Question

In: Operations Management

Data entry clerks at ARCO key in thousands of insurance records each day. They have just...

Data entry clerks at ARCO key in thousands of insurance records each day. They have just completed a new training program and want to establish a control chart based on the results of this training. Each day random samples of the work of the clerks were collected. The results are shown in the table below. Two hundred records were sampled daily and examined for errors. The number of records with errors was counted.

Day

Number of Records with Errors

Day

Number of Records with Errors

1

14

11

12

2

10

12

14

3

6

13

10

4

8

14

12

5

10

15

10

6

10

16

12

7

8

17

12

8

8

18

13

9

6

19

11

10

4

20

10

a) You want to set control limits for the proportion of records with errors. Assume that the past twenty days performance is adequate for establishing the control limits and performing the analysis. Using 95% control limits, what are the upper and lower control limits for the proportion of records with errors? Calculate your proportion defective and the lower and upper control limits to 3 decimal places (0.xxx). Assume that the data provided is sufficient for performing a statistical analysis.

b) Plot the control chart and the sample values.

c) What would you conclude about the process, in other words, is the process in control? Explain your decision.  

d) Suppose the industry’s lower and upper control limits are 0.01 and 0.06 respectively. What can this insurance company conclude about its process relative to the industry standards?

Solutions

Expert Solution

a.The required control chart is p-chart.For 95 % confidence interval, the z value =1.96

we first calculate p-bar i.e the center line

p-bar =sum of np values/sum of n values =200/4000=0.050

Next, we calculate Sp =sqrt(p-bar(1-p-bar)/n))

=sqrt(0.050*(1-0.95)/200))

=0.0154

UCLp =p-bar+z *Sp=0.050+1.96*0.0154=0.080

LCLp=p-bar-z*Sp=0.050-1.96*0.0154=0.020

Calculations are as shown below:

b.Control chart is as shown below

c.The process is in control because all the sample values lie within the control limits as clearly shown in the above control chart.

d.The process is out of control when compared to the control limits of the industry standard because there are sample value that are greater than the upper control limit value of 0.06.

keosha answered 2 years ago
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