Question

1 QUESTION 11 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 X R 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 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? 0, 44.18 7.70, 31.82 19.76, 20.90 4.66, 37.14

Answer 1

Upper & lower limits for R chart are -

LCL = D₃$\bar{R}$

UCL = D₄$\bar{R}$

Where, $\bar{R}$ - average of all sample ranges,

D₃ & D₄ are the constants calculated from the table provided below. Here, supervisor selected randomly 5 individuals per hour, so we take value corresponding to 5 of  D₃ & D₄.

From the given table -

We have -

Ri= 209

From the table - D₃ = 0 & D₄ = 2.114

R 209 ΣR, 20.9 n 10

So, control limits for R chart are -

LCL = D₃$\bar{R}$ = 0$\times$20.9 = 0

UCL = D₄$\bar{R}$ = 2.114$\times$20.9 = 44.1826 $\approx$ 44.18

So, control limits for R chart are (0, 44.18).

Option A is correct.