Statistical Process Control for Monitoring Failure Rates

Statistical Process Control for Monitoring Failure Rates

Figure07-01

Chapter 7 – Statistical Process Control for Monitoring Failure Rates
AMI, aspirin administrered at arrival, n = 20
Figure 7.1 – Indicators of Unstable Systems
Sample # p Ctr Line UCLp LCLp
Sample 1 1 0.05 0.0875 0.2771 0.0000
2 3 0.15 0.0875 0.2771 0.0000
3 4 0.20 0.0875 0.2771 0.0000
4 3 0.15 0.0875 0.2771 0.0000
5 2 0.10 0.0875 0.2771 0.0000
6 0 0.00 0.0875 0.2771 0.0000
7 3 0.15 0.0875 0.2771 0.0000
8 1 0.05 0.0875 0.2771 0.0000
9 0 0.00 0.0875 0.2771 0.0000
10 4 0.20 0.0875 0.2771 0.0000
11 1 0.05 0.0875 0.2771 0.0000
12 1 0.05 0.0875 0.2771 0.0000
13 0 0.00 0.0875 0.2771 0.0000
14 2 0.10 0.0875 0.2771 0.0000
15 2 0.10 0.0875 0.2771 0.0000
16 4 0.20 0.0875 0.2771 0.0000
17 0 0.00 0.0875 0.2771 0.0000 stable
18 1 0.05 0.0875 0.2771 0.0000
Sample 19 0 0.00 0.0875 0.2771 0.0000
20 3 0.15 0.0875 0.2771 0.0000
Total 35
pbar 0.0875
Sample # p Ctr Line UCLp LCLp
Sample 1 2 0.10 0.0875 0.2771 0.0000
2 3 0.15 0.0875 0.2771 0.0000
3 6 0.30 0.0875 0.2771 0.0000
4 4 0.20 0.0875 0.2771 0.0000
5 4 0.20 0.0875 0.2771 0.0000
6 1 0.05 0.0875 0.2771 0.0000
7 0 0.00 0.0875 0.2771 0.0000
8 1 0.05 0.0875 0.2771 0.0000
9 2 0.10 0.0875 0.2771 0.0000
10 0 0.00 0.0875 0.2771 0.0000
11 1 0.05 0.0875 0.2771 0.0000
12 0 0.00 0.0875 0.2771 0.0000
13 2 0.10 0.0875 0.2771 0.0000
14 1 0.05 0.0875 0.2771 0.0000
15 4 0.20 0.0875 0.2771 0.0000
16 0 0.00 0.0875 0.2771 0.0000
17 3 0.15 0.0875 0.2771 0.0000
18 0 0.00 0.0875 0.2771 0.0000 unstable breaches ucl in period 3
Sample 19 0 0.00 0.0875 0.2771 0.0000
20 1 0.05 0.0875 0.2771 0.0000
Total 35
pbar 0.0875
Sample # p Ctr Line UCLp LCLp
Sample 1 2 0.10 0.0875 0.2771 0.0000
2 2 0.10 0.0875 0.2771 0.0000
3 0 0.00 0.0875 0.2771 0.0000
4 3 0.15 0.0875 0.2771 0.0000
5 2 0.10 0.0875 0.2771 0.0000
6 0 0.00 0.0875 0.2771 0.0000
7 1 0.05 0.0875 0.2771 0.0000
8 1 0.05 0.0875 0.2771 0.0000
9 0 0.00 0.0875 0.2771 0.0000
10 1 0.05 0.0875 0.2771 0.0000
11 0 0.00 0.0875 0.2771 0.0000
12 1 0.05 0.0875 0.2771 0.0000
13 2 0.10 0.0875 0.2771 0.0000
14 1 0.05 0.0875 0.2771 0.0000
15 2 0.10 0.0875 0.2771 0.0000
16 3 0.15 0.0875 0.2771 0.0000
17 2 0.10 0.0875 0.2771 0.0000
18 4 0.20 0.0875 0.2771 0.0000 trend, upward starting in period 11 – unstable
