Chapter 12.
Quality Control
UCL
+3σ
Zone A  x  A2 R
+2σ
Zone B  x 
1
A2 R
2
+1σ
Zone C  x 
1
A2 R
3
CL
x
-1σ
1
Zone C  x  A2 R
3
-2σ
Zone B  x 
-3σ
1
A2 R
2
Zone A  x  A2 R
LCL
1
2
3
Chapter 12: Quantitatve
Methods in Health Care
Management
4
5
6
7
8
9
10
11
12
Sample number
Yasar A. Ozcan
1
Outline









Quality in Healthcare
Quality Experts
Quality Certification
TQM & CQI
Six-Sigma
Monitoring Quality through Control Charts
– Control Charts for Attributes
– Control Charts for Variables
Process improvement
Methods for Generating New Ideas
Tools for Investigation
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
2
A Broad Definition. . .



Quality refers to the ability of a product or
service to consistently meet or exceed customer
expectations
quality in healthcare is evaluated from differing
perspectives of providers, recipients and thirdparty payers.
Most clinicians accept the Institute of Medicine
(1990) definition: “Quality is the extent to which
health services for individuals and populations
increase the likelihood of desired health
outcomes and are consistent with current
professional knowledge.”
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
3
What is quality?
You are a world renowned surgeon that
has just completed a radical new
surgical technique. There were few
complications, largely due to the
excellence of the hospital’s staff and
technological capabilities.
QUALITY?
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
4
What is Quality?
You are a patient who has just undergone
radical new surgery. Although the surgery
went without technical difficulties, your were
upset at the doctor’s uncaring attitude.
Furthermore, the nursing staff often failed to
respond to your calls, and twice you were
served meat despite the fact that you are a
vegetarian. Also, there was a used bedpan
that sat next to your bed for three days.
QUALITY?
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
5
A question of perspective

Quality of care depends upon who is
making the assessment
– Clinician-- technical components, adequate
skills, resources, conditions
– Patients-- outcomes, interpersonal
processes, amenities, overall satisfaction
– Health Facility Managers- appropriate and
effective utilization
– Community-- availability, access,
reputations, general health status of
community
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
6
Quality Measurement




Clinicians-- cure rates, mortality, morbidity
Patients-- patient satisfaction surveys
Health facility managers-- cure rates,
mortality, morbidity, intermediate process
measures (patient falls, infection rates,
medication errors, appropriate staffing, etc.)
Community-- area service distribution,
insurance coverage, incidence and prevalence
rates, etc.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
7
Figure 12.1 Quality Measurement
Structure
Process
Outcome
Inputs
Conversion Process
(Throughput)
Outputs
Patient,
provider labor
equipment
supplies, etc.
Chapter 12: Quantitatve
Methods in Health Care
Management
Various hospital
and medical services
transform poor health
to wellness for patients
(diagnosis, procedures,
treatments)
Yasar A. Ozcan
Treated
Patient
8
Quality Measurement
Quality Gaps
Another
way to look at the maintenance of quality is how
mistakes are to be avoided – design mistake-proof processes
across the whole spectrum of the care, to reduce undesired
outcomes.
Variance
in diagnostic and therapeutic interventions and the
associated errors hamper the delivery of safe, effective
patient care and add to poor outcomes.
To
minimize the variation and the errors – sometimes
euphemistically called “quality gaps” – and work toward
completely eliminating them are major goals for healthcare
systems.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
9
Quality Measurement
Quality Gaps
Chassin (1998) classifies the underlying causes of “quality
gaps” into three categories:
1) Over-utilization. When the potential benefit of a therapy
is less than its risk, overuse of health services affects the
quality of care. Pressures for overuse of services may come
from either providers or patients.
2) Under-utilization. A patient’s lack of insurance or
insurance that has high co-payments and deductibles can
cause under-utilization of necessary health care.
3) Miss-utilization. Avoidable complications, negligent care,
mistakes, and mishaps create miss- utilization of services.
Healthcare providers who generate such conditions harm the
quality of patient care and produce poor outcomes; they also
waste the organization’s resources and increase lengths of
stay.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
10
Quality Measurement
Healthcare
providers do have an arsenal of methods to deal
effectively with the problems affecting quality of care.
They
include the programs called quality control (QC), total
quality management (TQM), continuous quality improvement
(CQI), reengineering, and Six-Sigma.
All
these programs include data gathering, analysis and
statistical monitoring to identify the problem and its cause.
Nevertheless,
the crux of the solution to quality problems
lies in changing human behavior, changing minds to perform
care in new ways.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
11
Quality Experts




