Need help in quality control

[Moderator’s Note:This forum post contains formulas that may not appear. Mr. Schlueter was kind enough to attach a Microsoft Word file — see below.]Dear Krish, What will happen, when you pass the training CD’s to your customer without checking them? I suppose the answer depends:·        When your customer can bear waiting for a replacement, his/her monetary loss will be low (transport + materials).·        When he/she has to send trainees home, his/her monetary loss can be as high as several k$. Can you estimate the average loss to your customer? That is that amount of money, 50% of your customers would loose when you ship defective CDs. (I’ll give an example below).  Reviewing the errors you’ve found, specifying error-tolerances:What do you think, how many errors will your customer accept on average?(tolerance D: 50% can bear this amount of errors, while 50% can’t.)  Let’s have a look at a low-loss scenario: Bearable error-tolerance                                   D = 10 errors               (just my wild guess) Cost of a defective CD (its price)                      A = 3$                         (just my wild guess)Cost of measurement                                        B = 2h * 40$ = 80$Cost of adjustment (=replacement)                    C = 8$                         (price + shipment) Current measurement interval                n0 = 1               (you measure each CD)Current control limit                                          D0 = 1              (1 error => CD rejected)Current adjustment interval                                u0 = 10             (just my wild guess)  Background:I suppose that you found both critical and minor errors. Try estimating a 50% tolerance value: 50% trainings will be ok, 50% will not be ok at that error level.All costs are average cost per CD.My assumptions: so far you measured each CD, rejected it when there was at least 1 error. You probably had time to investigate 10 CDs so far.The underlying production model (“you receive and ship CD’s”) assumes:You measure every n0th CDThis imposes an average measurement cost BYou readjust your process on target (=ask for replacement), when your measurement result exceeds the control limit D0This imposes an average adjustment cost CYou adjust (=replace) after every u0th adjustment (=replacement), when necessary (control limit D exceeded)On average A$ are incurred by a defective CD.  The average monetary loss L you pass with every CD to your customer is in this process-adjustment model:               (looks more complicated than it is) In the low-loss scenario this evaluates to:   or  = 80.98 $  As you can see, in this scenario the cost of measurement dominates, while the loss incurred to customer is very low. Can we optimize it? Can we minimize this total monetary loss? Better measurement interval n:    Better control limit D:                 Better adjustment interval u:                     Which yields for the low-loss scenario: n=230D=2.9 ~ 3U=29  ~ 30 It is economically justified in the low-loss scenario to:·        Measure each 230th CD·        To raise the control limit to 3   and pass it with 0,1,2 or 3 errors·        To ship all the other 229 CD’s without measurement (low loss to customer from defective CD`s)·        To adjust (=ask for replacement when D is exceeded) every 30th CD(which in fact means coupling replacement to the measurement rate) Average monetary loss will reduce to:       or  = 1.75 $ per CD  We can expect the total monetary loss to decrease by:  Lold      = 80.93 $(Lnew     =  1.75 $ )gain           79.18 $ per CD  Amazing, isn’t it? Just by tuning your measurement and replacement process.  Here is a high-loss scenario: Bearable error-tolerance                                   D = 10 errors               (just my wild guess) Cost of a defective CD                                    A = 20000 $                (training canceled)Cost of measurement                                        B = 2h * 40$ = 80$Cost of adjustment (=replacement)                    C = 8                           price + shipment) Current measurement interval                n0 = 1               (you measure each CD)Current control limit                                          D0 = 1              (1 error => CD rejected)Current adjustment interval                                u0 = 10             (just my wild guess)                (looks more complicated than it is)           or  = 167.40 $ per CD  Adapting the intervals:Better measurement interval n:    Better control limit D:                Better adjustment interval u:                   Which yields for the high-loss scenario: n=2.8 ~ 3D=0.58 ~ 1u=10 It is economically justified in the low-loss scenario to:·        Measure each 3rd CD·        To leave the control limit at 1   and pass it with 0 or 1 errors·        To ship all the other 2 CD’s without measurement (take a small risk)·        To adjust (=ask for replacement when D is exceeded) every 10th CD(which in fact means potential replacement by your supplier every 3rd measurement)            Average monetary loss will reduce to:          or  = 114.07 $ per CD  We can expect the total monetary loss to decrease by:  Lold      = 167.40 $(Lnew     = 114.07  $ )gain            53.33 $ per CD which origins completely from savings in measurement in this case. There is some risk of passing defective CD’s to customers, who are urgently waiting for training material. However, it is not justified to overdo measurements in this situation (shared risk).  I think you can adapt it now to your situation. This approach is heavily used by Mazda in manufacturing. I took the formulas from: “Taguchi on Robust Technology Development – Bringing Quality Engineering Upstream”, G. Taguchi, ASME Press, New York, 1993 Hope this helps,Michael Schlueter (A western member of the Quality Engineering Society, Tokyo) Download: Letter from Michael Schlueter [Word file]Viewing Tip: Usually, you can click on a link to view the document — it may open within your browser using the application (in this case Microsoft Word). If you are having difficulty, try right clicking the link and selecting “Save Target As…” or “Save As…” to save it to your computer harddrive.

This might seem simplistic, but I would recommend returning to manufacturer to do this whole evaluation.

Krish
As a first step, you should narrow the scope of the problem and the vendor must work with you on this. Some sample questions: Is there any marking traceability(CD Lot code, dates, times) that traces the CD’s packaging etc.. to the vendor’s production runs, disk burners, operators..?Was the Master ok or was it damaged?What type of Quality Specifications were listed in the contract and did the vendor follow Best Industry Practices? What is the acceptable defect level in the industry? Is there a better* way of checking the CD’s ? A superior supplier could guarantee CD critical defects in the PPM range and a rejection based on what you found would be obvious in this case.
In theory,I can appreciate the benefits of a risk cost benefits analysis. However, in the real world, elegant risk reduction mathematical models can often fail with disasterous financial consequences(example: Derivatives Trading). In lieu of the bad press that American Industry is getting with repect to financial reporting honesty, I don’t think that it is a good idea to pass off a quality problem to a customer because it is profitable to do so.  
This is a difficult problem.
Good Luck
John H.
*Perhaps the NIST, DOD or other Government Technical Agency could assist with this.