iSixSigma

Neil Polhemus

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  • #68131

    Neil Polhemus
    Participant

    Interaction effects are typically not calculated in a randomized block design, because blocking factors and experimental factors are usually assumed not to interact. Further, unless there is replication, there will be no degrees of freedom available to estimate the experimental error if you do estimate the interactions. However, you may estimate the interactions if you like by treating the randomized block design as a factorial with two experimental factors.

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    #67869

    Neil Polhemus
    Participant

    Good point. A special toolwear chart does have a couple advantages, however. (1) You can specify the slope of the line if desired, rather than estimating it from the data. (2) You can add a specification limit to the plot to tell when you are getting close to needing to change the tool.

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    #67866

    Neil Polhemus
    Participant

    There are control charts specifically designed to monitor tool wear. STATGRAPHICS contains one such chart designed to handle wear which follows a linear trend.

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    #67865

    Neil Polhemus
    Participant

    I don’t think you’d ever want to stop collecting data and plotting it on a routine basis. You can always learn from looking at your data. You’d also like the ability to detect changes before they cause a problem, and that’s what control charts are designed for.You might consider modifying the control limits, however, to allow for the wide specifications. Doug Montgomery’s book has a good chapter on charts such as Acceptance Control Charts, which relax the control limits for high Cpk processes.

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    #67846

    Neil Polhemus
    Participant

    Now that’s an intriguing question. If someone screws up, is that part of the measurement process? It may be.

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    #67754

    Neil Polhemus
    Participant

    I did some experimenting, and outliers actually seem to have a bigger impact on the ANOVA method than the Average and Range method (much bigger in the examples I tried).

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    #67753

    Neil Polhemus
    Participant

    The MSA manual recommends the use of the ANOVA method unless a computer is not available. One possible explanation for a dramatic difference between the results of the 2 methods is the optional inclusion of an appraiser by part interaction in the R&R term estimated by the ANOVA method. It would be surprising to see a large difference between the two analysis methods if the interaction term was not included. The presence of outliers could also impact the analyses, but would usually cause the Average and Range method to give a larger R&R estimate.

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    #67740

    Neil Polhemus
    Participant

    Before embarking on any SPC or DOE effort, you must be certain that you are capable of measuring the characteristics which are critical to your process. If you can’t measure those characteristics accurately and precisely, then you won’t be able to distinguish good parts from bad parts or be able to determine the effect of any changes you might make to the process.The basic goal of a gage R&R study is to estimate the variance of a measurement process to insure that it is small relative to the process tolerances. Otherwise, you’ll be wasting your time trying to apply statistical methods, since the information you need will be hidden in the measurement noise.

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    #67729

    Neil Polhemus
    Participant

    I also second the idea of putting the e-mail addresses back.

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    #67712

    Neil Polhemus
    Participant

    You can send it to me at P.O. Box 1124, Englewood Cliffs, N.J. 07632, or e-mail a file to [email protected]

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    #67671

    Neil Polhemus
    Participant

    What we are concerned about with gage linearity is that the measurements from a gage should increase linearly with the response or, if a gage is biased, the bias should remain constant over the range of measurements for which that gage is used. While we can tolerate a little non-linearity, it should be small with respect to the normal process variation. As typically defined, the percent linearity of a gage is related to the slope of a regression line fitting bias versus reference value. In general, the smaller the percent linearity the better.

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    #67668

    Neil Polhemus
    Participant

    I ran it through the Automatic Forecasting procedure in STATGRAPHICS. On the limited amount of data you provided, the winning method was a simple random walk: the forecast for next month equals this month’s amounts. If you provide more history, it is possible that we could do better.

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    #67531

    Neil Polhemus
    Participant

    That’s very interesting. Can you tell us how you set up the model for GLM? It’s not clear to me how you would do that.

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    #67480

    Neil Polhemus
    Participant

    I second Terry Harris’ suggestions. Anything beyond a two-level factorial makes no sense for the yes/no input factors. It might be simpler to go with a modified Box-Behnken design where you split the centerpoints amongst the levels of the attribute factors. I would not just go in and adjust the star points in the CCD. The resulting design will be considerably larger than necessary.