Deming-- poor quality caused by the system, not
employees; management’s responsibility to correct
system;” use 14 points to reduce variation caused by
special causes (correctable) and not common (random)
causes of variation.
Juran-- 80% of defects are controllable; three
elements: quality planning, quality control, and
continual quality improvement
Crosby-- zero defects; quality is free
Isikawa-- cause and effect diagrams, quality circles
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
12
Quality Certification



Organizations can earn awards or achieve
certification/accreditation by international organizations or
by their own trade organizations; for instance, hospitals
are evaluated periodically by the Joint Commission on
Accreditation of Healthcare Organizations (JCAHO).
For the medical group practices, the Medical Group
Management Association (MGMA) is the principal voice.
MGMA leads the profession and assists members through
information, education, networking and advocacy” (MGMA,
2004).
Quality is always a major concern in those advocacy and
accreditation bodies.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
13
Quality Certification




ISO 9000
Set of international standards on quality management
and Quality assurance, critical to international
Business
ISO 9000 series standards, briefly, require firms to
document their quality-control systems at every step
(incoming raw materials, product design, in-process
monitoring and so forth) so that they’ll be able to
identify those areas that are causing quality problems
and correct them.
ISO 9000 requires companies to document everything
they do that affects the quality of goods and services.
– Hierarchical approach to documentation of the
Quality Management System
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
14
Total Quality Management


A philosophy that involves everyone in an
organization in the quest for quality, with
customer satisfaction as the driving force
TQM involves:
– finding what customers want
– designing services to meet customer needs
– designing mistake proof delivery process
“pakayoke”
– monitoring results and continuous
improvement
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
15
TQM, cont.



TQM requires:
– continual improvement
– competitive benchmarking
– employee empowerment
– team approaches
– knowledge of tools
Quality at the source-- each worker responsible for
his/her own work
Quality function deployment-- involve customers in
service design
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
16
Controlling Quality



Quality control focuses on the conversion of
inputs into outputs, i.e., the processes
Goal is to reduce the need for inspection of
control efforts
Quality assurance efforts occurring during
production of services are referred to as
statistical process control
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
17
Figure 12.2 The Deming Wheel/Shewhart Cycle
Plan
Act
Do
Check
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
18
Continuous Quality Improvement



