Probable Error and Your Measurement System

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Thanks so much for reading our publication. We hope you find it informative and useful. Happy charting and may the data always support your position.


Dr. Bill McNeese
BPI Consulting, LLC

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Measurement Systems Analysis/Gage R&R

Comments (14)

  • Stanley AlekmanJuly 18, 2017 Reply

    If two measurements of the same sample differ by less than the probable error, is the difference meaningful? Or are both measurements effectively the same?

    • billJuly 18, 2017 Reply

      Both measurements are effectively the same in my opinion.  The difference is not meaningful.

  • Muhammad FahadSeptember 3, 2018 Reply

    Thanks alot ur work really have fone a lot for me 

    • billSeptember 3, 2018 Reply

      You are welcome!  Thanks for letting me know.!

  • ahmed abdelatyOctober 29, 2018 Reply

    please tell me how to obtain the constant in the probable error law 0.675

    • billOctober 30, 2018 Reply

      That is the value that defines where 50% of the values lie for a normal distribution.  Within +- 0.675 standard deviation of the mean.  See figure 5.

  • Ed SharApril 12, 2019 Reply

    Thank you for these really clear explanations. In order to get off to a right start though I am wondering, would the Probable Error in a single measurement eg. of time to the nearest whole minute be:-+/-0.5 minutes,or +/-0.25 minutes (50% or the range) or +/-0.34 minutes (1 Normal SD) ,bearing in mind that each time within the +/- 0.5 minutes range is equally likely for a single measurement? Understanding that Probable Errors add in quadrature, the Probable Error in a length of time between two such measurements would then be:-+/- Squrt (0.52 + 0.52) = +/- 0.707 or +/- Squrt (0.252 +0.252 ) = +/- 0.35or +/- Squrt (0.342 +0.342 ) = +/- 0.48 ?

    • billApril 14, 2019 Reply

      I am a little confused by what you are asking. The measurement system error is deteremine by repeated measurements on the same part.  Call that sigma.  Then the PE is 0.675(sigma).  50% of the measurements fall within +/- PE of the average.  You use the PE to determine if your measurement increment is valid – as described above.

  • Taft DingSeptember 23, 2019 Reply

    Where does the 0.2PE and 2PE come from?  How to interpret it? What's the impact of your measuring result if this is not followed, either smaller than 0.2 PE or larger than 2PE? Thanks, Taft

  • crystal thompsonFebruary 12, 2021 Reply

    I dont understand how to find σms

  • Ravi January 11, 2022 Reply

    Many thanks for the explanation as always!I dont know if this is related question, but is the probable error the same as error bars plotted on a graph?My second question would be in regards to the Standard Deviation, the example above shows a normal distribution. Does the same principle apply for a non normal distribution?Many thanks

    • billJanuary 11, 2022 Reply

      YOu are welcome.  I don't think it is the probably error, probably just one standard deviation.  I don't believe the same principle applies to non-normal distributions but I will have to check that.

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