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Reliability Prove-out Method

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  • #54087

    Jay
    Guest

    I have only 15 samples of a fuse available. Each fuse is 6″ long, containing a type of powder. The object is to prove with high reliability and confidence (~99%R/95%C) that the powder will burn continuously and not snuff or fizzle out.

    To achieve this reliability and confidence is difficult. The only response seems to be pass/fail. Logistic regression seems a logical choice, but the independent variable may be difficult to decide upon (say, % binder, or amound of another ingredient). Even if the independent variable is determined, samples are limited to 15. With logistic regression, proving margin gets one the most bang for the buck, but replication at numerous inputs would be needed for most high reliabilities & confidence combinations.

    DOE doesn’t appear an option. I’d think the high reliability & confidence would be more difficult to prove out with multiple factors changing.

    I see engineering confidence being shown, but not statistical confidence.

    I know this is a bit vague, but I’d appreciate any ideas. There will likely be 1 or 2 input factors that can change.

    More could be addressed (long term vs. short term lot production; homogeneity of the powder, more), but this seems enough for now.

    Appreciate your input.

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    #193498

    Robert Butler
    Participant

    So the parameters of the problem are as follows:

    1. You literally have just 15 fuses
    2. Each one of these 15 fuses has a type of powder
    3. The target is a complete and uniform burn of the powder
    4. There are variables of interest that apply to the powder – percent binder, ingredient X (or is it ingredients X1, X2, …Xn?)
    5. There are other unspecified factors in the process “…confidence would be more difficult to prove out with multiple factors changing.”
    6. There are some input factors not mentioned in #4 and #5 “…likely be 1 or 2 input factors that can change.” which are also of interest.
    7. There are also the variables of production cycle length and powder homogeneity.

    If this is a reasonable summation of the situation then you have the following:
    1. You have 15 and only 15 experimental(?) fuse types which you can build.
    2. You are allowed to build exactly one of each experimental type
    3. At a minimum you have 8 factors of interest: percent binder, ingredient X, unspecified factor #1 and #2, unspecified input factors 1 and 2, production cycle length, and powder homogeneity.

    If you chose to make your response variable length of time to first sputter or length of time to extinguishing then you would have a continuous variable to measure and you could build a fractionated design which would let you test 8 factors in 15 experiments (if you had one more fuse you could even go so far as to test 15 factors in 16 fuses).

    As for pass/fail and logistic regression, unless you have near quasi-separation of response due to a single factor it is very unlikely that you will get any measure which tests out as significant (P< .05) with only 15 measurements.

    Your post gives the impression that you still need to work on problem/variable definition so I'd recommend before you do anything you sit down with your crew and work on these two issues.

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    #193505

    MBBinWI
    Participant

    @Jeffrey – In addition to the excellent questions from Robert Butler, I would ask what is your critical Y criteria for acceptance/failure? You indicate 15 lengths of 6′ fuze, but that 6′ can be separated into many smaller lengths for analysis. You could thus do DOE or ANOVA depending on what specifically you would be looking to understand. As Robert said, you need to better describe your problem and what you are trying to understand.

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    #193506

    Jay
    Guest

    Robert and MBBinWI,

    Thank you for your responses. Sorry if my note was a bit rushed and vague. What can be done in an experiment is not squarely defined yet. Let me try and clarify a few things, though.

    A total of 60 fuses will exist for qualification.

    Two main objectives exist: (1) proving that the chosen powder (the composition chosen for qualification) will burn continuously/uniformly and not snuff; (2) determine a model to predict the fuse burn time with a precision of +/-10%.

    IΒ’d have to say that requirement #1 is more of a continuous burning. As the powder will be inside a metal tube, the uniformity of the burning would be difficult judge. It should be more of a judgment of whether itΒ’s continuous or not (and no snuffing seen).