A philosophy seeking to make never-ending
improvements to the process of converting inputs into
outputs
Kaizen-- Japanese term referring to CI
Environment must be conducive to CI
– appropriate vision statement, strategies, tactics
– management style encouraging trust, openness
– adherence to stated philosophy
– reward/incentive systems
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
19
Continuous Quality Improvement
1)
2)
3)
4)
5)
6)
7)
The CQI is a detailed version of a PDSA cycle that
comprises:
selecting a process that needs an improvement
studying and documenting the current process seeking
ways to improve it
designing an improved process
implementing the new process
monitoring and evaluation
documenting the process if it worked successfully and
publicizing it through the healthcare organization
if it did not achieve its goals, re-starting from step 1.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
20
Six-Sigma
•Six- Sigma is one of the latest quality improvement
concepts to have emerged during the 1990’s. Its
name comes from the measure of variation from the
normal distribution (six standard deviations).
•Adopting a six-sigma strategy as a quality goal
sets tolerance levels for errors (defectives) to
levels that occur only 3.4 times per million
observations.
•The defect rates in healthcare can be defined in
such distinct areas as public health, inpatient care,
ambulatory care, and so on.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
21
Six-Sigma
Healthcare organizations have reduced the deaths
caused by anesthesia from 25-50 per million cases
to 5 per million cases since the 1980s through
improved monitoring techniques, adaptation of
practice guidelines, and other systematic
approaches to reduce errors.
This is one area that comes very close to six sigma
standards (Chassin, 1998).
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
22
Six-Sigma
Deployment of six-sigma to improve the quality of
healthcare and delivery performance can be
considered in the following areas:
a) Clinical excellence
b) Service delivery
c) Service costs, and
d) Patient satisfaction.
The deployment can use either of these
methodological sequences:
DMAIC: define, measure, analyze, improve, and control
DMADV: define, measure, analyze, design, and verify.
DMAIC is generally used to improve existing systems that have
fallen the below six-sigma levels,
DMADV is used to design and develop new processes or products
at six-sigma levels (Stahl, Shultz, and Pexton, 2003).
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
23
Six-Sigma
The essence of six-sigma methodologies is both improvement
of the knowledge and capability of employees, and also
changes behavior through training. Thus six-sigma employs a
classification system that identifies education and training for
employees, project managers and executives.
Emulating karate honors, certification is granted at Green Belt
(GB), Black Belt (BB) and Master Black Belts (MBB) levels.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
24
Six-Sigma
Green Belts (GBs) are the employees who have taken the
training courses on implementing the projects.
Black Belts (BBs) are the project leaders, whose training may
be more intensive; they may complete several projects a year
depending upon their size and scope.
Master Black Belts (MBBs) are generally assigned to an area
that needs improvement (for example, human resources), to
ensure that objectives are set, targets are identified, plans are
made, and resources are secured to implement the projects in
their assigned area.
MBBs may oversee many six-sigma projects at a time, working
with various BBs.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
25
Six-Sigma
Six-sigma projects require BBs and MBBs to have expertise in
basic statistical tools such as Pareto Diagrams, descriptive and
higher level statistics including regression, and statistical
modeling techniques as well as control processes.
In addition to statistical concepts, they are expected
understand project management, finance, leadership,
measurement through socio-metric (survey) analysis,
reliability and validity.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
26
Six-Sigma
Examples of successful six-sigma deployments in healthcare
include:
•reduction of emergency room diversions
•fewer errors in operating rooms’ cart materials
•reduced bloodstream infections in an ICU, and
•improved radiology turnaround time (Stahl, Shultz, and
Pexton, 2003).
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
27
Quality Measurement and Control Techniques
Process Variability
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.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
28
Quality Measurement and Control Techniques
Process Variability
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.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
29
Quality Measurement and Control Techniques
Process Variability
Process variation is the range of natural variability
in a process for which healthcare managers use
control charts to monitor the measurements. If the
natural variability or the presence of random
variation exceeds tolerances set by control charts,
then the process is not meeting the design
specifications.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
30
Figure 12.3 Process Capability
Process Variability
UCL
Process variability meets
and exceeds specifications
Set design specifications
for process capability
Process variability
does not meet
design specifications
LCL
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
31
Figure 12.4 Control Limits, Random and Nonrandom Sample Observations
Non-random
α/2
Upper
Control
Limit
(UCL)
95.5%
+2σ
Process
Mean
-2σ
Lower
Control
Limit
(LCL)
α/2
1
2
3
4
5
6
7
8
9
10
11
12
Sample number
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
32
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 non-occurrences, 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.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
