Question

In: Statistics and Probability

An insurance company samples claim forms for errors created by its employees as well as the...

An insurance company samples claim forms for errors created by its employees as well as the amount of time it takes to process a claim. Repeated samples of six claims are taken over a twenty day period. In the table below are the average times and ranges for each of the samples.

X bar range

24.3 2.8

23.5 2.5

27.2 3.2

27.5 5.8

25.8 3.2

23.5 4

24.9 4.1

20.6 3.4

22.7 7.4

26 3.7

25.5 4.2

23.3 2.5

24.1 3

25.6 2.9

27.1 3.5

24.3 3.0

26.1 3.6

25.2 2.9

26.1 4.2

28.3 4.5

Construct and x bar and R chart. Comment on the operation of the insurance claims department based on this information.

Expert Solution

To construct the Xbar and R chart we will be going in a step by step manner:

Number of sample: 6 claims taken over 20 days period hence the total number of sample is 120.
Calculate : Calculate the average of the ’s. This is the centerline of the control chart.
Calculate Control Limits:
Calculate the R chart limit:

as sample size 6 is below 7, then D3 will be 0 and we have obtained the value from the table of D4 which is 2.004

Now for the A2, we again have taken help of the table and the value is 0.483

Now we will calculate the data for X bar and R chart


				Control Limits, X-bar Chart			Control Limits, R Chart
Sample	Sample Mean	Range		LCL	UCL	Mean	LCL	UCL	R-bar	Range
1	24.3	2.8		23.28324	26.87676	25.08	0	7.45488	3.72	2.8
2	23.5	2.5		23.28324	26.87676	25.08	0	7.45488	3.72	2.5
3	27.2	3.2		23.28324	26.87676	25.08	0	7.45488	3.72	3.2
4	27.5	5.8		23.28324	26.87676	25.08	0	7.45488	3.72	5.8
5	25.8	3.2		23.28324	26.87676	25.08	0	7.45488	3.72	3.2
6	23.5	4.0		23.28324	26.87676	25.08	0	7.45488	3.72	4.0
7	24.9	4.1		23.28324	26.87676	25.08	0	7.45488	3.72	4.1
8	20.6	3.4		23.28324	26.87676	25.08	0	7.45488	3.72	3.4
9	22.7	7.4		23.28324	26.87676	25.08	0	7.45488	3.72	7.4
10	26.0	3.7		23.28324	26.87676	25.08	0	7.45488	3.72	3.7
11	25.5	4.2		23.28324	26.87676	25.08	0	7.45488	3.72	4.2
12	23.3	2.5		23.28324	26.87676	25.08	0	7.45488	3.72	2.5
13	24.1	3.0		23.28324	26.87676	25.08	0	7.45488	3.72	3.0
14	25.6	2.9		23.28324	26.87676	25.08	0	7.45488	3.72	2.9
15	27.1	3.5		23.28324	26.87676	25.08	0	7.45488	3.72	3.5
16	24.3	3.0		23.28324	26.87676	25.08	0	7.45488	3.72	3.0
17	26.1	3.6		23.28324	26.87676	25.08	0	7.45488	3.72	3.6
18	25.2	2.9		23.28324	26.87676	25.08	0	7.45488	3.72	2.9
19	26.1	4.2		23.28324	26.87676	25.08	0	7.45488	3.72	4.2
20	28.3	4.5		23.28324	26.87676	25.08	0	7.45488	3.72	4.5
Mean	25.08000	3.72								3.72

	Factors
	n	A2	D3	D4
	6	0.483	0	2.004

The X bar chart will be like below:

And the R chart will be like below:

From the X bar chart, we can see that the sample number 4,8,9,20 has breached the range limit. But in R chart we can safely say that all the range values are within the limits.

Thanks !!

orchestra answered 2 years ago

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