916 samples of size 5 provided thed following 20 samples mea

9-16

samples of size 5 provided thed following 20 samples means for a production process that is belived to be in control

95.72               95.24                   95.18

95.44               95.46                   95.32

95.40               95.44                   95.08

95.50               95.80                   95.22

95.56               95.22                   95.04

95.72               94.82                   95.46

95.60               95.78

a.based on these data what is the estimate mean when the process is in control

b.Assume that the process standard deviation is o=.50 Develop the x control chart for the production process. Assume that the mean of the process is the estimate developed in part (a)

c.Do any of the 20 sample means indicate that the process was out of control

Solution

A) estimated mean =sum of sample means/20

sum of sample means =95.72+95.44+95.40+95.50+95.56+95.72+95.60+95.24+95.46+95.44+95.80+95.22+94.82+95.78+95.18+95.32+95.08+95.22+95.04+95.46

=1908

then estimated mean=1908/20 =95.40

B)

here standerd deviation =0.50

then standerd error

=0.5/square root(20)=0.5/4.47 =0.11

so

UCL    95.40 +3*0.11 =95.40 +0.33 =95.73

    CL 95.40

LCL 95.40 - 0.11*3 =95.40 -0.33 =95.07

C)yes

sample means 95.80,95.78,95.04