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Assuming Normality or Other Distribution

Discussion in 'Capability - Process, Machine, Gage …' started by rmf180, Feb 8, 2018.

  1. rmf180

    rmf180 New Member

    Sep 18, 2015
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    Most things in life follow the normal distribution left to their own nature. However, GD&T features and others which drive toward zero are by design not normal (log-normal, exponential, etc). Does anyone have a list beyond these few as to the appropriate non-normal distribution?

    The specific example I am working with is a water heater is controlled by PID system (non-normal or tampering) which constantly corrects for "error" from set point. Heated water from this system is cooling molds which contain internal thermocouples. The process is monitored and each cycle saves the temperature and dispositions product based upon alarm limits.

    What distribution would be appropriate for a system where the system is constantly being corrected?
  2. Miner

    Miner Moderator Staff Member

    Jul 30, 2015
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    Greater Milwaukee USA
    Dimensions that are affected by physical limits or where the machine utilizes a hard stop will exhibit skewed distributions. The following examples will help illustrate:
    • A drilled hole diameter: The drill might wander, which allows the hole to vary to the high side, but the hole cannot be smaller than the drill.
    • A drilled hole depth: The drill progress to a hard stop. The hole can vary before hitting the stop, but cannot progress deeper past the stop.
    • Physical parameters: For example, tensile strengths tend to be positively skewed.
    Skewed distributions are common for transactional metrics involving time, for an output that has a nonlinear relationship with the input variable, or from an interaction between input variables.

    Skewed distributions can also be caused by mixtures on process streams, reprocessing, and from unstable processes.

    Regarding your example for a controlled process, you would probably have a uniform distribution, but could conceivably have a truncated normal distribution. In the specific example you gave, I would expect to see a uniform distribution because a time series view of the temperature would probably appear to be saw-toothed (slow cooling to the set point followed by rapid heating).
    Last edited: Feb 8, 2018
    Atul Khandekar and Bev D like this.
  3. Bev D

    Bev D Moderator Staff Member

    Jul 30, 2015
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    So you will need to plot the histogram of your data to determine which distribution it follows.

    and now for our question: why do you need to know what the distribution is?

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