Question

Consider the two processes below with specifications 100 plus or minus 10:

• Process A: mean of 100, standard deviation of 3
• Process B: mean of 105, standard deviation of 1
• n=5 for both processes

Q. What is the fraction non-conforming for each process?

Answer 1

process 1:

DPMO is calculated using Excel formula

Yield =1-(DPMO/1000000)

99.91% of Items are fall in between USL or 110 and LSL or 90

hence, Fraction non conforming for this process=1-0.9991=0.0009

1	B	C	D	E
2	Continuous process (normally distributed)
3	Mean:	100	DPMO:	858.1
4	Standard Deviation	3	Yield	0.9991
5	LSL:	90
6	USL:	110

Formula:

1	B	C	D	E
2	Continuous process (normally distributed)
3	Mean:	100	DPMO:	=((1-NORMDIST(C6,C3,C4,TRUE))+(NORMDIST(C5,C3,C4,TRUE)))*1000000
4	Standard Deviation	3	Yield	=1-(E3/1000000)
5	LSL:	90
6	USL:	110

process 2:

here, we find that 100% items are falling in between USL or 110 and LSL or 90

so, we can conclude that fraction nonconforming for this process= 1-yield=1-1=0 or zero

1	B	C	D	E
2	Continuous process (normally distributed)
3	Mean:	105	DPMO:	0.3
4	Standard Deviation	1	Yield	1.0000
5	LSL:	90
6	USL:	110

1	B	C	D	E
2	Continuous process (normally distributed)
3	Mean:	105	DPMO:	=((1-NORMDIST(C6,C3,C4,TRUE))+(NORMDIST(C5,C3,C4,TRUE)))*1000000
4	Standard Deviation	1	Yield	=1-(E3/1000000)
5	LSL:	90
6	USL:	110