
Source: OZCAN Figure 12.7 Use of Mean and Range Charts
UCL
Process
Mean
LCL
Stable mean, increasing range process
UCL
LCL
17
Increasing mean, stable range process
ISE 491 Dr. Joan Burtner
Mean indicator
Ozcan Chapter 12 Part 2
Range indicator
Fall 2009
17
Control Charts for Variables: Mean Chart, σ Method
Example 12.3
With a time-motion study,
the IV startup process has
been examined in a medical
center nursing unit for five
weekdays to determine
whether in the future,
additional training of nurses
is required. Each day 9 new
patients’ IV startups were
observed and the
measurements recorded in
minutes, as shown below.
Construct 99.7% (z = 3)
confidence limits for IV
startup times.
ISE 491 Dr. Joan Burtner
Observation
Day1
Day2
Day3
Day4
Day5
1
5.1
4.9
5.5
6.1
6.0
2
5.4
5.7
5.6
5.8
5.2
3
5.5
6.3
5.3
5.9
6.3
4
5.8
7.5
4.9
6.0
5.0
5
5.6
5.8
5.2
6.2
5.5
6
5.8
5.9
5.4
5.7
5.1
7
5.3
5.5
6.4
4.8
5.9
8
4.9
5.8
7.5
6.3
5.3
9
6.2
5.5
5.8
5.9
4.8
Ozcan Chapter 12 Part 2
Fall 2009
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18
Control Charts for Variables: Mean Chart, σ Method
Solution
Observation means for
each day (sample) are
calculated and are
shown in the last rows
of the following table.
Sample
x
Day-1
Day-2
5.51
s
5.88
Day-3
5.73
Day-4
5.86
Day-5
5.46
0.6
= (5.51+5.88+5.73+5.86+5.46) ÷ 5 = 5.69.
with z = 3, n = 9 observations per sample (day), and s = 0.6, we
obtain:
x
UCL  5.69  3(0.6 / 9 )  5.69  3(0.2)  6.29.
LCL  5.69  3(0.6 / 9 )  5.69  3(0.2)  5.09.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
19
Fall 2009
19
Control Charts for Variables: Mean Chart, Range Method
Another way to construct a mean chart is to use the average
of sample distribution ranges,. This approach requires a
factor to calculate the dispersion of the control limits.
UCL  x  A2 R
.
UCL  x  A2 R
where A2 is a factor based on sample size
See Table 12.1 for actual values.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
20
Fall 2009
20
Table 12.1 Factors for Determining Control Limits for Mean and Range Charts
(for 3-sigma or 99.7% confidence level)
Sample Size
n
Factor for Mean Chart,
A2
Factors for Range Chart
LCL, D3
UCL, D4
2
1.88
0
3.27
3
1.02
0
2.57
4
0.73
0
2.28
5
0.58
0
2.11
6
0.48
0
2.00
7
0.42
0.08
1.92
8
0.37
0.14
1.86
9
0.34
0.18
1.82
10
0.31
0.22
1.78
21
Source: p. 143, Operations Management by Rusell & Taylor, 1995.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
21
Control Charts for Variables: Mean Chart, Range Method
Example 12.4
During 5 weekdays, each day the number minutes spent for each
of 10 patient registration operations were observed in a time
study as follows:
Observation
Day-1
Day-2
Day-3
Day-4
Day-5
1
10.2
10.3
8.9
9.5
10.5
2
9.7
10.9
10.5
9.7
10.2
3
10.3
11.1
8.9
10.5
10.3
4
8.9
8.9
10.5
9.8
10.9
5
10.5
10.5
9.8
8.9
11.1
6
9.8
9.7
10.2
10.5
9.8
7
10.0
8.9
8.9
10.4
9.5
8
11.3
10.5
10.5
8.9
9.7
9
10.7
9.8
9.7
10.5
10.5
10
9.8
11.3
10.5
9.8
8.8
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
22
22
Control Charts for Variables: Mean Chart, Range Method
Solution
The overall mean for each
sample and range is required to
Sample
Day-1
Day-2
apply the formulas, using the
Maximum
range approach. Here each day
11.3
11.3
is considered as a sample. The
Minimum
8.9
8.9
range is calculated by taking the
Range
2.4
2.4
difference between the maximum
and minimum of each sample
10.12
10.19
(day). The, mean for each day
also is calculated and shown as
follows:
= (10.12+10.19+9.84+9.85+10.13) ÷ 5 = 10.03.
x
Day-3
Day-4
Day-5
10.5
10.5
11.1
8.9
8.9
8.8
1.6
1.6
2.3
9.84
9.85
10.13
x
R
= (2.4+2.4+1.6+1.6+2.3) ÷ 5 = 2.06.
