A production line is in-control, centered and the quality characteristic of inte
ID: 365507 • Letter: A
Question
A production line is in-control, centered and the quality characteristic of interest is normally distributed. The Process Capability Ratio Cpk = 0.90 and the specifications limits (LSL, USL) are (75, 120). (a) How many process standard deviations separate the process mean from the upper specification limit (USL)? (b) What is the DPMO below the lower specification limit? (c) What is the sigma level for the process? (d) Calculate the Zbench and the Sigma Quality Level (SQL) for the process? (e) By how much would the process standard deviation have to be reduced to have a true six sigma (6) process?
Explanation / Answer
a)
Cpk=(USL)/3
0.9 =(USL)/3
therefore: (USL)/ = 0.9* 3 = 2.7
2.7 standard deviations separate the process mean from the USL
b) From the table, the DPMO below the lower specificatio limit at 2.7 sigma level is 1,15,070
c) Sigma level = 2.7 *2 = 5.4
d) Zbench =0.9965-0.0035 = 0.9930
from the Z table, this value is observed at 2.455
thus, Z bench = 2.455
e) ( USL - LSL)/ 6 = 120-75/6 = 7.5
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