# SPC that uses the variance among samples rather than among observations within a sample?

Discussion in 'SPC - Statistical Process Control' started by kmacqe, Sep 11, 2019.

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1. ### kmacqeNew Member

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We have a laboratory process that processes batches of 96 samples at a time. The average of each batch is recorded in an Xbar-s chart. The variability within a batch is very small and the variability between batches is much larger. It is expected that the batches will be quite variable and this does not indicate a process issue. Because the intra-batch variability is so small, the control limits are very narrow and every batch looks to be out of control, even though we know the process is not out of control (at least based upon this metric). As a result, we do not use the LCL and UCL to make determinations about process health and we do not apply the typical SPC tests because they fail with almost every batch. I would like to apply meaningful statistics to this metric and be able to detect when there is actually a process issue.

Is there an alternate way to compute control limits that uses the variance among samples (variance among batches) rather than among observations within a sample (among the 96 samples in a batch)? Or is there a different statistical test that I can apply that is more appropriate?

2. ### MinerModeratorStaff Member

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If the within batch variation is that small (possibly measurement variation), you might consider using an individuals control chart, which uses a moving range between batches.

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3. ### Bev DModeratorStaff Member

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This is not uncommon in batch processes. You have a non-homogenous process.

Remember that the ‘traditional’ Shewhart charts that use piece to piece (within subgroup) variation to create the control limits for the subgroup averages is only valid when the process is homogenous. In other words the process average is directly related to the standard deviation. In physics terms this occurs when the process location (average) and the process variation (standard deviation):are controlled by the same factor(s). Many batch processes have their location and variation controlled by different factors.

So Miner’s suggestion to use the I,MR chart for the batch averages is spot on. It is not a work around, it’s exactly what the physics and the statistics require. You can add a simple S chart to monitor the within batch variation.

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4. ### kmacqeNew Member

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Great suggestion! Thank you!

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