A quality control analyst for a light bulb manufacturer is c

A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.

Day

X (in minutes)

R

1

58.5

5.1

2

47.6

7.8

3

64.3

6.1

4

60.6

5.7

5

63.7

6.2

6

57.5

6

7

55

5.4

8

54.9

6.1

9

55

5.9

10

62.7

5

11

61.9

7.1

12

60

6.5

13

58.3

5.9

14

52

5.2

Referring to the table above, suppose the analyst constructs an R chart to se if the variability in production times is in control. What is the lower control limit for this R chart?

a.) 3.37

b.) 4.84

c.) 2.98

d.) 1.34

Day	X (in minutes)	R
1	58.5	5.1
2	47.6	7.8
3	64.3	6.1
4	60.6	5.7
5	63.7	6.2
6	57.5	6
7	55	5.4
8	54.9	6.1
9	55	5.9
10	62.7	5
11	61.9	7.1
12	60	6.5
13	58.3	5.9
14	52	5.2

Solution

Lower Control Limit for R Chart = D₃*R bar

R bar = Mean of Ranges for 14 days = 6

D₃ from the Table = 0.223

Lower Control Limit = 0.223*6 = 1.338 = 1.34

Option D is correct