Problem 1. The Watson Electric Company produces incandescent light bulbs. The following data on the

Problem 1. The Watson
Electric Company produces incandescent light bulbs. The following data on the number of lumens
for 40-watt light bulbs were collected when the process was in control.

Sample
1
2
3
4

1
614
602
598
600

2
597
601
590
606

3
581
603
585
599

4
620
605
595
588

5
a) (15
points) Calculate the control limits for an R-chart.
b) (15
points) Calculate the control limits for an x-bar chart
c) (10
points) Since these data were collected, some new employees were hired. A new sample obtained the following
readings: 575, 603, 623 and 583. Is the process still in control? (hint: use
the original sample set as a benchmark to assess the new sample)

Problem2:

An
insurance company wants to design a control chart to monitor whether
insurance claim forms are being completely correctly. The company intends to
sue the chart to see if improvements in the design of the form are effective.
To start the process the company collected data on the number of incorrectly
completed claim forms over the past 10 days. The insurance company processes
thousands of these forms each day, and due to the high cost of inspecting
each form, only a small representative sample was collected each day. The
data and analysis are shown in the table:

Sample
Number
# of Forms

Inspected
Completed

Incorrectly

1
300
10

2
300
8

3
300
9

4
300
13

5
300
7

6
300
7

7
300
6

8
300
11

9
300
12

10
a) (20 points) Assume that the process is “in control” during past
10 days. Calculate the mean and sigma.
b) (20 points) Calculate the upper control limit and the lower
control limit (use a multiple of 3 times sigma for the control limits).

Problem
3: (20 points) C-Spec, Inc. is attempting to determine
whether an existing machine is capable of milling an engine part that has a
key specification of 4±0.003 inches. After a trial run on this machine,
C-Spec has determined that the machine has a sample mean of 4.001 inches with
a standard deviation of 0.002 inch.

Should C-Spec use this
machine to produce this part? Why?

300
8
595
609
608
604