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Robert, Darth, Mike, Vinny, BTDT – need your help

Six Sigma – iSixSigma Forums Old Forums General Robert, Darth, Mike, Vinny, BTDT – need your help

Viewing 11 posts - 1 through 11 (of 11 total)
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  • #39647

    The Kid
    Member

    Dear Robert,Darth, Mike,Vinny, BTDT and all Guru’s,
    I am a BB aspirant and trying hard to digest Hypothesis concept.
    I have a query on hypothesis testing, that at times totally confuses. While i have a fairly good understanding of hypothesis test and its applications, there is one particular aspect to it where all my logic fails.
    We all know that Alpha is probability of type I error and Beta is probability of type II error, and why they are used. The point where i get confused is when we use the other definition of Alpha and Beta i.e Producer’s risk and Consumer’s risk.
    Typically for general applications we take Alpha as 5% (which i perfectly understand) and Beta as 10% (this is where the confusion starts). Now if we use the alternative definition of Alpha (producer’s risk) and Beta(Consumers risk), does that mean that i am exposing the customer to a higher risk factor ?? which goes against the very approach of Six Sigma (Customer first, right?). This is where the whole confusion sets in.
    Can any one help me clear the confusion? Thanks a tons to each and every one of you in Advance!!
    The Kid

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    #121013

    walden
    Participant

    This is how I’ve always looked at it in simple terms.
    Type I error is rejecting the null hypothesis when it is true. Producer’s risk is the probability of rejecting a good lot.(i.e. the null hypothesis is the lot is good, but you reject it, when in actuality lot is good).
    Type II error is failing to reject the null hypotheis when it is false. Consumer’s risk is the probability of accepting a bad lot. (i.e. the null hypothesis is the lot is good and you fail to reject it, when in actuality the lot is bad). 
    Hope this helps.

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    #121015

    BTDT
    Participant

    Here’s the example I always use:Pretend you are on final inspection at a parachute factory. Your job is to make sure the tension on the stitches is neither too tight, or too loose. If it is too tight, then the threads will cut the material of the straps. If the tension is too loose, then the stitches will rub and eventually fail. Your job is to make a random sample of the stitching at 10 places on each parachute. You will conduct a one sample t-test with your 10 readings and decide whether the average of the population of ALL stitches on the harness is within the specifications.Ready?The test fails (p

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    #121016

    Dayton
    Member

    Well done.   That was an interestingly constructed question. In attempting a response I’m not going to get into Bayesian-based statistical decision-making because I think you fully get the mechanics.
     
    But I think that you are looking at the question in an either/or situation where the Type-I error is the manufacturer’s risk and the Type-II is the consumer’s risk and there is no cross benefit.
     
    You can look at both Type I and Type II from either the consumer’s or the manufacturer’s vantage point.  Taking both types from the consumer’s vantage point Type I error occurs if the consumer incorrectly rejects a good product and Type II error occurs if the consumer fails to reject a problematic product.   And both in this description are determined or seen in relationship to rejection of the null hypothesis.
     
    In seeking to determine appropriate sampling levels and acceptance rates you are striking an economical risk based balance between the potentials for Type I and Type II occurrence.
     
    But like a many faceted jewel or blind men describing an elephant everyone is going to see this question differently or at least from different perspectives.
     Vinny

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    #121019

    The Kid
    Member

    Dear BTDT and Vinny,
    Thanks for your valuable inputs and clearing the myth of Beta=10%. and yes i agree with Vinny that many people will look at it from different perspective and that is the reason i had describbed by confusion elaborately to avoid misdirected responses.
    I hope i am not asking too much from you guys, but some amount of confusion still remains. Can any one of you give me a simple example w.r.t  to the determination of sample size , acceptance sampling and Alpha and Beta stuff put together (from the perspective of defination that i am  referring to)?
    Thanks again…
    The Kid

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    #121022

    Dayton
    Member

    Instead of trying to get something truly usable and practical from either one of us try the NIST/Sematech Engineering Statistics Handbook.   It will describe to you how to develop sampling plans taking into consideration Type I & II error.
     
    http://www.itl.nist.gov/div898/handbook/pmc/section2/pmc2.htm
     
    http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/singsamp.htm
     
    Vinny

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    #121046

    Ken Feldman
    Participant

    Let me give this a try as well and keep it high level and simplistic:
    1.  Company A produces drugs…the medicinal kind. Each lot has to be tested against some purity standard.  Because I take samples, I have a risk of rejecting a good lot.  This is my alpha risk and since I take the hit of rejecting good product that I produced, we can call that a Producer’s Risk.
    2.  There is also a risk that a bad lot mistakenly passes inspection and gets shipped to the consumer.  This beta risk now subjects the consumer to a risk of adverse effects thus it is now a Consumer’s Risk.
    3.  The level I set alpha and beta risk can be an economic decision based on the downside of incurring either.  In the case above, the Consumer risk will likely cost me a whole lot more in lawsuits than the Producer risk of throwing away a good lot.  Therefore, I might want to really minimize my beta risk and ease up a bit on my alpha risk.
    4.  Power is 1-beta and represents how good my sample and testing is in detecting a difference should it exist.  Confidence is 1-alpha and represents how confident I am in making some decision regarding my testing.

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    #122014

    C.R.Shetye
    Participant

    Hello Btdt,
    That is an excellent example. It is like asking, when did you stop beating your wife?
    CRS

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    #122015

    BTDT
    Participant

    CRS:Designing an good survey can be quite complex. For example, the order of names on ballots is usually scrambled to prevent bias.:) BTDT

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    #122019

    BTDT
    Participant

    CRS:I think we just responded to the wrong thread, oops.(5:35 am – still sleepy)BTDT

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    #122068

    Karel
    Participant

    I recall an example we worked with was around verdicts where the death penalty might be pursued.
    The Null Hypothesis Ho was the defendant was innocent, therefore the Alternative was the defendant was guilty.
    So the critical decision is usually the type 1 error, that is where you convict and innocent peson, so the alpha and beta (type 2 error where a guilty person is freed) were adjusted in some manner to reflect this. My apology for only giving part of the story, but if anyone has some data behind this I would be interested in seeing it

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