33
Control Charts for Attributes: c-Chart
UCL  c  z c
LCL  c  z c
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
34
Control Charts for Attributes: c-Chart
Example 12.1
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.
Months
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
The nurse manager who serves on the quality team wants to discover whether the
infections are in control within 95.5% confidence limits.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
35
Control Charts for Attributes: c-Chart
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.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
36
Figure 12.5 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
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
37
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
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
38
Control Charts for Attributes: p-Chart
Example 12.2
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
The manager in charge of quality wishes to construct a control chart for this data within 95.5%
confidence intervals.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
39
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.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
40
Figure 12.6 Holistic Care Corporation’s Quality Monitoring
Proportion of Families Dissatisfied
UCL=.118
p  .08
LCL=0.042
1
2
3
4
5
6
7
8
9
10
11
12
Sample number
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
41
Figure 12.7 Use of Mean and Range Charts
UCL
Process
Mean
LCL
Stable mean, increasing range process
UCL
LCL
Increasing mean, stable range process
Chapter 12: Quantitatve
Methods in Health Care
Management
Mean indicator
Yasar A. Ozcan
Range indicator
42
Control Charts for Variables
Mean Charts - Standard Deviation Approach.
In general the population standard is unknown, and so the average of sample means (x )
and the standard deviation of sample distribution σ
x
are used to construct the confidence limits as:
UCL  x  z x
LCL  x  z x
.
where σ x  s / n
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
43
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.
Observation
Day-1
Day-2
Day-3
Day-4
Day-5
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
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
44
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
Day-1
Day-2
Day-3
Day-4
Day-5
5.51
5.88
5.73
5.86
5.46
x
s
x
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:
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.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
45
Control Charts for Variables
Mean Charts - Range Approach.
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 from Table 12.1
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
46
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
Source: p. 143, Operations Management by Rusell & Taylor, 1995.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
47
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
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
48
Control Charts for Variables: Mean Chart, Range Method
Solution
The overall mean for each sample and range is required to apply
the formulas, using the range approach. Here each day is
considered as a sample. The range is calculated by taking the
difference between the maximum and minimum of each sample
(day). The, mean for each day also is calculated and shown as
follows:
Sample
Day-1
Day-2
Day-3
Day-4
Day-5
Maximum
11.3
11.3
10.5
10.5
11.1
Minimum
8.9
8.9
8.9
8.9
8.8
Range
2.4
2.4
1.6
1.6
2.3
10.12
10.19
9.84
9.85
10.13
x
x
= (10.12+10.19+9.84+9.85+10.13) ÷ 5 = 10.03.
R
= (2.4+2.4+1.6+1.6+2.3) ÷ 5 = 2.06.
UCL = 10.03 + 0.31 (2.06) = 10.67.
LCL = 10.03 – 0.31 (2.06) = 9.39.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
49
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
.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
50
Control Charts for Variables: Range Chart
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.
LCL = .22 (2.06) = 0.45.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
51
Investigation of Control Chart Patterns
Run-Based Pattern Tests.
A pattern in a control chart described by a sequence of
observations that have similar characteristics is called a “run.”
A simple classification of sample observations with respect to
the center line that identify consecutive patterns is called an
Above/Below run, or A/B run.
.
Up (U) and down (D) runs is another way to classify and
observe patterns. To classify sample observations as U or D, the
first observation is used as a reference point
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
52
Figure 12.8 Identification of Runs
UCL
CL
LCL
1
2
3
4
5
6
7
Sample number
8
9
10
11
12
Observed runs
A
B
1
*
B A
A
2
D
A
A
B
3
U U
1
Chapter 12: Quantitatve
Methods in Health Care
Management
2
U
B
A
4
D
D
D
A B
5
D U
3
Yasar A. Ozcan
4
6
6
D D
5
5
53
Investigation of Control Chart Patterns
Run-Based Pattern Tests.
Control chart patterns identified by runs require statistical
testing of whether the runs are within expectations and hence
the patterns are random, or beyond expectations and hence
non-randomness is present. It has been shown that runs are
distributed approximately normally (Stevenson, 2002, p.436)
and using the z-test the significance of too few or too many
observed runs can be determined as follows:
.
Observed runs  Expected runs
z
S tan dard deviation of runs
A z-value within ±2, which provides 95.5% confidence level,
would show that the runs are random; however, beyond
these values ≤ ±2 ≥, a non-random presence would be
shown.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
54
Investigation of Control Chart Patterns
Run-Based Pattern Tests.
It is necessary to calculate the expected runs and their standard
deviations. The formulas for expected A/B or U/D runs and
their standard deviations are as follows:
E (run) A / B
.
E (run ) U / D
Chapter 12: Quantitatve
Methods in Health Care
Management
N
 1
2
2N  1