Sample 19 3 0.15 0.0875 0.2771 0.0000
20 5 0.25 0.0875 0.2771 0.0000
Total 35
pbar 0.0875
Sample # p Ctr Line UCLp LCLp
Sample 1 4 0.20 0.0875 0.2771 0.0000
2 2 0.10 0.0875 0.2771 0.0000
3 1 0.05 0.0875 0.2771 0.0000
4 3 0.15 0.0875 0.2771 0.0000
5 4 0.20 0.0875 0.2771 0.0000
6 2 0.10 0.0875 0.2771 0.0000
7 1 0.05 0.0875 0.2771 0.0000
8 4 0.20 0.0875 0.2771 0.0000
9 4 0.20 0.0875 0.2771 0.0000
10 3 0.15 0.0875 0.2771 0.0000
11 1 0.05 0.0875 0.2771 0.0000
12 1 0.05 0.0875 0.2771 0.0000
13 0 0.00 0.0875 0.2771 0.0000
14 1 0.05 0.0875 0.2771 0.0000
15 1 0.05 0.0875 0.2771 0.0000
16 0 0.00 0.0875 0.2771 0.0000
17 1 0.05 0.0875 0.2771 0.0000
18 1 0.05 0.0875 0.2771 0.0000 series of points below (above) the centerline, indicates change in the system
Sample 19 0 0.00 0.0875 0.2771 0.0000 unstable
20 1 0.05 0.0875 0.2771 0.0000
Total 35
pbar 0.0875
Sample # p Ctr Line UCLp LCLp
Sample 1 3 0.15 0.0875 0.2771 0.0000
2 1 0.05 0.0875 0.2771 0.0000
3 2 0.10 0.0875 0.2771 0.0000
4 1 0.05 0.0875 0.2771 0.0000
5 3 0.15 0.0875 0.2771 0.0000
6 1 0.05 0.0875 0.2771 0.0000
7 2 0.10 0.0875 0.2771 0.0000
8 1 0.05 0.0875 0.2771 0.0000
9 2 0.10 0.0875 0.2771 0.0000
10 1 0.05 0.0875 0.2771 0.0000
11 3 0.15 0.0875 0.2771 0.0000
12 0 0.00 0.0875 0.2771 0.0000
13 3 0.15 0.0875 0.2771 0.0000
14 1 0.05 0.0875 0.2771 0.0000
15 2 0.10 0.0875 0.2771 0.0000
16 1 0.05 0.0875 0.2771 0.0000
17 3 0.15 0.0875 0.2771 0.0000
18 1 0.05 0.0875 0.2771 0.0000
Sample 19 3 0.15 0.0875 0.2771 0.0000 pattern, unstable, could be result of different staff, equipment
20 1 0.05 0.0875 0.2771 0.0000
Total 35
pbar 0.0875
Sample # p Ctr Line UCLp LCLp
Sample 1 4 0.20 0.0875 0.2771 0.0000
2 4 0.20 0.0875 0.2771 0.0000
3 4 0.20 0.0875 0.2771 0.0000
4 4 0.20 0.0875 0.2771 0.0000
5 4 0.20 0.0875 0.2771 0.0000
6 4 0.20 0.0875 0.2771 0.0000
7 1 0.05 0.0875 0.2771 0.0000
8 1 0.05 0.0875 0.2771 0.0000
9 0 0.00 0.0875 0.2771 0.0000
10 2 0.10 0.0875 0.2771 0.0000
11 1 0.05 0.0875 0.2771 0.0000
12 0 0.00 0.0875 0.2771 0.0000
13 1 0.05 0.0875 0.2771 0.0000
14 1 0.05 0.0875 0.2771 0.0000
15 0 0.00 0.0875 0.2771 0.0000
16 0 0.00 0.0875 0.2771 0.0000
17 2 0.10 0.0875 0.2771 0.0000
18 1 0.05 0.0875 0.2771 0.0000
Sample 19 0 0.00 0.0875 0.2771 0.0000
20 1 0.05 0.0875 0.2771 0.0000 unstable, series of points close to an upper or lower limits.
Total 35
pbar 0.0875

