Consider given Exercise. If you were interested in detecting an improvement in the process using a one-sided limit, what should the minimum sample size be for an α of 0.005? What should it be for an α of 0.05? What conclusions can you draw from these results?
Exercise
The number of heart surgery complications is rare. To monitor the effectiveness of such surgeries, data are recorded on the number of such procedures until a complication occurs. These complications occur independently with a constant probability of occurrence and follow a geometric distribution. Table shows such data for a sequence of 25 complications. It is estimated from past data that the complication rate is 0.1%.
Construct an appropriate control chart and comment on the process assuming a type I error rate of 0.005. What would the control limits be for a type I error rate of 0.05? What factors would influence your selection of the type I error rate?
|
Complication Sequence
|
Number of Procedures
|
Complication Sequence
|
Number of Procedures
|
Complication Sequence
|
Number of Procedures
|
|
1
|
654
|
10
|
1654
|
18
|
1794
|
|
2
|
981
|
11
|
892
|
19
|
1112
|
|
3
|
1508
|
12
|
750
|
20
|
652
|
|
4
|
436
|
13
|
1333
|
21
|
1050
|
|
5
|
1202
|
14
|
1404
|
22
|
1085
|
|
6
|
889
|
15
|
909
|
23
|
1422
|
|
7
|
1854
|
16
|
822
|
24
|
688
|
|
8
|
3068
|
17
|
1609
|
25
|
1095
|
|
9
|
704
|
|
|
|
|