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    #67481

    Neil Polhemus
    Participant

    If you can collect a lot of samples at each combination of the factors, then you can use the proportion of failures as the response. You could then do a logistic regression. However, you may be able to use a standard ANOVA approach with an arc sine square root transformation (Box, Hunter and Hunter discuss this approach on p. 134). If you are getting only one response at each combination of the factors, then you may have to resort to simply plotting the outcome.

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    #67298

    Neil Polhemus
    Participant

    The inequalities give the worst case scenario and the maximum possible DPM. The whole idea of analyzing data, however, is that we can get much better estimates from the data that from such bounds.

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    #67288

    Neil Polhemus
    Participant

    You can sample the world with 10? An election poll with 10 respondents? A sample of 10 items from a lot of 10,000? Not my world.

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    #67287

    Neil Polhemus
    Participant

    Interesting question. Both inequalities make statements about the minimum percentage of a distribution which must lie with k standard deviations of the mean. Chebyshev’s inequality says that for any distribution, at least 100(1-1/k^2)% of the distribution must lie within the interval xbar-k*sigma to xbar+k*sigma. The Camp-Meidel inequality says that for any unimodal distribution, at least 100(1-1/(2.25k^2))% of the distribution must lie within that interval.

    Consider a value of Cpk=1.5, which equates to k=4.5. For the normal distribution, the DPM is 3.4. According to Chebyshev, the DPM could be as large as 49,383 if the distribution wasn’t normal. According to Camp-Meidel, the DPM could be as large as 21,948 if the distribution were unimodal but not normal. These are both bounds, however, and it would take a very extreme case to come anywhere near those values.

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    #67165

    Neil Polhemus
    Participant

    If the data is balanced, as it appears to be (2 replicates at each of the 12 factor combinations), then I suggest you check your arithmetic. The factor and interaction sums of squares must add to less than the total and the error sum of squares can’t be negative.

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    #67033

    Neil Polhemus
    Participant

    In Version 5 of STATGRAPHICS Plus, we added the capability to link a StatFolio (our basic document) to various data sources, including Excel. You can set the program to poll the Excel file at regular intervals and automatically update any charts you have created. These charts can also be automatically posted to a web server whenever they are updated.

    You can find a white paper describing this approach at http://www.statpoint.com/rscenter/six_sigma.htm.

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    #67021

    Neil Polhemus
    Participant

    The basic principle of controlling to a standard is certainly sound, and solving backwards for the required sigma is commonly done. You might also check out the discussion of Acceptance Control Charts in Doug Montgomery’s book “Introduction to Statistical Quality Control”, where he works the specs into the establishment of the control limits from a different angle.

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    #66847

    Neil Polhemus
    Participant

    It is important not to confuse the concept of capability with that of control. The control limits do not provide your estimate of process capability. That comes directly from the mean DPU. The control limits simply allow you to determine whether the process has been stable over the sampling period.

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    #66751

    Neil Polhemus
    Participant

    The Anderson-Darling statistic is a statistic which compares the empirical distribution function of your data to that of a fitted distribution. It is popular because of its sensitivity to deviations in the tails of the selected distribution.

    The value of the statistic itself is of little interest, although it is related to the integral of the squared difference between the empirical and fitted cumulative distribution functions. Instead, you should concentrate on the P-value of that statistic, which indicates how likely it is that your sample comes from the selected distribution.

    One caution: the standard P-values computed by many statistical software programs are not valid when the distribution parameters are estimated from the data (which is the usual case). You should check your software carefully to be sure that they adjust the statistic properly based on the distribution you have selected.

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    #66698

    Neil Polhemus
    Participant

    As you will quickly find out, good statisticians are like good psychiatrists: they always answer your question with a question of their own. In this case, the first question is: what are you trying to estimate?

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    #66680

    Neil Polhemus
    Participant

    I used an OC type acceptance sampling plan with a producer’s risk of 5% against a 1% defect rate and a consumer’s risk of 5% against a 5% defect rate. The program searches for the smallest sampling plan which meets the specified risk levels. For a lot size of 6000, it found a plan with n=179 and c=4. For a lot size of 500, it found a plan with n=139 and c=3.

    I think we are on the same page here.