Figure07-01

p
Ctr Line
UCLp
LCLp
Failure Rate
Stable System

Figure07-02

p
Ctr Line
UCLp
LCLp
Failure Rate
Control Limit Breach

Figure07-03

p
Ctr Line
UCLp
LCLp
Failure Rate
Upward Trend

Figure07-04

p
Ctr Line
UCLp
LCLp
Failure Rates
Series on One Side of Center Line

Figure07-05

p
Ctr Line
UCLp
LCLp
Failure Rate
Pattern

Figure07-06

p
Ctr Line
UCLp
LCLp
Failure Rate
Series Close to Control Limit

Figure07-07

Chapter 7 – Statistical Process Control for Monitoring Failure Rates
Table 7.2 – Errors in Surgical Coding
Figure 7.2 – p chart
Sample Non-conforming sample p CL UCLp LCLp
Jan 2 50 4% 0.0683 0.1754 0.0000
Feb 3 50 6% 0.0683 0.1754 0.0000
Mar 1 50 2% 0.0683 0.1754 0.0000
Apr 2 50 4% 0.0683 0.1754 0.0000
May 3 50 6% 0.0683 0.1754 0.0000
Jun 1 50 2% 0.0683 0.1754 0.0000
Jul 11 50 22% 0.0683 0.1754 0.0000
Aug 7 50 14% 0.0683 0.1754 0.0000
Sep 5 50 10% 0.0683 0.1754 0.0000
Oct 2 50 4% 0.0683 0.1754 0.0000
Nov 3 50 6% 0.0683 0.1754 0.0000
Dec 1 50 2% 0.0683 0.1754 0.0000
Total 41 600
pbar 0.0683
1
incorrect sample p CLst UCLst LCLst Clun UCLun LCLun
Jan 2 50 4% 1 1 0 0.0683333333 0.1753823875 0
Feb 3 50 6% 1 1 0 0.0683333333 0.1753823875 0
Mar 1 50 2% 1 1 0 0.0683333333 0.1753823875 0
Apr 2 50 4% 1 1 0 0.0683333333 0.1753823875 0
May 3 50 6% 1 1 0 0.0683333333 0.1753823875 0
Jun 1 50 2% 1 1 0 0.0683333333 0.1753823875 0
Jul 1 1 0 0.0683333333 0.1753823875 0
Aug 7 50 14% 1 1 0 0.0683333333 0.1753823875 0
Sep 5 50 10% 1 1 0 0.0683333333 0.1753823875 0
Oct 2 50 4% 1 1 0 0.0683333333 0.1753823875 0
Nov 3 50 6% 1 1 0 0.0683333333 0.1753823875 0
Dec 1 50 2% 1 1 0 0.0683333333 0.1753823875 0
30 600
0.05

Figure07-07

0.04 0.0683333333 0.1753823875 0
0.06 0.0683333333 0.1753823875 0
0.02 0.0683333333 0.1753823875 0
0.04 0.0683333333 0.1753823875 0
0.06 0.0683333333 0.1753823875 0
0.02 0.0683333333 0.1753823875 0
0.22 0.0683333333 0.1753823875 0
0.14 0.0683333333 0.1753823875 0
0.1 0.0683333333 0.1753823875 0
0.04 0.0683333333 0.1753823875 0
0.06 0.0683333333 0.1753823875 0
0.02 0.0683333333 0.1753823875 0
p
CL
UCL
LCL
% Claims with Errors
Surgical Coding Accuracy

Figure07-08

0.04 0.05 0.14246621 0 0.0683333333 0.1753823875 0
0.06 0.05 0.14246621 0 0.0683333333 0.1753823875 0
0.02 0.05 0.14246621 0 0.0683333333 0.1753823875 0
0.04 0.05 0.14246621 0 0.0683333333 0.1753823875 0
0.06 0.05 0.14246621 0 0.0683333333 0.1753823875 0
0.02 0.05 0.14246621 0 0.0683333333 0.1753823875 0
0.05 0.14246621 0 0.0683333333 0.1753823875 0
0.14 0.05 0.14246621 0 0.0683333333 0.1753823875 0
0.1 0.05 0.14246621 0 0.0683333333 0.1753823875 0
0.04 0.05 0.14246621 0 0.0683333333 0.1753823875 0
0.06 0.05 0.14246621 0 0.0683333333 0.1753823875 0
0.02 0.05 0.14246621 0 0.0683333333 0.1753823875 0
p
CLst
UCLst
LCLst
Clun
UCLun
LCLun
% Claims with Errors
Surgical Coding Accuracy without July

Figure07-09

Chapter 7 – Statistical Process Control for Monitoring Failure Rates
Figure 7.3– np chart
Sample Non-conforming CL UCLp LCLp
2011 Jan 2 3.4167 8.7691 0.0000
Feb 3 3.4167 8.7691 0.0000
Mar 1 3.4167 8.7691 0.0000
Apr 2 3.4167 8.7691 0.0000
May 3 3.4167 8.7691 0.0000
Jun 1 3.4167 8.7691 0.0000
Jul 11 3.4167 8.7691 0.0000
Aug 7 3.4167 8.7691 0.0000
Sep 5 3.4167 8.7691 0.0000
Oct 2 3.4167 8.7691 0.0000
Nov 3 3.4167 8.7691 0.0000
Dec 1 3.4167 8.7691 0.0000
Total 41
p bar 0.0683
npbar 3.4167

Figure07-09

Non-conforming
CL
UCLp
LCLp
Number of Claims with Errors
Non-conforming Surgical Claims

