1. Quality inspector took five samples (K=5), each with four observations (n=4), of the length of time for the glue to dry. The analyst computed the mean of each sample and then computed the grand mean. All values are in minutes. Use this information to obtain the upper control limit and lower control lime of the process.

Observationon	1	2	3	4	5	X-bar	R
1	12.11	12.15	12.09	12.12	12.09
2	12.10	12.12	12.09	12.10	12.14
3	12.11	12.10	12.15	12.08	12.13
4	12.08	12.11	12.11	12.10	12.12

1. Determining control limits for means

X-double bar=

R-bar

UCL= X-double +( bar R-bar*A2)

LCL =X-double bar - (R-bar*A2)

A2= Find a factor from table

2. Determining control limits for ranges

R-bar

UCL=R-BAR*d4

LCL= R-bar*D3

D3, and D4= Find a factors from table