Setting specification limits

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    Ronan McGinley

    What techniques or data should I use to establish correct specification limits for a process, assuming that these have not been set by the customer’s requirements? If the process is normally distributed, can I set them to mean +/-3 standard deviations and accept that the process wil be within specification 99.73% of the time, or +/-4 std dev if I want 99.9937% within specification? Or is there another rule that should be used?


    Bruce Floyd

    Are you setting the +/- 3 SD limits on the average of a subgroup or on the individual samples?  How many samples are in the subgroup, if there is one?  Will the +3SD and -3SD production function as intended? 


    Ronan McGinley

    In this particular case, it is individuals. I am also interested if there is a rule of thumb. The purpose of this would be that we could inform the customer what practical spec limits would be, based on a statistical rationale. If I have interpreted the last part of your reply correctly, does that go back to the customer setting the specification for us?



    It depends on the case. If there is an optimum (lower cost, best function, easier to manufacture, etc.) and the characterisitic is not critical to quality (no “sound” deviation will produce a significant worsening in performance, function, fit, etc), then do not bother in putting specifications. If you want something for your operators give them a control chart centered in the optimum and let them react only when the process goes out of control. In that case, they only have to fix the process (no sorting/rework needed).
    If, on the other hand, the characteristic can affect the customer satisfaction, then put a tolerance as wide as possible leaving a safety margin, regardless of how capable the process is. If the process variation is to large for that tolerance, then it is to large to ensure customer satisfaction, so using an even wider tolerance will make your process people happier, and your customer more unsatisfied.
    The SPC handbook – AIAG says something like:
    There are two ways to improve the process capability. Reduce variation or increase the tolerance. The last one does not improve neither the process, nor the product quality, nor the customer satisfaction.
    But what if the tolerance defined as above is too easy for the process (like ±10 sigmas)? Great! Why would you set a tolerance any stricter than what is needed? You can have a 10 sigma process and want to make it a 3 or 4 sigma one? That’s not sound.
    Now, if you are doing the design, the key is to make a design robust enough to satisfy your customer with your process variation.


    Bruce Floyd

    It would be hoped that the process will make product within 3 SD that will work for the customer.  Since you are sampling individuals, there is less concern that averages could cover a wide range in results.  Taking enough consecutive samples to determine the mean and SD are important.  You would not want to go to the customer with a control chart based upon limited data. 
    It is customary in many industries to present the customer with samples near the midpoint as well as both extremes to varify that the customer can live with the specifications.  This will establish that the customer knows what they want and that everyone has agreed to the specification.  It is always preferable to have the customer agree to your process limits than to have artificial limits impossed upon your process.



    So you submit to the customer samples in the average and in + and – 3SD ad they say “Ok, that works for us”. What do you do next? Set specification limits at ±3SD? Why? Maybe if you had submited samples at + and – 5 SD they would still have worked, but now you are limiting your process capability to Cp=1 max. And even small shifts of the process (no process is in-control 100% of the time) will make bad parts that maybe they are not so bad after all (in fact, with a Cp=Cpk=1 you will have about 3000 PPM even with no shift!), adding extra recheck, rework and scrap costs. And what if + and -3SD is already too bad?
    The maximum variation that will not adversely affect the customer satisfaction is what it is, regardless of what a tight or lose specification you set and regarless of what your process variation is.
    The ideal situation is that the specification is set at the maximum variation that will not worsen the customer satisfaction (may be with some safety margin) and that the process spread fits many times inside that. In that case it is said that the specification is representative of the customer’s needs so the specification becomes the “voice of the customer”, and that the “voice of the process” is compatible with the “voice of the customer”. If this is not the case, setting another “artificial” specification will not fix the problem. The solution is such a case would be to improve the process to reduce variation or to improve the design to make the customer satisfaction less sensitive to the process variation (i.e. to enlarge the maximum variation that will not worsen the customer satisfaction). Some times none of those solutions are readily possible, so one of the following three happen: The customer is not satisfied, or the contract is not accepted/terminated, or extra costs are accepted to sort 100% and scrap (or rework and recheck) the bad parts.
    There are many areas of the technology where state-of-the-art manufacturing processes have not achived a point that allows enough capability so as to avoid a 100% check yet, either because the allowed rate of failure is too low, or the process variation is to high, or the check is inexpensive so it is worth doing even for an “acceptably” low rate of failures. Examples: Aircraft engine blades and vanes are 100% checked for cracks, rolling bearings are 100% tested for noise, faucets are 100% checked for leakage, integrated circuits are 100% checked for proper function.
    This is just my point of view.


    DANG Dinh Cung

    Good morning,
    There are two uses of control chart : following up a process and selecting a process or a manufacturing.
    1. Following up a process.
    Suppose you take LCL and UCL equal to X_bar minus and plus 3 Sigmas. That means that there is normally (or customary, or usually) a probability of 99,75 % a measure to be inside the [LCL;UCL] interval and the probability that the measure is outside the [LCL;UCL] interval is so tiny that there must be some abnormal phenomena. In this last case, your process is out of control, you have to stop you process, find out what is wrong, remove it and restart.
    The control chart is here used to detect unsual events which may be triggered off by some thing going wrong.
    2. Selecting a process or a manufacturing.
    Your issue is relating to protecting against the risk of producing defects when
    (a) having a machine (thus a process) you want to manufacture according to a specification,
    (b) having to manufacture according to some specification you want to choose your machine (thus your process). 
    It is generally accepted that the risk you miss an unsual event is 0,25 %. That is why LCL and UCL are equal to X_bar minus and plus 3 Sigmas.
    In Vietnam, we frequently have to solve this kind of problems. As a poor country, we have a lot of old machines which are not accurate. That means we have processes with large sigmas and when we test manufacturing something our capability is poor. So we have to decide
    (a) to accept a contract with tight tolerance and to have a lot of out of specification products,
    (b) to limit contracting with large tolerances specifications,
    (c) to accept adjusting frequently the machines spending a lot of our manpower time,
    (d) to invest in new and more accurate equipments (if we can finance them).
    Best regards,
    DANG Dinh [email protected]


    Chip Hewette

    One should always seek to link upstream processes with downstream measures through proper experimentation.
    If upstream process A is allowed to vary naturally, determine the bounds of that natural process.  Then, create samples or choose samples at those bounds.  How do components with these upstream values affect downstream measure B?  Use statistical experimentation techniques to identify if these levels create a meaningful difference in measure B.
    Without evidence of longterm process average and range, setting limits can be tricky.



    We can speak during hours and days about the subject.
    Personnaly I’m using a book as my “bible” on the SPC chart subject and I recommend it in each of my training sessions :
    “Understanding Statistical Process Control”
    by Donald J. Wheeler and David S.Chambers
    Foreword by worlwide Quality Sensei W.Edwards Deming
    SPC Press, Inc – ISBN = 0-945320-13-2
    Enjoy your reading.

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