Question

2. 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.

Answer 1

In usual notation ,

For n = 6, we have A₂ =0.483, D₃ =0, D₄ = 2.004

Chart

R Chart, since all tha ranges fall within the control line, the process variability is in control.

From X bar Chart, the process average is out of control since the sample means corresponding to 3rd, 4th, 8th, 9th ,15th and 20th samples lie outside the control limits.

From