Figure07-10

Chapter 7 – Statistical Process Control for Monitoring Failure Rates
Table 7.3 – Heart Failure and Smoking Cessation
Sample p Ctr Line UCLp LCLp Figure 7.4 – Breach of Lower Control Limit
2011 Jan 0.50 0.3800 0.7056 0.0544
Feb 0.45 0.3800 0.7056 0.0544
Mar 0.60 0.3800 0.7056 0.0544
Apr 0.55 0.3800 0.7056 0.0544
May 0.40 0.3800 0.7056 0.0544
Jun 0.55 0.3800 0.7056 0.0544
Jul 0.45 0.3800 0.7056 0.0544
Aug 0.50 0.3800 0.7056 0.0544
Sep 0.40 0.3800 0.7056 0.0544
Oct 0.30 0.3800 0.7056 0.0544
Nov 0.35 0.3800 0.7056 0.0544
Dec 0.40 0.3800 0.7056 0.0544
2012 Jan 0.30 0.3800 0.7056 0.0544
Feb 0.45 0.3800 0.7056 0.0544
Mar 0.35 0.3800 0.7056 0.0544
Apr 0.40 0.3800 0.7056 0.0544
May 0.25 0.3800 0.7056 0.0544
Jun 0.40 0.3800 0.7056 0.0544
Jul 0.00 0.3800 0.7056 0.0544
Aug 0.00 0.3800 0.7056 0.0544
pbar 0.3800

Figure07-10

p
Ctr Line
UCLp
LCLp
% Smokers not receiving smoking cessation counseling
Heart Failure Treatment Jan 2011 – Aug 2012

Problem07-03

Chapter 7 – Statistical Process Control for Monitoring Failure Rates
Figure 7.5 – Establishing Valid Control Limits
Sample Non-conforming sample p Ctrline valid UCL valid LCL Valid Ctrline invalid UCL invalid LCL invalid
Jan 2 50 4% 0.0545 0.1509 0.0000 0.0683 0.1754 0.0000
Feb 3 50 6% 0.0545 0.1509 0.0000 0.0683 0.1754 0.0000
Mar 1 50 2% 0.0545 0.1509 0.0000 0.0683 0.1754 0.0000
Apr 2 50 4% 0.0545 0.1509 0.0000 0.0683 0.1754 0.0000
May 3 50 6% 0.0545 0.1509 0.0000 0.0683 0.1754 0.0000
Jun 1 50 2% 0.0545 0.1509 0.0000 0.0683 0.1754 0.0000
Jul 0.0545 0.1509 0.0000 0.0683 0.1754 0.0000
Aug 7 50 14% 0.0545 0.1509 0.0000 0.0683 0.1754 0.0000
Sep 5 50 10% 0.0545 0.1509 0.0000 0.0683 0.1754 0.0000
Oct 2 50 4% 0.0545 0.1509 0.0000 0.0683 0.1754 0.0000
Nov 3 50 6% 0.0545 0.1509 0.0000 0.0683 0.1754 0.0000
Dec 1 50 2% 0.0545 0.1509 0.0000 0.0683 0.1754 0.0000
Total 30 550
pbar 0.0545

Problem07-03

p
Ctrline valid
UCL valid
LCL Valid
Ctrline invalid
UCL invalid
LCL invalid
% Claims with Errors
Valid Control Limits without Special Cause Variation

Problem07-04

Chapter 7 – Statistical Process Control for Monitoring Failure Rates
Table 7.4 (A) – Constant Control Limits Based on Average Sample Size
Month Errors n p Ctr Line UCLp LCLp
Jan 2 45 0.0444 0.0683 0.1754 0.0000
Feb 3 55 0.0545 0.0683 0.1754 0.0000 Figure 7.6 (A) – Constant Control Limits
Mar 1 50 0.0200 0.0683 0.1754 0.0000
Apr 2 48 0.0417 0.0683 0.1754 0.0000
May 3 52 0.0577 0.0683 0.1754 0.0000
Jun 1 44 0.0227 0.0683 0.1754 0.0000
Jul 11 52 0.2115 0.0683 0.1754 0.0000
Aug 7 53 0.1321 0.0683 0.1754 0.0000
Sep 5 51 0.0980 0.0683 0.1754 0.0000
Oct 2 48 0.0417 0.0683 0.1754 0.0000
Nov 3 52 0.0577 0.0683 0.1754 0.0000
Dec 1 50 0.0200 0.0683 0.1754 0.0000
41 50
pbar 0.0683
Table 7.4 (B) – Variable Control Limits Based on Period Specific Sample Size
Errors n p Ctrline UCL LCL
Month 2 45 0.0444 0.0683 0.1812 0.0000
Jan 3 55 0.0545 0.0683 0.1704 0.0000 Min
Feb 1 50 0.0200 0.0683 0.1754 0.0000
Mar 2 48 0.0417 0.0683 0.1776 0.0000 Figure 7.6 (B) – Variable Control Limits
Apr 3 52 0.0577 0.0683 0.1733 0.0000
May 1 44 0.0227 0.0683 0.1824 0.0000 Max
Jun 11 52 0.2115 0.0683 0.1733 0.0000
Jul 7 53 0.1321 0.0683 0.1723 0.0000
Aug 5 51 0.0980 0.0683 0.1743 0.0000
Sep 2 48 0.0417 0.0683 0.1776 0.0000
Oct 3 52 0.0577 0.0683 0.1733 0.0000
Nov 1 50 0.0200 0.0683 0.1754 0.0000
Dec
UCLp
Maximum 0.1824
Minimum 0.1704
Difference 0.0120