    The non-snuffing requirement is new. Originally, there was only the objective to model burn time. 45 fuses have already been dedicated for modeling the burn time (the experimentΒ’s target is a certain # of minutes +/- 10%). These 45 fuses will all be made of the powder composition that is eventually chosen. Each of these 45 fuses will have the same powder composition (binder, ingredients, homogeneity Β– should be as all will be made from one lot). Based on the historical variability of other powders (which are most likely more variable than the powder weΒ’re testing), this 45 run test matrix will give adequate precision. There are only two factors involved in this 45 run experiment: temperature and conditioning time. The response here is certainly a variable one (burn time).

    There shouldnΒ’t be any reason why these 45 fuses canΒ’t also be used to prove that the powder will burn continuously/uniformly and not snuff.

    The response for the snuffing prove-out, though, is likely a pass/fail response (snuff / no snuff). IΒ’d like to have a critical Y which is variable for acceptance/failure. Chances are slim, though. This will be discussed early this week and confirmed or not, but my hopes are not high.

    15 additional fuses will be available that can be 100% dedicated for determining if the powder will burn continuously and not snuff. It may be advantageous to change a powder ingredient (if one is thought to be correlated to the chance of snuffing) in the testing of these 15 fuses. This is something that should be discussed early this coming week with the team involved. If an ingredient is changed, then it seems that these 15 additional fuses would become separated from the first 45 fuses due to the composition of the 45 fuses being the same, while the composition of the additional 15 fuses would be mostly different (vs. the 45 fuses). Robert Β– as you say, if a single factor can be used, then possibly enough margin can be shown via logistic regression to show a high reliability of not snuffing with this ingredient/factor in a certain range. Not sure yet if a correlation like this exists Β– again, a discussion for early this week.

    The fuse is actually about 6 inches in length (sorry Β– rushed and poor typing earlier). MBBinWI Β– one of the criteria for success will be the continuous and complete burn of a fuse’s powder. Since a fuse would need to burn completely, I donΒ’t see our being able to split a fuse into multiple fuses (as shorter fuses would not prove a full 6 inch burn).

    Sorry for giving the idea that there are many factors involved. ItΒ’s likely few.

    Hope this clarifies things a bit better. IΒ’d like to have 60 samples which I could test in a logistic regression manner with only one factor. That might get me to the reliability I want (not considering lot to lot variation). This scenario doesnΒ’t exist, though.

    I appreciate your input,

    Jay

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    #193507

    Jay
    Guest

    @MBBinWI
    @rbutler

    To notify you of my response in the attached note. Thanks again.

    Jay

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    #193508

    Jay
    Guest

    @rbutler
    @MBBinWI

    Just to notify you of my reply in the note below

    Thanks again,

    Jay

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    #193512

    Robert Butler
    Participant

    A few thoughts:

    I hope that the final powder chosen for testing is the result of organized research (DOE) and not a WGP (Wonder Guess Putter) effort because if it isnΒ’t then choices concerning which (if any) variable to change should you decide to do something with those 15 fuses is going to amount to, at best, an educated coin toss.

    It sounds like you have no choice with respect to fuse powder batch testing. I agree that powder from a single batch should prove to be homogeneous, however, it is extremely likely that it will grossly under estimate the ordinary variation of the process and what you and the customer can expect with respect to performance. This, in turn, could prove to be an issue later when you deliver product that is under control but is outside the artificially small estimates of variance which were based on tests from a single lot of material.

    It still isnΒ’t clear to me why you would want to use logistic regression for this assessment. Logistic regression provides odds ratios and confidence intervals around those odds ratios. Odds ratios arenΒ’t the same thing as measures of reliability.

    Based on my understanding of your posts it would seem that what you really want to know is the probability of a single fuse having a burn rate within +- 10% of some population mean. If this is the case then after you have measured the burn time of two of the randomly chosen fuses you can start looking at estimates of means and standard deviations and estimates of percent of your production population that have burn rates in excess of 10%. You can run real time updates and estimates of all of these things after each burn and by the time you get up to 10 or so your data should be able to give you a very good estimate of the mean burn rate, the spread of the burn rates and the percent of the population likely to exceed the +-10% limits. This information, in turn, should allow you to make some decisions concerning additional testing and/or composition changes (again, assuming the composition is based on a design effort)

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