Question

n/Obs	1	2	3	4	μ	Range
1	30.1	29.0	28.1	27.0	28.700	2.0
2	31.4	30.7	32.7	29.7	31.020	3.1
3	28.2	29.5	30.6	30.9	29.777	2.5

(a) find ucl for r chart

(b) find lcl for r chart

(c) is it in control?

(d) find ucl for x bar chart

(e) find lcl for x bar chart

(f) is it in control

Answer 1

X bar chart

(d) find ucl for x bar chart

Upper control limit:

X= 29.82

Rbar=2.53

UCL= 29.82 + A2 (2.53)

A2 value from chart

A2=1.023

UCL=29.82 + 1.023 *(2.53) = 32.42

(e) find lcl for x bar chart

UCL=29.82 -1.023 *(2.53)=27.24

(f) is it in control

the observation 32,7 is out of upper control limit , process is out of control

R Chart

(a) find ucl for r chart

D4= 2.574

D3= 0

UCL=2.53*2.57=6.51

(b) find lcl for r chart

LCL=2.53*0=0

(c) is it in control?

all rage values withen the range, process is in control

Thanks