Question

Design specifications require that a key dimension on a product measure 106 ± 12 units. A process being considered for producing this product has a standard deviation of five units.

a. What can you say (quantitatively) regarding the process capability? Assume that the process is centered with respect to specifications. (Round your answer to 4 decimal places.)

	Process capability index ?

b. Suppose the process average shifts to 98. Calculate the new process capability. (Round your answer to 4 decimal places.)

	New process capability index ?

c. What is the probability of defective output after the process shift? (Use Excel's NORM.S.DIST() function to find the correct probability. Round "z" values to 2 decimal places. Round your answer to 4 decimal places.)

Probability of defective output ?

Answer 1

Given, Product Measure = 106±12

Product’s Standard Deviation = 5

Upper Specification Limit or USL = 106 +12=118

Lower Specification Limit or LSL = 106 -12=94

As Process is Centered, so Process Mean = (94+118)/2 = 106

Now Process Capability = (USL –LSL)/6 X Standard Deviation = (118-94)/6 X5 = 0.8

And

Cpu= (USL – Process Mean)/3 X Standard Deviation = (118 -106)/3 X 5 = 0.8

Cpl =(Process Mean –LSL)/3 X Standard Deviation = (106-94)/3 X 5 =0.8

Answer of a.

Process Capability Index, Cpk= Min. of (Cpu and Cpl) = 0.8000

Now New Process Mean =98

Cpu = (USL-Process Mean)/3 X Standard Deviation = (118-98)/3 X 5 = 20/15 = 1.3333

Cpl = (Process Mean –LSL)/3 X Standard Deviation = (98 – 94)/ 3 X 5 = 4/15 =0.2667

Answer of b.

New Process Capability Index, Cpk= Min. of (Cpu and Cpl) = Min. of (1.3333 and 0.2667) = 0.2667

C. Calculation of Probability of Defective Output after the Process Shift:

1	B	C	D	E	F	G	H
2	DPMO & Sigma Level Calculator
3		Continuous process (normally distributed)					Formula
4		Mean:	98		DPMO:	211887.1	=(IF(D6<>"",NORMDIST(D6,D4,D5,TRUE),0)+IF(D7<>"",1-NORMDIST(D7,D4,D5,TRUE)))*1000000
5		Standard Deviation	5			0.21188707	=G4/1000000
6		LSL:	94		Yield	0.78811293	=1-G5
7		USL:	118		Probability of Defective Output	21.19%	=(1-G6)