ozcan: chapter 12 quality assurance and quality control part 2

Ozcan: Chapter 12Ozcan: Chapter 12Quality Assurance and Quality ControlQuality Assurance and Quality Control

Part 2Part 2

Dr. Joan Burtner, Certified Quality Engineer

Associate Professor of

Industrial Engineering and Industrial Management

Fall 2009ISE 491 Dr. Joan Burtner Ozcan Chapter 12 Part 2

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Topics

Part 1 Quality in Healthcare Quality Experts Quality Certification TQM & CQI Six-Sigma

Part 2 Monitoring Quality through Control Charts

Control Charts for Attributes Control Charts for Variables

Process improvement Methods for Generating New Ideas Tools for Investigation


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Quality Measurement and Control TechniquesProcess 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 randomrandom and non-randomnon-random variation.


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Quality Measurement and Control TechniquesProcess 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 randomrandom variation. If the cause of variation is systematic, not natural, and thesource of the variation is identifiable, the process variationis called non-randomnon-random variation.

In healthcare, non-random variation may occur by notfollowing procedures, using defective materials, fatigue,carelessness, or not having appropriate training ororientation to the work situation, among many reasons.


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Control Limits, Random and Nonrandom Sample Observations

UpperControlLimit(UCL)

LowerControlLimit(LCL)

ProcessMean

Sample number

1 3 4 5 6 7 8 92 10 11 12

Non-random

99

.7%

+3σ

-3σ

Source: Ozcan Figure 12.4 (Modified for Three Sigma Limits)

Non-random


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Control Charts Overview

Attributes

Mean-Charts X-bar Charts

c-chart p-chart

Variables

Range-Charts

σ Method Range Method


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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 because it is based on the binomial distribution.


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Control Charts for Attributes: c-Chart

czcUCL

czcLCL


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Source: Quantitatve Methods Source: Quantitatve Methods in Health Care Managementin Health Care Management

99

Control Charts for Attributes: c-Chart Example

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.


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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:

.82*24424 czcUCL

.02*24424 czcLCL


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ABC Medical Center Infection Control Monitoring

UCL=8

LCL=0

Sample number

1 3 4 5 6 7 8 92 10 11 12 13 14 15 16 17 18 19 20 2221 23 24

Infe

ctio

ns

pe

r m

on

th

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.

4c


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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:

nppzp )1( UCL

nppzp )1( LCL


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Source: Quantitatve Methods in Health Care ManagementSource: Quantitatve Methods in Health Care Management

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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

PercentDissatisfied

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.


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Solution:First, we need to estimate the proportion mean, 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:


p

.118.0208. 200)08.1(08.

UCL

.042.0208. 200)08.1(08.

LCL


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Holistic Care Corporation’s Quality Monitoring

UCL=0.118

LCL=0.042

Sample number

1 3 4 5 6 7 8 92 10 11 12

Pro

port

ion

of F

amili

es D

issa

tisfie

d

08.p

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.


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Mean Charts - Standard Deviation Approach.

Control Charts for Variables

zxUCL

In general the population standard deviation 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:

xzxLCL

where σ x ns /

.


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Source: OZCAN Figure 12.7 Use of Mean and Range Charts

UCL

LCL

ProcessMean

Range indicatorMean indicator

UCL

LCL

Stable mean, increasing range process

Increasing mean, stable range process


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Example 12.3With 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.

Control Charts for Variables: Mean Chart, σ Method

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


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SolutionObservation means for each day (sample) are calculated and are shown in the last rows of the following table.

Control Charts for Variables: Mean Chart, σ Method

x

Sample Day-1 Day-2 Day-3 Day-4 Day-5

5.51 5.88 5.73 5.86 5.46

s 0.6

x = (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:

.29.6)2.0(369.5)9/6.0(369.5 UCL

.09.5)2.0(369.5)9/6.0(369.5 LCL


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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.

.

RAxUCL 2

RAxUCL 2

where A2 is a factor based on sample size

See Table 12.1 for actual values.

Control Charts for Variables: Mean Chart, Range Method


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Table 12.1 Factors for Determining Control Limits for Mean and Range Charts (for 3-sigma or 99.7% confidence level)

Sample Sizen

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.


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Example 12.4During 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


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SolutionThe 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:


x

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 = (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.


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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:.

RDUCL 4

RDLCL 3


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Example 12.5Use 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:

Control Charts for Variables: Range Chart Example

UCL = 1.78 (2.06) = 3.67.

LCL = .22 (2.06) = 0.45.


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Investigation of Control Chart 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.

.

RAxAZone 2 RAxBZone 23

2 RAxCZone 23

1

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.

For ISE 491, we will use the tests listed in Minitab 15 to evaluate the existence of special cause variation in p-charts, c-charts, range charts and x-bar charts.


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Control Chart Zone TestUCL

LCL

Sample number

1 3 4 5 6 7 8 92 10 11 12

CL x

+1σ

-1σ

-2σ

-3σ

+2σ

+3σ


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Process Improvement Methods

Methods for Generating New Ideas:

The 5W2H Approach Brainstorming Nominal Group Technique Interviewing Focus Groups Quality Circles Kaizen Teams Benchmarking

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Yasar A. OzcanYasar A. Ozcan 2929

Process Improvement Tools

Tools for Investigating the Presence of Quality Problems and Their Causes

Check SheetHistogram Scatter Diagram Flow ChartCause-and-Effect Diagram Pareto Chart

.


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Check Sheet and Histogram for Emergency Room Wait Times (Ozcan)

WeeksWeeks

AAWait time Wait time to register to register

>10 >10 minutesminutes

BBRegistratiRegistration time > on time > 5 minutes5 minutes

CCWait time Wait time for MD > for MD >

15 15 minutesminutes

11 ////// ////////////

22 //////// // //

33 //////////// ////// ////////////

44 // //// //////////

55 //////////// //// //////////

0

1

2

3

4

5

6

Week 1 Week 2 Week 3 Week 4 Week 5

A

B

C


31

3131

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0 5 10 15 20

Number of Infections per Month

Morb

idity R

ate

sty

Scatter Diagram


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E.D. MD Requests X-ray

Obtain Form

Hand WritePatient

DemographicInformation

NO

YES

1

Physician Completes Form

Computer-Prepared FormAvailable?

Flow Chart X-Ray Order Process in an Emergency Department


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PatientWait is TooLong

Equipment/MaterialRewardsPeople

FunctionsStructureTests not coordinated

Delays in ordering tests

Test errors

Missing paperwork

Lack of supplies

Lack of ER beds

Design is not efficient

Lack of automated system

Lab/Rad./ER Depts. report to different VPs

Lack of feedback

Lack of incentives

Too many steps

Hospital room not available if admitted

Private MDs not on site

Lack of transporters

Healthcare Cause and Effect Diagram


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100%

75%

50%

25%

0Lack of info.

to patientToo many

stepsDelays intest orders

Lack of automation

Ineffective/voluminous

documentation

Other

80%

Pareto Diagram


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Dr. Joan Burtner Quality [email protected]

Contact Information

ozcan: chapter 12 quality assurance and quality control part 2

Documents

control chartscontrol

control limits

various charts

appropriate control

monitoring quality

attributebased control

attributescontrol charts

quality measurement