Problem07-04

p
Ctr Line
UCLp
LCLp
% Claims with errors
Constant Control Limits

Problem07-05

p
Ctrline
UCL
LCL
% Claims with errors
Variable Control Limits
Chapter 7 – Statistical Process Control for Monitoring Failure Rates
Table 7.5 – Aspirin Administration among AMI Patients
Month Not Given n p Ctr line UCLp LCLp Figure 7.7 – p chart for Aspirin Delivery to AMI Patients
Jan 2 10 0.20 0.1688 0.5241 0.0000
Feb 3 10 0.30 0.1688 0.5241 0.0000
Mar 2 10 0.20 0.1688 0.5241 0.0000
Apr 4 10 0.40 0.1688 0.5241 0.0000
May 3 10 0.30 0.1688 0.5241 0.0000
Jun 3 10 0.30 0.1688 0.5241 0.0000
Jul 2 10 0.20 0.1688 0.5241 0.0000
Aug 3 10 0.30 0.1688 0.5241 0.0000
Sep 1 10 0.10 0.1688 0.5241 0.0000
Oct 0 10 0.00 0.1688 0.5241 0.0000
Nov 1 10 0.10 0.1688 0.5241 0.0000
Dec 1 10 0.10 0.1688 0.5241 0.0000
Jan 0 10 0.00 0.1688 0.5241 0.0000
Feb 1 10 0.10 0.1688 0.5241 0.0000
Mar 0 10 0.00 0.1688 0.5241 0.0000
Apr 1 10 0.10 0.1688 0.5241 0.0000
Total 27 160
pbar 0.1688
UCLp 0.5241
LCLp -0.1866
0.2 0.16875 0.5240612632 0
0.3 0.16875 0.5240612632 0
0.2 0.16875 0.5240612632 0
0.4 0.16875 0.5240612632 0
0.3 0.16875 0.5240612632 0
0.3 0.16875 0.5240612632 0
0.2 0.16875 0.5240612632 0
0.3 0.16875 0.5240612632 0
0.1 0.16875 0.5240612632 0
0 0.16875 0.5240612632 0
0.1 0.16875 0.5240612632 0
0.1 0.16875 0.5240612632 0
0 0.16875 0.5240612632 0
0.1 0.16875 0.5240612632 0
0 0.16875 0.5240612632 0
0.1 0.16875 0.5240612632 0
p
Ctrline
UCL
LCL
% Not Delivered within 2 hrs
Control Limits for Aspirin Administration
% Not Delivered within 2 hrs
Rebased Control Limits for Aspirin Administration
Chapter 7 – Statistical Process Control for Monitoring Failure Rates
Table 7.5 – Aspirin Administration among AMI Patients
Month Not Given n p Ctr line UCLp LCLp Figure 7.7 – p chart for Aspirin Delivery to AMI Patients (for comparison to figure 7.8)
Jan 2 10 0.20 0.1688 0.5241 0.0000
Feb 3 10 0.30 0.1688 0.5241 0.0000
Mar 2 10 0.20 0.1688 0.5241 0.0000
Apr 4 10 0.40 0.1688 0.5241 0.0000
May 3 10 0.30 0.1688 0.5241 0.0000
Jun 3 10 0.30 0.1688 0.5241 0.0000
Jul 2 10 0.20 0.1688 0.5241 0.0000
Aug 3 10 0.30 0.1688 0.5241 0.0000
Sep 1 10 0.10 0.1688 0.5241 0.0000
Oct 0 10 0.00 0.1688 0.5241 0.0000
Nov 1 10 0.10 0.1688 0.5241 0.0000
Dec 1 10 0.10 0.1688 0.5241 0.0000
Jan 0 10 0.00 0.1688 0.5241 0.0000
Feb 1 10 0.10 0.1688 0.5241 0.0000
Mar 0 10 0.00 0.1688 0.5241 0.0000
Apr 1 10 0.10 0.1688 0.5241 0.0000
Total 27 160
pbar 0.1688
UCLp 0.5241
LCLp -0.1866
periods 1-8 0.2750
UCLp 1-8 0.6986
LCLp 1-8 -0.1486
Figure 7.8 – Rebased Control Limits for Aspirin Delivery to AMI Patients