UCL = 10.03 + 0.31 (2.06) = 10.67.
23
LCL = 10.03 – 0.31 (2.06) = 9.39.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
23
Control Charts for Variables: Range Charts
.
Process dispersion is best monitored by range charts. The
control limits for range charts are constructed using
factors. To calculate LCL, factor score D3 is obtained from
a factor chart (Table 12.1) based on the number of
observations in the sample distributions. Similarly, to
calculate UCL, factor score D4 is required. Control limits
for range charts using these factor scores are then
constructed as follows:
UCL  D4 R
LCL  D3 R
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
24
Fall 2009
24
Control Charts for Variables: Range Chart Example
Example 12.5
Use the information provided in Example 12.4 to
construct a range chart.
Solution
For n = 10, D3 and D4 from Table 12.1 are 0.22 and 1.78,
respectively. Using formulas we obtain:
UCL = 1.78 (2.06) = 3.67.
25
LCL = .22 (2.06) = 0.45.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
25
Investigation of Control Chart Patterns
Consistent patterns, even within the UCL and LCL indicate
nonrandom causes that require investigation. Patterns
include upward or downward runs, avoidance or presence
in certain zones, and zigzagging patterns.
.
The essence of the zone test rests on deviation from the
center line by 1-sigma, 2-sigma, or 3-sigma limits. Zone
C, zone B and Zone A are identified by these upper limits,
respectively.
Zone A  x  A2 R
Zone B  x 
2
A2 R
3
Zone C  x 
1
A2 R
3
For ISE 491, we will use the tests listed in Minitab 15 to
evaluate the existence of special cause variation in pcharts, c-charts, range charts and x-bar charts.
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
26
26
Control Chart Zone Test
UCL
+3σ
+2σ
+1σ
CL
x
-1σ
-2σ
-3σ
LCL
27
1
2
3
4
5
6
7
8
9
10
11
12
Sample number
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
27
Process Improvement Methods
Methods for Generating New Ideas:
.
The 5W2H Approach
Brainstorming
Nominal Group Technique
Interviewing
Focus Groups
Quality Circles
Kaizen Teams
Benchmarking
28
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
28
Process Improvement Tools
Tools for Investigating the Presence of Quality
Problems and Their Causes
.
Check Sheet
Histogram
Scatter Diagram
Flow Chart
Cause-and-Effect Diagram
Pareto Chart
29
ISE 491 Dr. Joan Burtner
YasarChapter
A. Ozcan12 Part 2
Ozcan
Fall 2009
29
Check Sheet and Histogram for Emergency Room Wait Times (Ozcan)
Weeks
A
B
C
Wait time
to register
>10
minutes
Registrati
on time >
5 minutes
Wait time
for MD >
15
minutes
6
5
1
2
///
////
//////
/
/
3
////// ///
//////
4
/
/////
5
//
////// //
/////
4
A
B
C
3
2
1
0
Week 1
Week 2
Week 3
Week 4
Week 5
30
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
30
Scatter Diagram
0.14
0.12
Morbidity Ratesty
0.10
0.08
0.06
0.04
0.02
0.00
0
5
10
15
20
31
Number of Infections per Month
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
31
Flow Chart
X-Ray Order Process in an Emergency Department
E.D. MD Requests X-ray
NO
ComputerPrepared Form
Available?
Obtain Form
Hand Write
Patient
Demographic
Information
YES
Physician
Completes Form
32
1
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
32
Healthcare Cause and Effect Diagram
Structure
Functions
Tests not coordinated
Too many steps
Hospital room not
available if admitted
Lab/Rad./ER
Depts. report to
different VPs
Delays in ordering tests
Test errors
Patient
Wait is Too
Long
Private MDs
not on site
Lack of
transporters
Missing paperwork
Lack of feedback
Design is not efficient
Lack of supplies
Lack of incentives
Lack of ER beds
People
ISE 491 Dr. Joan Burtner
Lack of automated system
33
Rewards
Equipment/Material
Ozcan Chapter 12 Part 2
Fall 2009
33
Pareto Diagram
100%
80%
75%
50%
25%
0
Lack of info. Too many
to patient
steps
ISE 491 Dr. Joan Burtner
Delays in
Lack of
test orders automation
Ozcan Chapter 12 Part 2
Ineffective/
Other
voluminous
documentation
Fall 2009
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34
Contact Information
Dr. Joan Burtner
Quality Engineering
[email protected]
35
ISE 491 Dr. Joan Burtner
Ozcan Chapter 12 Part 2
Fall 2009
35