Question

A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.

Hour

R

1

18.4

30

2

16.9

27

3

14.0

25

4

21.2

25

5

21.0

24

6

33.0

23

7

19.3

18

8

15.8

14

9

20.0

12

10

14.0

11

Total: 193.6 209


1. Referring to the table, suppose the supervisor constructs an   chart to see if the process is in-control. What are the lower and upper control limits of this chart?

A. 12.92, 25.80

B. 8.59, 32.13

C. 7.30, 31.42

D. 19.36, 20.90

2. Referring to the table, suppose the supervisor constructs an R chart to see if the variability in collection times is in-control. What are the lower and upper control limits for this R chart?

A. 4.66, 37.14

B. 19.76, 20.90

C. 0, 44.18

D. 7.70, 31.82

3. Which expression best describes the R chart ?

A. A point is outside of the control limits

B. Hugging the center line

C. Decreasing trend

D. in-control

Answer 1

1.

​​​​​​Ans.:- C. 7.30, 31.42

bolun. Here n = 5 individuals per hour Bor period o2 John we have given values o2 X ond R 301 period of To by Loy 5 individuals -per Given IX-193:6 ER žt ZX N. hour i N = 10 209 | * 1936 19.36 10 š= 19.36 I X 209 20.9 10 R-1ER N. R=20.9 control limits for x chart are lower controllimit Ă - AR upper controllimit R 1 - Here : n=5 C subgroup size) .: A2 = 0.577 lower control limit Ž - A₂ R 19.36 – 0.577 * 20.9 19.36 – 12.0593 7.3001 7.30 Upper conto limit = 7+ AR Ž + A₂ R 201 19.36 +1.577 * 2o.9 - 19.36+ 12.0593 31.4193 ~ 31:42 lower and upper control frmits of T-chaul are Ans. = 7.30, 31,42

2.

We know the control limits for R chart are given by,

Lower control limit = $D_{3}*\bar {R}$

Upper control limit = $D_{4}*\bar {R}$

Here subgroup size is 5 for which &

Lower control limit = 0*20.9 = 0

Upper control limit = 2.1138 * 20.9 = 44.178 = 44.18

Ans.:- C. 0, 44.18

3.

Here control limits of R chart are

Lower control limit = 0 & Upper control limit = 44.18

Here all R points are clearly within the control limits so R chart is in-control

Ans.:- D. in-control