periods 9-16 0.0625
UCLp 9-16 0.2921
LCLp 9-16 -0.1671
Rebased Control Limits p Ctr line UCLp LCLp
Jan 0.20 0.2750 0.6986 0.0000
Feb 0.30 0.2750 0.6986 0.0000
Mar 0.20 0.2750 0.6986 0.0000
Apr 0.40 0.2750 0.6986 0.0000
May 0.30 0.2750 0.6986 0.0000
Jun 0.30 0.2750 0.6986 0.0000
Jul 0.20 0.2750 0.6986 0.0000
Aug 0.30 0.2750 0.6986 0.0000
Sep 0.10 0.0625 0.2921 0.0000
Oct 0.00 0.0625 0.2921 0.0000
Nov 0.10 0.0625 0.2921 0.0000
Dec 0.10 0.0625 0.2921 0.0000
Jan 0.00 0.0625 0.2921 0.0000
Feb 0.10 0.0625 0.2921 0.0000
Mar 0.00 0.0625 0.2921 0.0000
Apr 0.10 0.0625 0.2921 0.0000
0.2 0.16875 0.5240612632 0
0.3 0.16875 0.5240612632 0
0.2 0.16875 0.5240612632 0
0.4 0.16875 0.5240612632 0
0.3 0.16875 0.5240612632 0
0.3 0.16875 0.5240612632 0
0.2 0.16875 0.5240612632 0
0.3 0.16875 0.5240612632 0
0.1 0.16875 0.5240612632 0
0 0.16875 0.5240612632 0
0.1 0.16875 0.5240612632 0
0.1 0.16875 0.5240612632 0
0 0.16875 0.5240612632 0
0.1 0.16875 0.5240612632 0
0 0.16875 0.5240612632 0
0.1 0.16875 0.5240612632 0
p
Ctrline
UCL
LCL
% Not Delivered within 2 hrs
Control Limits for Aspirin Administration
p
Ctr line
UCLp
LCLp
% Not Delivered within 2 hrs
Rebased Control Limits for Aspirin Administration
Chapter 7 – Statistical Process Control for Monitoring Failure Rates
Duclos et al. (2009)
Month n=1114 p pbar UCLp LCLp Figure 7.9 – Duclos et al. SPC Charts
2006 Jan 46 0.03 0.0738 0.1894 0.0000
Feb 49 0.08 0.0738 0.1858 0.0000
Mar 49 0.06 0.0738 0.1858 0.0000
Apr 46 0.07 0.0738 0.1894 0.0000
May 47 0.04 0.0738 0.1881 0.0000
Jun 48 0.12 0.0738 0.1869 0.0000
Jul 49 0.05 0.0738 0.1858 0.0000
Aug 42 0.04 0.0738 0.1947 0.0000
Sep 52 0.04 0.0738 0.1825 0.0000
Oct 52 0.08 0.0738 0.1825 0.0000
Nov 42 0.1 0.0738 0.1947 0.0000
Dec 46 0.13 0.0738 0.1894 0.0000
2007 Jan 48 0.09 0.0738 0.1869 0.0000
Feb 45 0.11 0.0738 0.1906 0.0000
Mar 46 0.11 0.0738 0.1894 0.0000
Apr 47 0.06 0.0738 0.1881 0.0000
May 46 0.03 0.0738 0.1894 0.0000
Jun 45 0.06 0.0738 0.1906 0.0000
Jul 46 0.18 0.0738 0.1894 0.0000
Aug 38 0.01 0.0738 0.2009 0.0000
Sep 44 0.12 0.0738 0.1920 0.0000
Oct 47 0.04 0.0738 0.1881 0.0000
Nov 48 0.04 0.0738 0.1869 0.0000
Dec 47 0.08 0.0738 0.1881 0.0000
pbar 0.0738
Month n=1114 p pbar UCLp LCLp
2006 Jan 46 0.32 0.2092 0.3891 0.0293
Feb 49 0.17 0.2092 0.3835 0.0349
Mar 49 0.14 0.2092 0.3835 0.0349
Apr 46 0.19 0.2092 0.3891 0.0293
May 47 0.21 0.2092 0.3871 0.0312
Jun 48 0.22 0.2092 0.3853 0.0331
Jul 49 0.19 0.2092 0.3835 0.0349
Aug 42 0.21 0.2092 0.3974 0.0209
Sep 52 0.14 0.2092 0.3784 0.0400
Oct 52 0.17 0.2092 0.3784 0.0400
Nov 42 0.2 0.2092 0.3974 0.0209
