Question

Suppose that you have a process that is stable with data for a critical characteristic that is known to be normally distributed.  For this example, assume that the mean is known to be 42.18 and the standard deviation is 0.21.  The specifications for this process are LSL = 41 and USL = 43.  Solve the following:

1. What is the z-score of the LSL?
2. What percentage of the product will measure below the LSL for this characteristic?
3. What is the z-score of the USL?
4. What percentage of the product will measure above the USL for this characteristic?
5. What is the total DPMO for this process?

Answer 1

1)z-score of the LSL =(x-mean)/standard deviation =(41-42.18)/0.21 =-5.6190

2)percentage of the product will measure below the LSL for this characteristic =9.60*10^-7 %

(from excel function : normsdist(-5.62)*100)

3)

z-score of the USL =(43-42.18)/0.21 =3.9048

4)

percentage of the product will measure above the USL for this characteristic =0.0047 %

(from excel function : (1-normsdist(3.9048))*100)

5) total DPMO for this process =proportion outside control limt *10⁶ =((0.0047+9.60*10^-7)/100)*10⁶

=47.2 DPMO