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    #66679

    Neil Polhemus
    Participant

    Calculating sigma from Rbar/d2 as suggested is the way which many software packages such as Minitab and STATGRAPHICS compute Cp and Cpk from the MR(2) control charts. Please beware that this gives a short-term estimate of the process sigma which may not be attainable over a long period of time. Capability indices based on the overall sample standard deviation, often labeled Pp and Ppk, may give estimates which are closer to what can actually be achieved.

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    #66665

    Neil Polhemus
    Participant

    I ran your problem through the Acceptance Sampling procedure in STATGRAPHICS Plus. To distinguish between a defect rate of 1% and a defect rate of 5%, you will need to sample about 180 of the 6000 items and about 140 of the 500 items.

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    #66570

    Neil Polhemus
    Participant

    Good point. “Simple” only in the sense that it is a dimensionless quantity which does not depend on the units of measurement.

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    #66556

    Neil Polhemus
    Participant

    Cpk is an index (a simple number) which measures how close a process is running to its specification limits, relative to the natural variability of the process. The larger the index, the less likely it is that any item will be outside the specs. If you like, you can then relate specific values of Cpk to the proportion of items which would be beyond the specs. Don’t start talking about standard deviations. If he has an MBA, he will be used to indices, which are designed to hide the complexity behind a calculation and come up with a single number which is easy to understand.

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    #66520

    Neil Polhemus
    Participant

    Thanks for the comments. I’m sorry to hear that Manugistics wasn’t able to negotiate a deal with you. I think you’d find us much more responsive today.

    With respect to the Attribute Gage R&R procedure Minitab added in 13.3, I can’t say we have anything exactly like it in 5.0. However, you can expect to see something in the very near future. We have some very interesting graphics to go along with it, too.

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    #66515

    Neil Polhemus
    Participant

    I’m in charge of development for STATGRAPHICS, and I must say that almost all of the enhancements we make come from suggestions by current and prospective users. Part of my motivation for monitoring this board is to understand what practitioners need. Like Minitab, we have fashioned our Gage R&R, Gage Linearity, and Process Capability procedures to follow the AIAG standards. Is Minitab a popular choice for Six Sigma? Obviously. Do STATGRAPHICS, Jmp, and several other packages contain the same tools? Absolutely.

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    #66511

    Neil Polhemus
    Participant

    P.S. If you are attending the ASQ meeting in Charlotte next week, stop by the Manugistics booth and I’ll be happy to continue our discussion.

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    #66510

    Neil Polhemus
    Participant

    Thanks for the response. I would be happy to correct anything I got wrong in the comparison. With respect to the Box-Cox transformation, STATGRAPHICS automatically determines the optimal Box-Cox power in both the univariate analysis, multiple regression, and GLM procedures. While Minitab can compute the transformation if you specify the power, I don’t think it automatically optimizes it. With respect to the OC Curves, they are generated in the following STATGRAPHICS analyses:
    1. Hypothesis Testing (one sample)
    2. Hypothesis Testing (two samples)
    3. Sample Size Determination (one sample)
    4. Sample Size Determination (two samples)
    5. Create Design (in the DOE section)
    6. Xbar and R Charts
    7. Xbar and S Charts
    8. Xbar and S-squared Charts
    9. Individuals Charts
    10. P Chart
    11. NP Chart
    12. C Chart
    13. U Chart
    14. Moving Average Chart
    15. EWMA Chart
    16. Acceptance Charts
    17. Acceptance Sampling for Variables
    18. Acceptance Sampling for Attributes

    In #6-17, STATGRAPHICS also creates a plot of the Average Run Length of the chart, which is closely tied to the OC Curve.

    If you’d be more specific about the “gossip”, I’ll be happy to respond. While every program has bugs, I know of no major problems.

    P.S. I guess you figured out that the URL I provided had a misplaced period at the end. It should have been http://www.statpoint.com/sixsigmacomparison.pdf

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    #66504

    Neil Polhemus
    Participant

    I’m the only one with a bias that posts here. The others are long-time STATGRAPHICS users. Anyway, for an admittedly biased comparison, check out http://www.statpoint.com/sixsigmacomparison.pdf.

