Question

University Hospital has been concerned with the number of errors found in its billing statements to patients. An audit of 100 bills per week over the past 12 weeks revealed the following number of errors:

Develop control charts with z = 3: (a) CL, (b) UCL, (c) LCL. (If the lower control limit is negative, round the LCL to zero and all other answers to 2 decimal places, e.g. 15.25.)

CL:

UCL:

LCL:

Is the process in control?

Week		Number of Errors
1		4
2		5
3		6
4		6
5		3
6		2
7		6
8		7
9		3
10		4
11		3
12		4

Answer 1

To solve this given problem, we'll first find the mean and standard deviation of the five samples through MS Excel functions Average and STDEV respectively

The mean of the given data = 4.42

The Standard deviation of the given data = 1.56

Sample size = n = 10

Since the required sigma level = 3

UCL = Mean + [3 x (SD / Sqrt(n)] = 4.42 + [3 x (1.56/10)] = 4.89

LCL = Mean - [3 x (SD / Sqrt(n)] = 4.42 - [3 x (1.56/10)] = 3.95

So the control limits are (3.95, 4.89)

Since, many values fall outside the control range of (3.95, 4.89), the process is out of control.