Dec 46 0.19 0.2092 0.3891 0.0293
2007 Jan 48 0.22 0.2092 0.3853 0.0331
Feb 45 0.19 0.2092 0.3911 0.0273
Mar 46 0.2 0.2092 0.3891 0.0293
Apr 47 0.19 0.2092 0.3871 0.0312
May 46 0.33 0.2092 0.3891 0.0293
Jun 45 0.24 0.2092 0.3911 0.0273
Jul 46 0.4 0.2092 0.3891 0.0293
Aug 38 0.12 0.2092 0.4071 0.0112
Sep 44 0.26 0.2092 0.3931 0.0252
Oct 47 0.19 0.2092 0.3871 0.0312
Nov 48 0.19 0.2092 0.3853 0.0331
Dec 47 0.14 0.2092 0.3871 0.0312
pbar 0.2092
Data reconstructed by the author.
p
pbar
UCLp
LCLp
% Recurrent laryngeal nerve palsy
Duclos et al. Nerve Palsy
p
pbar
UCLp
LCLp
% Hypocalcaemia
Duclos et al. Hypocalcaemia
Chapter 7 – Statistical Process Control for Monitoring Failure Rates
Fasting & Gisvold (2003)
Month n p pbar UCLp LCLp
1997 Jan/Feb 1501 0.0300 0.0250 0.0371 0.0129 Figure 7.10 – Fasting and Gisvold SPC Charts
Mar/Apr 1545 0.0310 0.0250 0.0369 0.0131
May/Jun 1522 0.0300 0.0250 0.0370 0.0130
Jul/Aug 1401 0.0350 0.0250 0.0375 0.0125
Sep/Oct 1623 0.0290 0.0250 0.0366 0.0134
Nov/Dec 1512 0.0240 0.0250 0.0370 0.0130
1998 Jan/Feb 1560 0.0290 0.0250 0.0369 0.0131
Mar/Apr 1511 0.0260 0.0250 0.0370 0.0130
May/Jun 1587 0.0320 0.0250 0.0368 0.0132
Jul/Aug 1397 0.0370 0.0250 0.0375 0.0125
Sep/Oct 1602 0.0230 0.0250 0.0367 0.0133
Nov/Dec 1554 0.0310 0.0250 0.0369 0.0131
1999 Jan/Feb 1559 0.0310 0.0250 0.0369 0.0131
Mar/Apr 1548 0.0290 0.0250 0.0369 0.0131
May/Jun 1601 0.0160 0.0250 0.0367 0.0133
Jul/Aug 1405 0.0210 0.0250 0.0375 0.0125
Sep/Oct 1697 0.0180 0.0250 0.0364 0.0136
Nov/Dec 1322 0.0190 0.0250 0.0379 0.0121
2000 Jan/Feb 1568 0.0140 0.0250 0.0368 0.0132
Mar/Apr 1520 0.0250 0.0250 0.0370 0.0130
May/Jun 1574 0.0220 0.0250 0.0368 0.0132
Jul/Aug 1388 0.0190 0.0250 0.0376 0.0124
Sep/Oct 1701 0.0220 0.0250 0.0364 0.0136
Nov/Dec 1504 0.0260 0.0250 0.0371 0.0129
2001 Jan/Feb 1578 0.0120 0.0250 0.0368 0.0132
Mar/Apr 1539 0.0250 0.0250 0.0369 0.0131
May/Jun 1521 0.0230 0.0250 0.0370 0.0130
Jul/Aug 1426 0.0210 0.0250 0.0374 0.0126
Sep/Oct 1624 0.0260 0.0250 0.0366 0.0134
Nov/Dec 1589 0.0240 0.0250 0.0367 0.0133
Average 1532.6 0.0250
Month n p pbar UCLp LCLp
1997 Jan/Feb 1501 0.03 0.0298 0.0429 0.0129
Mar/Apr 1545 0.031 0.0298 0.0428 0.0131
May/Jun 1522 0.03 0.0298 0.0429 0.0130
Jul/Aug 1401 0.035 0.0298 0.0434 0.0125
Sep/Oct 1623 0.029 0.0298 0.0424 0.0134
Nov/Dec 1512 0.024 0.0298 0.0429 0.0130
1998 Jan/Feb 1560 0.029 0.0298 0.0427 0.0131
Mar/Apr 1511 0.026 0.0298 0.0429 0.0130
May/Jun 1587 0.032 0.0298 0.0426 0.0132
Jul/Aug 1397 0.037 0.0298 0.0434 0.0125
Sep/Oct 1602 0.023 0.0298 0.0425 0.0133
Nov/Dec 1554 0.031 0.0298 0.0427 0.0131