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    #66499

    Neil Polhemus
    Participant

    Much depends upon what you are doing and what your process capability is. For high Cpk processes, there is a type of control chart called an Acceptance Control Chart where the control limits are set based upon the location of the specification limits, not plus and minus 3 sigma. The limits may be considerably wider than on standard charts. Check out Doug Montgomery’s book on SPC. You can also download an evaluation copy of STATGRAPHICS Plus. Acceptance control charts are located on the main menu under Special – Quality Control – Special-Purpose Control Charts.

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    #66456

    Neil Polhemus
    Participant

    In all hypothesis tests, the P-value represents the probability of getting a sample like yours if the null hypothesis is true. In tests for normality, the null hypothesis is that the data come from a normal distribution. If the probability of getting your data from a normal distribution is reasonably high (at least 5%), then you have failed to demonstrate BEYOND A REASONABLE DOUBT that the distribution is not normal, so you treat it as coming from a normal distribution.

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    #66455

    Neil Polhemus
    Participant

    Don’t confuse the population with the sampling distribution of the mean. As the sample size increases, the distribution of the sample mean converges to a normal distribution around the true mean with a STANDARD ERROR which goes down as sigma/sqrt(n). But the population never changes.

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    #66454

    Neil Polhemus
    Participant

    There are two types of model-building approaches that are commonly used: mechanistic modeling, where you attempt to build a model which describes the true behavior of the process, and empirical modeling, where you are satisfied with a reasonable approximation. If your purpose is prediction only, then I would choose the latter approach and not worry about the underlying physics. In such a case, you can let the data suggest the distribution to use. If you need to understand the mechanisms of the process, then you have to approach it from the theoretical viewpoint.

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    #66237

    Neil Polhemus
    Participant

    While I disagree with some of the other respondents as to which is the “premier statistical software on the market”, page 80 of the AIAG manual is very specific as to the definitions of Cpk versus Ppk. Cpk uses an estimate of sigma derived from Rbar divided by d2, which is quite clearly an estimate of within group variability only. It in no way measures anything but short-term variability.

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    #66186

    Neil Polhemus
    Participant

    Assuming the occurrence of defects is independent from component to component, then the probability of an item being free of defects is .999 raised to the power 1000.

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    #66167

    Neil Polhemus
    Participant

    An interesting point about Cpk. I’m not sure I’d call it meaningless, however, just not sufficient by itself to guarantee the desired DPMO. I would suggest a dual criterion requiring Cpk to be less than 1.5 and Cp to be less than 2.0 might be a good idea.

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    #66164

    Neil Polhemus
    Participant

    I will second the suggestion that everyone be careful about stating how they calculate the indices. In both STATGRAPHICS Plus and Minitab, we distinguish between “Capability” (Cpk) and “Performance” (Ppk) based on how the estimate of the process sigma is computed. There are many ways to estimate sigma, of course. Two of the most common:
    1. Use the sample standard deviation s. This gives an index which is usually labeled Ppk.
    2. Use the mean range / d2. This gives an index which is usually labeled Cpk.
    The first method gives a “long-term” estimate of performance, while the second gives a “short-term” estimate of capability. Breyfogle lists several other methods in his text.

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    #66105

    Neil Polhemus
    Participant

    As I understand it, the ANOM bases its decision concerning rejection of the null hypothesis on a multivariate t distribution. This distribution looks at the position of the k means in a k-dimensional space surrounding the grand mean (in a manner similar to a multivariate control chart). If the point lies too far away from the centroid, it indicates that at least 1 mean does not equal the grand mean. The decision bands show which of the means are beyond their expected distance. At least, that’s my best understanding with the somewhat sketchy explanations that one finds in most sources. If anyone has a good reference where all of the details are carefully laid out, I’d appreciate knowing about it.
    The problem with multiple comparisons is that although two means may individually not be far enough away from the grand mean to be declared significantly different from that mean, they may be far enough away from each other to declare statistical significance if that comparison is the only one of interest or one of a small subset. What we do in the post hoc comparisons in ANOVA is carefully control the Type I error of each comparison we plan to make so that all or a selected set of pairwise comparisons may be made without exceeding an experimentwide error rate of 5% (or some other predefined value). There is no such control in the ANOM for pairwise comparisons, so that if you do make pairwise comparisons the overall Type I error is not controlled. As always, the question is “Have we demonstrated a difference large enough that it could not have happened just by chance with a probability of 5% or higher?” Lack of statistical significance does not prove the null hypothesis, it just shows a lack of sufficient evidence to reject it.

