[Dr. Steve W.]

If you are running one-way ANOVA in Mini, the sample sizes can be different (I am assuming that is what you meant by “the samples are different”). You have to have balanced data only when you are running two-way ANOVA.

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[Dr. Steve W.]

Yes—it would be y^2 if your target is zero.
I now see where you were coming from when you said the loss function is 1-N(0,1). I am not supprised that the 2nd order Taylor expansion of 1-N(0,1) looks just  like a loss function y^2 b/c they are both second order polynomials having the same stationary point.

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[Dr. Steve W.]

No, the loss function is not 1-N(0,1). Rather, it is (y-target value)^2, where y is the performance measurement.

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[Dr. Steve W.]

FYI, I did not train Mr. Lewis and if I did, I would not have made the statement that he was trained by probably the best trainer in this business.

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[Dr. Steve W.]

understand, the control limit  for xbar is 3 times the SD of group average which is the SD of individual divided by sqrt of sample size. Xbar being in control and within the spec does not imply the individual data are also within the spec. The professor is good.

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[Dr. Steve W.]

your between run variation is much larger than your within run variation. That indicates that your process is not in control and if it is not in control, it is not meanful to even calculate process capability.
To answer whether you should reduce your sampling frquency, you need to know your rational subgroup. Since your within run variation is small, you probably should just use samples within production run as a group. If you are going to use Xbar & R, you need to maintain constant sample size and you can get away by taking 3 to 9 samples per sub group. If you can not maintain constant sample size, you have to use xbar & s chart and in that case, you might want to have about 10 data points per sub group.  Since your production runs are typically 16~24 hrs, I would take 1 sample every other hr.
Hope this helps.

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[Dr. Steve W.]

you and Vince by any chance the same person?

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[Dr. Steve W.]

not equivalent to “all of the BB’s and MBB’s heading for the exits” as was stated by Vince. Based on what I have observed, no single MBB has lost job to the merger. It is obvious that Vince is bitter toward BOA and is trying to use this public domain to viciously attack BOA 6S program. I am quite well connected with about 8 major 6S companies and based on what gathered, BOA has by far the best amongst them. All I can say is, if you are a good 6S profession and likes new challenges, come to BOA—-you will enjoy being part of BOA 6S program.

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[Dr. Steve W.]

standard deviation, what do you need CI for?

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[Dr. Steve W.]

You can have a process with Cp > 2 but all your parts or service are out of spec.! Cp fails to recognize that your process mean has to be in the spec. in order to have a good process. Cp only tells you how good your process can potentially be and it will reach its entitlement only when your process mean is at the middle of the spec. limits. That is why we need Cpk. The difference between Cp and Cpk is not that the latter looks at both spec. limits—-Cp looks at them too —you look at the formula you provided. The difference is that Cp ignores process average but Cpk uses it as a key element of its calculation, recognizing the process average has to be within the spec. in order for the process to even have a chance to be good.

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[Dr. Steve W.]

long as your subgroup size is 4 or more. The C chart is a little bit more sensensive to deviation from Poission distribution.

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[Dr. Steve W.]

If so, it is called over dispersion. There are a lot of text books out there that talks about how to handle overdispersion. Overdispersion is very common situation for sount data.

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[Dr. Steve W.]

you accurately control your type I error (false positive) and it is .3% if you 3 sigma as the control limit. Now if the conditions for normal approximation do not hold, your normal approxmation is not going to be very accurate and hence the type I error can deviate from .3%. Is that going to be a big deal? More often than not, it is not. So do not get overly concerned about it.

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[Dr. Steve W.]

failed at a U, (s)he tends to have bitter feeling toward that U.. He is trying to launch a personal attack when he does not have facts.
BOA has about 200 MBBs/BBs and majority of them like what they see and the direction the 6S program is moving. Opinions vary and you can never make everyone happy even with a great program.
Anyone is entitled to his/her own feeling, but do not viciously attack a program on this public domain and that is when I feel like I need to defend.

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[Dr. Steve W.]

The commitment from the senior manage is 2nd to none. Mr. Lewis believes in 6S more than probably any active CEO, he is very knowledgable and probably more knowledgable than you are b/c he was trained by probably the best 6S trainer in this business.
A lot of BBs and MBBs have been promoted to leadership roles. A lot of MBBs and BBs at BOA are from GE speak very highly of BOA 6S program even in private. These former MBBs feel BOA’s commitment to 6S is as strong as, if not stronger than, GEs.
 

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[Dr. Steve W.]

greater than 10 (where n is the subgroup size), the normal approximation is pretty good. For U chart, since we are plotting xbar with x being count, the normal approximation is probably pretty good as long as n is large (having a large c would help but not necessary) due to CLT.

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[Dr. Steve W.]

sample size n: if n is small, even “bad” looking histogram might give you a high p-value; if n is large, a good looking (bell shape) might give you a small p-value as when n goes large, the power of a test will be high—so even a tiny deviation from normal will be detected.

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[Dr. Steve W.]

p-values for 14 (I believe) different distributions. I am not aware any table though. But go to NIST web and you will find some reference on this topic. I would be surprised that some stats handbooks have table for some distributions.
 

