Ben Johnson
@wbjohnson  Reputation - 24 Rank - Aluminum
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I’m reading through a quality engineer handbook en route to becomming a CQE. In the section on probability, one of the examples has caused some “disagreement” within the engineering staff at our plant. We would like some more outside voices to weigh in.
The word problem is as follows (carefully paraphrased, both sides agree on this paraphrase):
***A certain population of cell phones are 100% inspected prior to shipping. Out of the population, it was found that 5% of phones had only critical defects, 2% of phones had only major defects, and 1% of the phones had both critical and major defects.
Complete rework is necessary “if the phone has critical or major defects or both”. What percentage of the phones need rework?***
One group of engineers answers 8%, the other group answers 6%. To all of us regardless of our answer, it seems pretty obvious. :) I am interested in the reasoning, so please provide a suitable reason for your response.
If allowed and requested, I can repeat the entire question verbatim and provide all information on the book.
Thanks!
Ben J.
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MBBinWI
@MBBinWI Reputation - 2656 Rank - Titanium
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@wbjohnson – Ben, draw this picture: A big circle that is labled 100 phones. Within this circle draw a smaller circle and label that one 5% ONLY critical defects. Draw another circle inside the largest, but not overlapping the other circle and label it 2% ONLY major defects. Finally, draw a third circle inside the largest but not overlapping the other two, label this one BOTH critical and major defects. Now, as stated you rework anything with critical, major or both. So add up the contents of the 3 circles – you get 8%. Everyone should now understand.
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Ben Johnson
@wbjohnson Reputation - 24 Rank - Aluminum
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Thanks MBB. As you have struck upon, the general disagreement here is whether or not there are three *distinct / mutually exclusive* categories or not.
Also – love the avatar – who is John Galt again? ;)
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Gary Cone
@garyacone Reputation - 1319 Rank - Silver
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@wbjohnson the key word is only.
@MBBinWI Your answer, as usual, is correct. BUT, the truth is no phone should be shipped without finding out how the process can let 8% escape to a inspection prior to shipment. The is the real issue with the CQE, they talk prevention, but emphasize containment.
And where is the R&R on this inspection? How do you know any result can be trusted?
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Mike Paulonis
@paulonis Reputation - 8 Rank - Aluminum
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I like the visualization approach by MBBinWI. If the group is having a tough time believing that there should be three separate circles, another way to show this is to draw a small circle for the critical defects and then draw a smaller circle yet that very slightly overlaps the first small circle. This is the circle of major defects. Label the portion of the first small circle that is not overlapping the second as 5% (only critical defects). Label the portion of the second small circle that is not overlapping the first as 2% (only major defects). Label the portion that is overlapping as 1% (both critical and major defects). Clearly the total area of the circles is 8%.
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MBBinWI
@MBBinWI Reputation - 2656 Rank - Titanium
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@paulonis – Mike: Yes, a better description as the third group is actually the intersection of the other 2, but as described is in addition to the other two (which are mutually exclusive).
@garyacone – Gary: Comes from their long history of quality being inspected in. The only real Quality Engineers are those practicing DfSS – but then I might be slightly biased.
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MBBinWI
@MBBinWI Reputation - 2656 Rank - Titanium
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@wbjohnson – just my little non-political protest. Look for AS 2 out this October.
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June 28, 20120
