Question

Non-Conforming Parts (NCP) Presume; Production makes 250,000 Parts per year. Each Part Sells for $100. If no issues, Each Part cost $90 to make. The Critical Operation is the last operation - Unfortunately. If it’s too long – it can be reworked. If it’s too short – it’s scrap. If rework is needed, there is an additional $0.70 added to the production cost. If the part must be scrapped, there is a $6 disposal fee as it contains mercury (Hg). The Final Operation’s Critical Dimension is 100mm +/-10 mm. We have 3 (Bell Curve) Processes: FOR EACH SCENARIO; What would be the -- Percent First Time Capable within Tolerances -- Percent Rework -- Percent Scrap -- Percent between 99 mm and 101 mm -- and Profit?? 1) A Process Centered at 100mm with a Standard Deviation of +/- 5mm?? 2) A Process Centered at 105mm with a Standard Deviation of +/- 5mm? 3) A Process Centered at 100mm with a Standard Deviation of +/- 1mm? 4) A Process Centered at 100mm with a Standard Deviation of +/- 0.1mm? a. In this scenario, If it were “better” (Cost, performance, etc.) to move change the tolerances to 95mm +/- 5mm; would you be comfortable with the change? Why?

Answer 1

SOLLUTION:-

I believe the tolerance given is misprinted. It should be 100 +/- 1 (i.e. 99 to 101) and not 100 +/ 10 .

The calculation follows:

Process	Mean (μ)	Sigma (σ)	USL	LSL	Prob(> USL) i.e. % rework	Prob( < LSL) i.e. % scrap	Rework per day	Scrap per day	Defect-free parts per day
1	100	5	101	99	42.07%	42.07%	105185	105185	39630
2	105	5	101	99	78.81%	11.51%	197036	28767	24196
3	100	1	101	99	15.87%	15.87%	39664	39664	170672
4	100	0.1	101	99	0.00%	0.00%	0	0	250000
Process	Profit from defect-free parts	Profit from reworked parts	Loss from scrap	Net profit
1	$396,299	$978,221	$10,097,767	($8,723,247)
2	$241,964	$1,832,436	$2,761,672	($687,272)
3	$1,706,724	$368,873	$3,807,726	($1,732,129)
4	$2,500,000	$0	$0	$2,500,000

P A D G 1 Rework per day Scrap per day Defect-free Prob( <LSL) ie. % scrap Mean (u) Sigma (a) USL LSL Prob(> USL)ie. % rework Process parts per day 2 =1-NORMDIST(E3,C3,D3,1) =NORMDIST(F3,C3,D3,1) G3*250000 =250000*H3 =250000-13-J3 = 1-NORMDIST(E4,C4,D4, 1) =NORMDIST(F4,C4,D4,1) G4*250000 250000*H4 =250000-I14-J4 - 1-NORMDIST(E5,C5,D5,1) NORMDIST(F5,C5,D5,1)G5*250000 250000*H5 =250000-I5-J5 = 1 -NORMDIST(E6,C6,D6,1) NORMDIST(F6,C6,D6,1)G6*250000 250000*H6 250000-I6-J6 1 100 5 100+1 100-1 3 = 100-1 2 105 5 100+1 4 = 100+1 = 100-1 3 100 100 0.1 100+1 100-1 6 4 7 Profit from Loss from Profit from Process defect-free Net profit reworked parts scrap 8 parts = K3* ( 100-90) 13* (100-90-0.7) J3* ( 90+6 ) C9+D9 - E9 K4*(100-90) 14*(100-90-0.7) 14"(90+6) =C10+D10-E10 =K5*(100-90) 15*(100-90-0.7) J5*(90+6) C11+D11-E11 1 9 10 2 3 11 4 =K6*(100-90) 16*(100-90-0.7) =J6*(90+6) C12+D12-E12 12

Process	First time capable %	Rework %	Scrap %	% between 99-101 (i.e. rework + first-time ok)	Profit
1	15.9%	42.07%	42.07%	57.93%	($8,723,247)
2	9.7%	78.81%	11.51%	88.49%	($687,272)
3	68.3%	15.87%	15.87%	84.13%	($1,732,129)
4	100.0%	0.00%	0.00%	100.00%	$2,500,000