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[Dr. Steve W.]

what I observed:
1) The consolidated version does not work as well as the deployed version.
2) BBs does not have to report to MBBs but MBBs should have input when it come the PR time for BBs.
3) A structure that has BB reporting to BB can cause issues as BBs are supposed to be measured by similar deliverables. The boss BBs tend to take credits from the subordinate BBs.
4) HR has to be on board —when it comes to promotion time, make sure certified BBs or MBBs or even GBs gets first consideration
5) Champions have to be held reponsible for the Belt productivity and knows how to select projects.

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[Dr. Steve W.]

dependent in the sense that the same AD value will have different p-values if the AD value is calculated from different distributions. The p-value calculation is VERY involved.

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[Dr. Steve W.]

Sample 100,000 data from the distribution with smaller mean (Calc>random data >..) and store them in Column 1; then do the some thing from the distribution with larger mean and stroe them in a different Column 2. For each of the 100,000 row, count the number of rows for which Column 1 data is bigger than the Column 2 data, and divide that number by 100,000—-there is your probability.
If you have more questions, email me at [email protected] 

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[Dr. Steve W.]

I am talking joint density which is represented in 2-demensional space and the joint density for 2 independent random variables (RV) are just the product of the 2 individual densities. A 2-D joint density is a surface instead just a curve. If you can find someone with MS degree in statistics or industrial engineering, he or she should be able to help.

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[Dr. Steve W.]

helps. But it is still challenging for the BB candidates to carry out projects without infrastructure supporting from their companies.

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[Dr. Steve W.]

addressed your question of how to analyze attribute DOE data. The article is published in Technometrics in either 1994 or 1995. You might want to check that out. Given you have 7 factors, you need to  do a fractional factorial DOE. I am assuming all your factors are 2-levels; otherwise, you are talking about a lot of runs. You should  get a good (experienced) statistician to help you with this DOE project.

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[Dr. Steve W.]

you need to integrate the joint density over the left side of the 45 degree line going through the origin, provided that the horizontal axis is the random variable with larger mean and the vertical axis is for the RV with smaller mean.

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[Dr. Steve W.]

yes—they have the technical knowledge but being a BB needs a lot more than just technical knowledge. You have to be a leader, a change agent, have great interpersonal skills and know how to get project done under any circumstance. These university professors know nothing about these. I won’t hire any BB or MBB who are certified by a university.

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[Dr. Steve W.]

Bank of America, GE, Ford motor, TRW, ITT Indsutries, Lear, Johnson Controls, Johnson & Johnson, Baxter, Textron, JPMorgan, Citigroup, Merril Lynch, Washington Mutual, FleetBoston, Capital One, BlueCross &BLueShield, Visteon. And a lot more can be added to this list. 

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[Dr. Steve W.]

how you really learn. Read those statistics books and books on process tools! There is no short cut if one really wants to learn.

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[Dr. Steve W.]

Xbar actually converges to mu almost surely according SLLN (strong law of large numbers) —-you can see that by noting that var(x)/n goes to zero as  n goes to infinity.
The correct CLT is that as n goes to infinity, sqrt (n) * (Xbar-mu) has N(0, sigma), where sigma is the variance to individual x.
Hope I am not confusing everyone. 

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[Dr. Steve W.]

a lot of banks that embarked on six sigma. City Groups,  J. P. Morgan,
Bank of America, Merill Lynch are all using 6-sigma to improve their
service processes. In my opinion, 6-sigma suit better for service and
manufacturing process than product design.

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[Dr. Steve W.]

a lot of banks that embarked on six sigma. City Groups,  J. P. Morgan,
Bank of America, Merill Lynch are all using 6-sigma to improve their
service processes. In my opinion, 6-sigma suit better for service and
manufacturing process than product design.

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[Dr. Steve W.]

Do not work for GE—they do not treat employees very well, but you can buy their stcoks—it is a company that place a lot of focus on shareholder value but little on employee morale.

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[Dr. Steve W.]

is normally distributed. However, the variace and typially mean will be different.

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[Dr. Steve W.]

of defective rate (1%, 5% etc.) is acceptable first. With that established, you can compare it with your confidence interval for the proportion of defetive parts based on the out come of your test. The confident level dictates how many you need to sample. This is a traditional inspection issue and any well trained statistician can help you.

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[Dr. Steve W.]

calll it xbar if it is the average of  3 measurements taken on the same parts because the independence assumption is severely violated: the 3 readings tend to be very close—knowing one tells a lot about the other 2 readings. Xbar has to be average of readings from different samples. 

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[Dr. Steve W.]

very successful during last decade and SS has been with GE for about 8 years. Ford was struggling big time before they intruduced SS. Big 3 will continue its losing battle against the Japanese competitors due to their culture disadvantage, w/ or w/o six sigma.Six sigma does not work if you do not know how to use it or if you do not have the right infrastructure to support its deployment.

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[Dr. Steve W.]

it is not going to be us and if industries will come up some thing new, we will lead it again b/c we are the best trained group. Live with it!

