Given Data :
sample sapce = 5 and
after 25 samples have been collected. we calculate x bar =20 and R bar 4.56
a) the three control limits for X bar and R bar are:
So,
The three-sigma control limits for xbar is
lower control limit :
20-0.153*4.56 =19.30232
upper control limit:
20+0.153*4.56 = 20.69768
the three-sigma control limits for R is
lower control limit :
0.459*4.56 =2.09304
upper control limit:
1.514*4.56 = 6.90384
(b)
We use Average of Subgroup Ranges to estimate the process standard
deviation:
= 4.56/3.931
=1.1600
(c)
the conclusion regarding the process capability by assuming that the process output is normally distributed with the specifications are 19(+ or -)5
because the specificantions are within the range
(d)
The probability of not detecting this shift on the first
subsequent sample is
P(X<24) = P((X-mean)/s <(24-20)/1.16001)
=P(Z<3.45)
=0.9997 (from standard normal table)
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Samples of n5 units are taken from a process every hour. The and R values for a particular quality char acteristic are determined. After 25 samples have been collected, we calculate 20 and R 4.56 (a)...
Samples of n5 units are taken from a process every hour. The and R values for a particular quality char acteristic are determined. After 25 samples have been collected, we calculate 20 and R 4.56 (a) What are the three-sigma control limits for x and R? (b) Both charts exhibit control. Estimate the process standard deviation (c) Assume that the process output is normally dis- tributed. If the specifications are 19 t 5, what are your conclusions regarding the process...
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