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    #66080

    Neil Polhemus
    Participant

    If you put the data in the form of a contingency table, there are a number of tools that could be helpful in analyzing that data.

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    #66079

    Neil Polhemus
    Participant

    Following up on the other responses, I like to define the LTPD as the poorest level of quality that a consumer is willing to tolerate in any lot. In constructing many acceptance sampling plans, you specify the LTPD and the consumer’s risk of accepting a lot with that level of quality (often a 10% risk, but not necessarily). When you create an acceptance plan in STATGRAPHICS Plus, you define both the LTPD and the AQL, the latter being the Acceptable Quality Level at which the producer’s risk is set.

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    #65983

    Neil Polhemus
    Participant

    What questions do you want to ask of the data? If your desire is to compare the men with the women, there are much better ways to handle it.

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    #65953

    Neil Polhemus
    Participant

    The International Civil Aviation Organization (ICAO) was the body that established the TLS, after considerable research into the risks encountered in other modes of transportation, various occupations, diseases, etc. I forget the exact number, but basically they set it up so that a reasonably healthy person had an order of magnitude greater chance of dying from natural causes (heart attack, stroke, etc) while on the plane than from running into another aircraft.
    In fact, the TLS probably had little relationship to reality, just as the 3.4 PPM has little relationship to reality in many Six Sigma efforts. What a target such as that does, however, is force you to collect and actually LOOK AT data. What we found was:
    1. We could give basic guidance on what type of separation standards were necessary to reduce the risk from common cause variation (equipment errors and such) to essentially zero.
    2. After that, the risk what dominated by human factors, such as a pilot entering the wrong latitude and longitude.
    With Six Sigma, you do the same. Force the common cause nonconformities to a very low number (3.4, 34, 0.34, it probably doen’t matter which). Then working on solving the human factors problems.

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    #65951

    Neil Polhemus
    Participant

    I agree with you regarding the arbitrary nature of the 3.4 PPM. But lack of a reasonable target also has its problems. Some years ago, I did some work for the FAA on jet route separation in the North Atlantic. Part of that work involved assuring that we met an established TLS (Target Level of Safety), defined as the maximum acceptable rate of mid-air collisions. If you wish to use statistical methods, a target of 0 can never be met. So you establish a target which you can design to. Is it the right target? Obviously, that depends a lot upon the process. Are we filling boxes of cereal or are we making jet engines? The hard decisions aren’t statistical in nature.

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    #65947

    Neil Polhemus
    Participant

    “Four and One-Half Sigma” it is, although I might modify that slightly. Since the 3.4 out of a million is a one-tailed probability, a process with both an upper and a lower spec, each 4.5 standard deviations from the mean, would have a DPMO of 6.8, even if it never drifted away from the mean. “Four Point Six Five Sigma” would hold the two-tailed DPMO at 3.4. But then again, whose process is ever in a perfect state of statistical control?

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    #65946

    Neil Polhemus
    Participant

    Fact: 3.4 out of a million is the probability that an observation randomly sampled from a normal distribution will be more than 4.5 standard deviations above the mean. Assumption: measurements taken from your process behave like random samples from a normal distribution. Assumption: the long-term mean of your process is at least six standard deviations away from any spec limit (hence “Six Sigma”). Assumption: the short-term mean of your process is never more than 1.5 standard deviations away from the long-term mean. Conclusion: no more than 3.4 out of a million measurements will be beyond the spec. In practice, validation of those assumptions is critical, including normality, amount of drift in the mean, randomness of deviations around that mean, and an accurate enough measurement process that meeting the “Six Sigma” criteria actually says something about the true state of your process.

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    #65935

    Neil Polhemus
    Participant

    Download an evaluation copy of STATGRAPHICS Plus from http://www.statpoint.com. Go to Quality Control, Acceptance Sampling. It will do just that.

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    #65920

    Neil Polhemus
    Participant

    I wish it were that simple. There’s no closed form. It has to be done numerically, often using some power series approximation. The journal Applied Statistics has published several appoximations over the years.