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[Dr. Steve W.]

derived and what are the conditions?
I know there are a lot of low quality professions in SS but some of us are VERY good.

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[Dr. Steve W.]

Terry,
Six Sigma suits  Banking/Financial Industry very well as they are process-oriented business. You can use SS to reduce error rate in your service, reduce turn around time in your mortgage approval process, reduce wait time in your banking/call centers, re-design various process in banking/insurance businesses.
I am a lead MBB for a major bank and we have made great stride in getting the most out of SS. There are several major banks that embarked on SS. Among these banks are The Citigroup, JP Morgan, Bank of America, Merril Lynnch and American Express. I heard Wachovia will be launching SS initiatives in a couple of months.
I did find that talent pool in banking industry is not nearly as good as in manufacturing industry.
The key to success is to make sure the CEO and HR head are really supportive; otherwise, it is going to be tough journey.
Good lucy, Terry.

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[Dr. Steve W.]

Terry,
Six Sigma suits  Banking/Financial Industry very well as they are process-oriented business. You can use SS to reduce error rate in your service, reduce turn around time in your mortgage approval process, reduce wait time in your banking/call centers, re-design various process in banking/insurance businesses.
I am a lead MBB for a major bank and we have made great stride in getting the most out of SS. There are several major banks that embarked on SS. Among these banks are The Citigroup, JP Morgan, Bank of America, Merril Lynnch and American Express. I heard Wachovia will be launching SS initiatives in a couple of months.
I did find that talent pool in banking industry is not nearly as good as in manufacturing industry.
The key to success is to make sure the CEO and HR head are really supportive; otherwise, it is going to be tough journey.
Good lucy, Terry.

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[Dr. Steve W.]

to talk to a PhD level statistician about it. I can probably give an answer but I am worried about the fact that you mentioned 5  groups. There might be issue with independence assumption needed for making  statistical inference.

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[Dr. Steve W.]

sfdsafdd

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[Dr. Steve W.]

what is the problem statement? What is it that bothers you so bad that you want to do a 6-sigma project on it? Capacity, cost, inventory or defect rate? What is the metric? If you can answer these questions, I think we have got a starting point. You do not need DOE to baseline. DOE is for optimization purpose.
 

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[Dr. Steve W.]

is no. 6-Sigma is a customer focused and data driven problem sovling process. An organization will not be certified even if it successfully implemented 6-sigma, but individuals get certified for completing training and closing certain no. of projects and delievering certain amount of $ savings. In order to successfully implement 6-Sigma, you have to have commitment from high level management and build the right infrastructure.

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[Dr. Steve W.]

z-score can be defined for any value of interest and that value can be the SL of course. Let’s say we are talking about just one-side SL. Here is the definition: z-score is the # of SDs that can be fitted in between the SL and the process mean, or is the distance between SL and process mean measured in no. of SDs. If SD=0, you have a perfect process as long as the process mean is on the correct side of the SL.

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[Dr. Steve W.]

afraid you might have run out of dfs if you do not have enough no.of runs. Also, if you have too many factors to start with, you should run a screening DOE before your try to build sophisticate equations.

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[Dr. Steve W.]

I checked, I realized that the CCP did much more brain-wash on me than any other government. This guy could not tell a biased media from a government-controlled media. I feel embarrassed by his post; otherwise, I would not have told him to wake up. Moreover, he was not being nice either.

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[Dr. Steve W.]

for someone who has never been to China to talk about issues on China. I am from China too but I agree with some of these assessments about China.
To say that the mass media here is controlled by the US government is ignorant. It just shows that you are totally brain-washed by the CCP. I feel sad for you, really. If the government here controls the media like the CCP does, the Clinton and Monica thing would not have come out during Clinton presidency.
It is time for you to wake up, my fellow country man.

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[Dr. Steve W.]

it is the inverse funciton of cumulative normal CDF: it maps the (0, 1)
interval into (-inf, +inf) and maps .5 to 0, .68 to 1, etc…

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[Dr. Steve W.]

stack up and Cp (or Cpk) are different animals. Having the right tolerance stackup does not ensure good Cp and/or Cpk. The latter are determined by your tolerance spec., your assembly process mean and process variation. Tolerance spec allocation is typically finalized at product design stage while process capability won’t be known until you collect some products from your manufacturing line. As a PD person, you can set target for process mean and upper bound for process variation so that you will have a good Cpk.

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[Dr. Steve W.]

dealing with data that varies with time. You should get a book on Time Series model. A regular regression approach won;t work. Get a book by the great George Box.

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[Dr. Steve W.]

First of all, Cpk has nothing to do with control limit except that before you calculate Cpk, you should make sure your process is in control. Secondly, no. of samples required depends on what level confidence you want to have on your Cpk estimation. 
A good resource is the book by Douglas M. of Arizona State U.

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[Dr. Steve W.]

your MS? If not, you might consider doing so. If yes, do you have enough historical data on this same process? If you do, control chart will tell you whether you are dealing with a unstable process. If you do not have much historical data, there is not much you can do: two sample t won’t work as you only got one data point on Day 2. I-MR chart is the only chart but with only 4 data points, your Beta risk is very high. Hope this is helpful.

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