3
 (run) A / B 
 (run)U / D
Yasar A. Ozcan
N 1
4
16 N  29

90
55
Investigation of Control Chart Patterns
Example 12.6
Determine the presence/absence of non-randomness for the
example presented in Figure 12.8, with 95.5% confidence limits.
Solution
The example has twelve observations, so N=12. Using the
formulas we get:
E (run ) A / B
E (run) U / D 
12
  1  7. 0
2
 (run) A / B
12  1
11


 2.75  1.66
4
4
(2 * 12)  1
(16 * 12)  29
163
 7.67  (run)U / D 

 1.81  1.35
3
90
90
67
zA/ B 
 0.60 conclude that the A/B runs exhibit randomness.
1.66
5  7.67
zU / D 
 1.98 conclude that U/D runs exhibit randomness.
1.35
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
56
Investigation of Control Chart Patterns
Zone Tests.
An alternative method that is often used by quality control
software packages is called the “zone test.” The essence of the
zone test rests on deviation from the center line by 1-sigma, 2sigma, or 3-sigma limits. Zone C, zone B and Zone A are
identified by these limits, respectively.
.
To create the zones, the formulas for constructing mean chart
with range approach formulas are used. Those formulas,
presented earlier, use A2 from Table 12.1, and the values for this
table were calculated for 3-sigma levels (or 99.7% confidence
level). Thus, in constructing the zones, one must reduce the A2
factor proportionately, according to the sigma level. Since A2 is
designated for 3-sigma, for 2-sigma 2/3 of A2, and for 1-sigma
1/3 of A2 would be appropriate. The zone formulas can be
written as:
Zone A  x  A2 R
1
A2 R
2
1
Zone C  x  A2 R
3
Zone B  x 
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
57
Figure 12.9 Zone test
UCL
+3σ
Zone A  x  A2 R
+2σ
Zone B  x 
1
A2 R
2
+1σ
Zone C  x 
1
A2 R
3
CL
x
-1σ
1
Zone C  x  A2 R
3
-2σ
Zone B  x 
-3σ
1
A2 R
2
Zone A  x  A2 R
LCL
1
2
3
Chapter 12: Quantitatve
Methods in Health Care
Management
4
5
6
7
8
9
10
11
12
Sample number
Yasar A. Ozcan
58
Process Improvement
Methods for Generating New Ideas:
The 5W2H Approach
Brainstorming
Nominal Group Technique
Interviewing
Focus Groups
Quality Circles “Kaizen Teams”
Benchmarking.
.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
59
Process Improvement
Tools for Investigating the Presence of Quality Problems and
Their Causes
Check Sheet
Histogram
Scatter Diagram
Flow Chart
Cause-and-Effect Diagram
Pareto Chart
.
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
60
Figure 12.10. A Check Sheet and Corresponding Histogram
for Emergency Room Wait Times
A
Wait time to
register >10
minutes
Weeks
1
2
3
4
5
6
///
////
//////
/
//////
B
Registration
time > 5
minutes
C
Wait time for
MD > 15
minutes
//////
/
//////
/////
/////
/
///
//
//
5
4
A
B
C
3
2
1
Chapter 12: Quantitatve
Methods in Health Care
Management
0
Week 1
Week 2
Week 3
Week 4
Yasar A. Ozcan
Week 5
61
Figure 12.11 Scatter Diagram
Morbidity Rate
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0
5
10
15
20
Number of Infections per Month
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
62
Figure 12.12 A Flow Chart for the X-Ray Order Process in an Emergency Department
E.D. MD
Requests X-ray
ComputerPrepared Form
Available?
NO
Obtain Form
Hand Write
Patient
Demographic
Information
YES
Physician
Completes Form
1
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
63
Figure 12.13 Cause and Effect Diagram
Structure
Methods/Processes
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 Too
Long
Private MDs
not on site
Boring Environment
Lack of Feedback
Lack of Supplies
Lack of
transporters
Design is
not efficient
Lack of incentives
Lack of ER Beds
Lack of automated
system
People
Chapter 12: Quantitatve
Methods in Health Care
Management
Rewards
Equipment/Material
Yasar A. Ozcan
64
Figure 12.14 Pareto Diagram
100%
80%
75%
50%
25%
0
Lack of info. Too many
to patient
steps
Chapter 12: Quantitatve
Methods in Health Care
Management
Delays in
Lack of
test orders automation
Yasar A. Ozcan
Ineffective/
Other
voluminous
documentation
65
The End
Chapter 12: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
66