A normally distributed quality characteristic is monitored through use of an and an R chart. These...

Question

A normally distributed quality characteristic is monitored through use of an and an R chart. These charts have the following parameters (n =4):

Chart	R Chart
UCL = 626.0	UCL = 18.795
Center line = 620.0	Center line = 8.236
LCL = 614.0	LCL = 0

Both charts exhibit control.

(a) What is the estimated standard deviation of the process?

(b) Suppose an s chart were to be substituted for the R chart. What would be the appropriate parameters of the s chart?

(c) If specifications on the product were 610 ??15, what would be your estimate of the process fraction nonconforming?

(d) What could be done to reduce this fraction nonconforming?

(e) What is the probability of detecting a shift in the process mean to 610 on the first sample following the shift (σ remains constant)?

(f) What is the probability of detecting the shift in part (e) by at least the third sample after the shift occurs?

David · Accepted Answer

Given that: 4n   
626.0 18.795
620.0 8.236
614.0 0
x chart RChart
UCL
CL
LCL


a) 
What is the estimated standard deviation of the process? 
8.236
ˆ
2.059
4
 


Hence, the required estimated standard error is: 4.
b) 
The appropriate parameters of the s chart is, 
 
4
ˆ
0.9213 4
3.865
xS C 


 
 
 
4
3
2.266 3.685
8.351
0 3.685
0
S
S
UCL B S
LCL B S







c) 
What would you be your estimate of the process fraction nonconforming? 
   
   
 
ˆ
1
ˆ ˆ
595 620 625 620
1
4 4
6.25 1 1.25
0.0000 1 0.8944
0.0000 0.1056
0.

A normally distributed quality characteristic is monitored through use of an and an R chart. These charts have the following parameters ( n =4): Chart R Chart UCL = 626.0 UCL = 18.795 Center line =...

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