Consider given Exercise. However, now assume that the interval between complications follows an exponential distribution. Construct an appropriate control chart and comment on the process assuming a type I error rate of 0.005.
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
|
|
|
|
|