Question

QUESTION 10 10)-12) 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 B 1 18.4 30 2 16.9 27 3 140 25 4 21.2 25 5 21.0 24 6 33.0 23 7 193 18 8 14 9 200 12 10 14.0 11 Total: 193.6 209 15.8 Referring to the table, suppose the supervisor constructs an X chart to see if the process is in-control. What are the lower and upper control limits of this chart? 19.36, 20.90 8.59, 32.13 7.30, 31.42 12.92, 25.80

Answer 1

Question 10

Ans.:- 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

Question 11

Ans.:- 0, 44.18

5 D4 R = 2:113* 20.9 = 44.199 = 44.18 control limits for Ř chart are given by lower bound = lower controllimit = D3 R upper bound = upper control limit = 04 R Here bupgroup size is 5 = D3=0 and 04=2.11 : lower bound = D3 Ř = 0 * 20.9 = 0 ... Suppose supervisor constructs R chart ; lower and upper control limits for R-chart are Ans. = 0, 44.18

Question 12

Control limits for R chart are given by

Lower control limit = 0

Upper control limit = 44.18

All the R points lies within the control limits of R chart so process is for R-Chart

Ans. in-Control