# Relating DPM, Sigma Quality, and Centering

B

#### bamsler

Hello all,

I am an operations student at Purdue University. I am having trouble figuring out how to compute the following problems:

1. Compute DPM for a process, having 4.5-sigma quality with 1.5-sigma off-centering. The result is
a. 2,700
b. 1,350
c. 233
d. 3.4

2. If a centered process has a Cp value of 1.5, then the sigma value of the process is
a. 1.5
b. 3
c. 4
d. 4.5

Any help on understand how to arrive at the correct answer would be very much appreciated.

--B

T

#### t.PoN

Q1: b. 1350
Q2: d.4.5

Solution:
Q1:
Draw a normal distribution to understand, the sum of area (z score)

Proportion within specification = 0.99865
Proportion of defects = 1-0.99865 = 0.00135
DPM = 1,000,000 * 0.00135 = 1350

Q2:
Cp = (USL - LSL)/6sigma
1.5 = ((X'+ysigma) -(X'-ysigma))/6sigma
1.5 = 2y/6
y=4.5

Last edited by a moderator:

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
well, the math part is fairly easy but rather than doing the math for you, can you tell us what you don't understand? that way you learn something in addition to being able to get the right answer on these two questions.

I will say that the questions are poorly worded - especially the first one. it is not clear if the 4.5 sigma level is after the 1.5 sigma shift or before the shift. (aside from the fact that anyone still teaching the 1.5 sigma shift is horribly behind the times and is teaching bad statistics)

Also it is not clear if you have been taught to include BOTh tails for defect rate calculations or only one tail. this will matter in getting the answer yoru instructor wants you to get.

tPon - can you work out your math for question 1? are you using both tails (aka Zbench approach)