Sample Measurements 1 17 15 15 17 2 16 25 18 25 3 23 24 23 22 What are the three

Question

Sample

Measurements

1

17

15

15

17

2

16

25

18

25

3

23

24

23

22

What are the three sigma upper and lower control limits for the MEAN chart?

A)22 and 18 B) 23.29 and 16.71 C) 23.16 and 16.84 D) 23.5 and 16.5

Is the machine producing the circular product in control?

A) It cannot be decided because of incomplete information B) No, the machine is not in control C) Yes, the machine is in control D) The machine is not capable, so the machine is not in control

Sample

Measurements

1

17

15

15

17

2

16

25

18

25

3

23

24

23

22

Explanation / Answer

Solution ;

Q1)First we calculate the sample means and sample ranges of the measurements as

X1-=[17+15+15+17]/4=64/4=16 ; R1=17-15=2

X2-=[16+25+18+25]/4=84/4=21 ; R2=25-16=9

X3-=[23+24+23+22]/4=92/4=23 ; R3=24-2=2

mean of sample mean=X==[16+21+23]/3=60/3=20

mean of sample ranges=R-=[2+9+2]/3=13/3=4.33

For the mean chart the 3 sigma control limit is given as

Upper Control limit= X=+A2R-=20+0.729(4.33)=23.16

Lower Control limit= X=-A2R-=20-0.729(4.33)=16.84

Hence option C is the correct answer.

* value of A2 depends on the sample size. Here for sample size =4, A2 is given to be 0.729.

Q2) Now we see that there lies a point corresponding to sample 1 that falls below Lower 3 sigma control limit (viz. 16<16.84). This tells us that the machine is not in the statistical control. Hence option B is the correct option.

Thank you.

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