1999 Jan/Feb 1559 0.031 0.0298 0.0427 0.0131
Mar/Apr 1548 0.029 0.0298 0.0427 0.0131
May/Jun 1601 0.016 0.0208 0.0315 0.0101
Jul/Aug 1405 0.021 0.0208 0.0322 0.0094
Sep/Oct 1697 0.018 0.0208 0.0312 0.0104
Nov/Dec 1322 0.019 0.0208 0.0326 0.0090
2000 Jan/Feb 1568 0.014 0.0208 0.0316 0.0100
Mar/Apr 1520 0.025 0.0208 0.0318 0.0098
May/Jun 1574 0.022 0.0208 0.0316 0.0100
Jul/Aug 1388 0.019 0.0208 0.0323 0.0093
Sep/Oct 1701 0.022 0.0208 0.0312 0.0104
Nov/Dec 1504 0.026 0.0208 0.0319 0.0098
2001 Jan/Feb 1578 0.012 0.0208 0.0316 0.0100
Mar/Apr 1539 0.025 0.0208 0.0317 0.0099
May/Jun 1521 0.023 0.0208 0.0318 0.0098
Jul/Aug 1426 0.021 0.0208 0.0322 0.0095
Sep/Oct 1624 0.026 0.0208 0.0314 0.0102
Nov/Dec 1589 0.024 0.0208 0.0316 0.0101
Control Limits 1997 to 1999 Mar/Apr
0.0297857143
Control Limits 1999 May/Jun to 2001
0.0208125
p
pbar
UCLp
LCLp
% Difficult Emergence
Fasting & Gisvold
p
pbar
UCLp
LCLp
% Difficult Emergence
Fasting & Gisvold – Rebased Limits
Chapter 7 – Statistical Process Control for Monitoring Failure Rates
Problem 7.3 – Semmelweis
Month Births Deaths Rate
Jan 1846 336 45 13.4
Feb 293 53 18.1
March 311 48 15.4
April 253 48 19.0
May 305 41 13.4
June 266 27 10.2
July 252 33 13.1
August 216 39 18.1
September 271 39 14.4
October 254 38 15.0
November 297 32 10.8
December 298 16 5.4
Jan 1847 311 10 3.2
Feb 312 6 1.9
March 305 11 3.6
April 312 57 18.3
May 294 36 12.2
June** 268 6 2.4
July 250 3 1.2
August 264 5 1.9
September 262 12 5.2
October 278 11 4.0
November 246 11 4.5
December 273 8 2.9
Jan 1848 283 10 3.5
Feb 291 2 0.7
March 276 0 0.0
April 305 2 0.7
May 313 3 1.0
June 264 3 1.1
July 269 1 0.4
August 261 0 0.0
September 312 3 1.0
October 299 7 2.3
November 310 9 2.9
December 373 5 1.3
Source: Semmelweis I, 1983, The Etiology, Concept, and Prophylaxis of Childbed Fever, The University of Wisconsin Press, Madison WI (originally published 1860) pp. 85, 90-91.
Chapter 7 – Statistical Process Control for Monitoring Failure Rates
Problem 4 – Surgical Infections
Sample
Patient 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
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
5 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Chapter 7 – Statistical Process Control for Monitoring Failure Rates
Problem 7.5 – Readmission Rates
Month Readmits Sample
Jan 3 10
Feb 3 10
Mar 4 10
Apr 3 8
May 3 10
Jun 3 9
Jul 3 10
Aug 3 9
Sep 3 9
Oct 3 10
Nov 3 9
Dec 2 10
Jan 3 10
Feb 2 8
Mar 3 10
Apr 2 9
May 3 10
Jun 2 9
Jul 3 10
Aug 3 10
Sep 2 10
Oct 2 10
Nov 2 8
Dec 2 9

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