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    #65918

    Neil Polhemus
    Participant

    As a consulting statistician, I will tell you what I tell everyone I work for. Alone, a statistician is basically useless. We can prevent you from reading too much into small samples, and we can help you design a good experiment, but we can’t solve your problems for you. That’s why at least half our time is spent helping YOU master statistical techniques. Statistics is but one tool you need to master, and you can only make progress when you combine what we offer with everything else you know about your process.

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    #65913

    Neil Polhemus
    Participant

    I put up a free wizard recently which allows you to input up to 50 data values. It then generates a set of “optimal” forecasts by trying several models and selecting the one with the smallest historical errors. Go to http://www.statpoint.com and look for “on-line wizards”. Let me know how they work.

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    #65896

    Neil Polhemus
    Participant

    If you download an evaluation copy of STATGRAPHICS Plus from our site at http://www.statpoint.com, you can generate various types of sampling plans. On the main menu, choose Special…Quality Control…Acceptance Sampling…Attributes. On the initial dialog box, set Action to “Analyze Existing Plan”, specify your lot size, and select the AQL and LTPD for your process. Then set the acceptance number to c=0 and the sample size n to a size you would like to evaluate. The program will compute the producer’s and consumer’s risks and plot the AOQ curve. You can quickly evaluate the efficacy of various sample sizes and select one which gives you the risk levels or AOQL you require.

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    #65855

    Neil Polhemus
    Participant

    Both techniques construct a statistical model in which a dependent variable Y is a function of one or more independent variables X. The primary difference is that regression typically deals with quantitative X’s, while ANOVA deals with categorical X’s (although any ANOVA model may be written as a regression model using indicator variables). The advantage of using the ANOVA approach when the X factors are categorical is the manner in which the statistical tests are framed. The significance of each factor is generally tested through an F test which groups all of the coefficients for that factor together into a single test. Also, interesting multiple comparisons can be constructed in terms of the group means, rather than the regression coefficients (which are usually harder to interpret). You would do well to look into using ANOVA.

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    #65789

    Neil Polhemus
    Participant

    It was great to see you also. Hey, I’ve got a new forecasting Wizard that I intend to put on the site soon. If you (or anyone else) have time to give me your comments, I’ll e-mail you a beta copy.

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    #65749

    Neil Polhemus
    Participant

    It has been shown statistically that one should choose
    a model which minimizes the “one-ahead” forecast errors, which are the errors made in predicting the demand for time period t+1 given all of the information available at time period t. If the error distribution for demand follows a normal distribution (the errors are additive), then one minimizes the mean squared error (MSE). If the errors are proportional in nature,
    then you pick a model which minimizes the mean absolute percentage error (MAPE).

    One caveat: in selecting a forecasting model, you must be careful not to overmodel the data. It is very important to apply the K.I.S.S. principle (Keep It Simple Statistically), and not to use too complicated a model. In STATGRAPHICS, our Automatic Forecasting procedure selects a model which penalizes those with too many parameters. This is most commonly done by minimizing the Akaike Information Criterion (AIC), although the Hannan-Quinn and Swarze-Bayesian Criterion are sometimes used.

    In practice, it is very important to plot the historical data with the one-ahead forecasts. Forceasting is still part science and part art.

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    #65742

    Neil Polhemus
    Participant

    The Bible on the subject is the booklet by AIAG. You will find that most stat packages, including STATGRAPHICS and Minitab, use their examples.

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    #65736

    Neil Polhemus
    Participant

    The ARL calculations performed by STATGRAPHICS Plus use the results of Crowder from “A Simple Method for Studying Run-Length Distributions of Exponentially Weighted Moving Average Charts.” Technometrics 29, pp. 401-407 (1987). Crowder also had an article in the Journal of Quality Technology that same year. The formula is given on p. 83 of my book on Statistical Analysis Using STATGRAPHICS Plus. Note: the resulting equations must be solved numerically using Gaussian quadrature. Or you could download an evaluation version of STATGRAPHICS and it will do the calculations for you.

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    #65737

    Neil Polhemus
    Participant

    The newly released STATGRAPHICS Plus Version 5 has a new automatic forecasting procedure which is designed to take historical data and automatically select the model which minimizes the forecasting errors. This type of methodology is often used in supply chain demand forecasting software. You can download an evaluation copy and give it a try.

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