Sampling size in continuous process

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    Rakesh Patnaik

    I am from cement business. Packing plant of our unit have two rotary packer having 12 spouts on each packer. Process of bag filling is 24 Hrs basis per day (Continious basis filling). Recently we have decided to implement six sigma on bag weight variation. The very first problem we are encountering is what no. of bags to be weighed for sample collection which will represent the the total population. History data is not availble with us since it is a recent project.Can any one help me? Please provide the detail calculation. The USL for bag weight is 50.25Kg and LSL is 49.75Kg. Target is 50.07Kg. Historical Standard deviation is not availbale with us. RegardsRakesh Patnaik 



          I am not sure my answer is going to help you or not.
    What i feel is , first you develop a decision model like i will reject this bag if it is above USL or below LSL. Now develop a sample size depending on the attribute type of data. For this you need to assume the following
    1. Confidence level
    2. Proportion of bad or good ( take 0.5 for max sample size)
    3. Margin of error (in percentage)
       then you calculate the sample size with the above assumed parameters. Once the process gets matured, you will get the std deveiation then you can recalculate your sample size.
    hope this helps you.



    What is the sample for? Lot approval? SPC? Process capability study?



    I feel you are feeling constrained in deploying SPC.
    You do not need to know historical standard deviation. All you need to know is what kind of changes you are trying to detect in your process average. An OC curve is what will be useful for you.
    You need to deploy group control charts in your situation.


    RR Kunes

    Go on the internet and search under Mil-Std-105. It is the sampling plans that everyone uses.



    I saw several posts from you suggesting the use of Mil-Std 105 everytime anybody asks anything about sampling. I think you are giving a bad advice. This is how I see it:
    1) Mil-Std is a sampling and approval standard for LOT APPROVAL only, mainly used in incoming inspection. It is not used for SPC, capability studies, DOE, and a lot of other things.
    2) Mil-Std 105 is used for ATTRIBUTE DATA only (i.e. good – bad), not for variable data. Using variable data you can get a lot more of information, and then you can reduce dramatically the sample size.
    3) Mil-Std is not used by everyone a you state, and one of the reasons for that is that you must accept a certain % of non conforming product as “Acceptable quality”. QS-9000 states “The acceptance criteria for any sampling plan for attribute data is 0 defects”, and that is like saying “you can not use Mil-Std 105”. That’s why all the automotive industries and its suppliers (among a lot of other companies that do not want to name a non-quality level as “acceptable”) do not use this standard.
    Just my opinion


    RR Kunes

    Like most Mil Stds you have to read between the lines. Anything can be considered a lot. Mil-105 requires continuous sampling from ic-control processes.
    Another option is Mil-std-1235. It is desginged specifically for continuous sampling.
    If you study the OC curvers in the back of Mil-105 you can select and customize the sampling program to meet almost every application.


    RR Kunes

    Here is the equation for determining sample size for estimating means:
    Where d = how close to the true mean we want our estimate to be.
                V = variance in the population
                 Z = confidence level = (1-alpha)
                  n = sample size
    then  n = Zsquared * Vsquared / d squared



    Not sure how we got to finding the mean. I think the poster origionally wants to know what sort of control charting to do, although he is not clear about his objectives. The formula RR Kunes posted is close but not quite on.
    We want to add the Z values of both alpha and Beta risks and then square. Also, it is the variancce i.e the squared standard deviation, not the variance squared which would be the fourth power of the standard deviation. n = (Zalpha+Xbeta)squared * sigma(squared) / d squaredIf the sample size is desired to be small ;typically less than 30, adjustment must be made to the risk numbers by using the t-distribution. This usually requires a “guestimate of sample size” and iterative solutions to the best sample size. The formula would then be n = (t(alpha,n-1)+t(beta,n-1))squared *sigma(squared)/d(squared).Hope I got the parenthesis right.



    According my oppinio do you need the next steps as follows:

    Define CpK value during long term study.(in order to identify process variation) effects!!!
    Develop process map to determine factors to be considered for study and factors that must be constant.(causes of variation)
    Determine DOE strategy in order to get the optimal setup parameters and  reduce process variation.
    Establish SETUP parameters.(I don’t know what kind of parameters use on this machine ) PRESSURE,CICLE TIME,SPEED,ETC.
    After PROCESS VALIDATION (MACHINE PARAMETERS) we can develop SPC CHART in oder to get statistical process control throught long term period.
    I hope this can help you.


    Erik L

    One of the questions that you’ll need answered is what is the population size you’re looking to approximate with the sample?  A days output, week, month, quarter, year?  If you know this and the precision that you’re desiring to see in a shift of weight, then you can come up with an estimate of sample size.  If you come up with the estimate of the population size and use 1/6th of the range of values that you measure in weight as a first swag (very rough estimate of standard deviation) I can send you an excel template that will give you a suggested sample size based on a 95% confidence interval.  Good luck!

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