## Z1.9 Sigma for Variability Known Method

Q: I have a question about  Z1.9-2008: Sampling Procedures and Tables for Inspection by Variables for Percent Nonconforming. I have seen there is a “Variability Known” method. However I don’t know how to get a Sigma, so I don’t know how to use this method. Could you please share how to get a Sigma?

A: To get a Sigma to use for the Variability Known method is to have data that has been collected over a period of time and calculate the standard deviation. The rule here is at least six months of data with at least 50 data points.  Depending on the process, if the data has been collected and there is over 1000 data points, the time limitation goes away since you have an extremely large data set to work with.

Q: During the 6 months, the process should be under control, right? And data should be normal distribution, right? Is there any process control needed? And how do I maintain this process and Sigma?

A: Yes, there is the assumption that the process is normally distributed and is stable.  That means some type of process control is being used.  Ideally this would be an X-bar and r or an X-bar and S chart. If an out of control situation occurs and you can bring the process back into control, then you are ok.

Q: Could you tell me the meaning of “data point”? As you know, during the 6 months, we will get lots of batches. For each batch, we will have a certificate of analysis (COA), and many data. I am not sure how do you combine data for different batches. How do you calculate this?

A: Data point, in the most simple format, could be the statistics associated with a batch or a mean and standard deviation/range. Each batch gives you a new set of data points. You can combine the time based data in a couple of different ways:

1. You can take each batch and use the means and plot them on an X-bar and R or an X-bar and S-chart.
2. You can take the raw data and combine it into one large distribution.

The preferred way is the control chart approach since you will know if the process is stable since it is already plotted.

Jim Bossert
SVP Process Design Manger, Process Optimization
Bank of America
ASQ Fellow, CQE, CQA, CMQ/OE, CSSBB, CMBB
Fort Worth, TX

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