# Statistical Process Control-What is Std. Deviation

Discussion in 'SPC - Statistical Process Control' started by Mahesh jadhav, Aug 19, 2016.

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Whats is standard deviation?
How to calculate it?

2. ### Bev DModeratorStaff Member

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The Standard deviation is a quantification of the variation (of a data set or the process from which the data came). The basic formula is straightforward:
SD = square root[sum(the average - each data point)/n]. If the sample is smaller than 30, we divide by n-1 instead of n.

HOWEVER: the data we use in the formula is critical and depends on what we are trying to do. This is particularly true for SPC which is the title of your post. So can you clarify what you really want to know?

Also, this is a very basic question. Can you elaborate on your situation? Have you had any training in statistics, SPC or quality? Why are you interested in SPC?

3. ### tony sWell-Known Member

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If there are 100 people with different ages, get the average age. If you will get the difference of the ages of each individual against the average age, you'll get several values of deviation from the average age (i.e. deviation from the average age of the youngest and the deviation from the average age of the oldest are different). However, the standard deviation is the single common value that any individual age has against the average age. The youngest and the oldest will have the same standard deviation away from the average age.

4. ### Bev DModeratorStaff Member

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This is only true when the data are perfectly symmetrical about the average...

5. ### Ravi KhareMember

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Agree with what Bev and Tony have said above.

In context to SPC there is more to it. I like the way Donald Wheeler has put it.

One of the uses of Standard deviation is to calculate the Process Capability. A histogram with a coverage of +/- 3(standard deviations) is superimposed on the specification limits. This tells us the probability of producing out-of-specification work. Further, standard deviation can be calculated in two ways.

1. The root-mean-square formula the Bev has cited above. This standard deviation tells you about how much space the process has been occupying in the period when the data was collected. It does not have a predictive value, meaning it is unable to say what the Process would do in the future.

2. As predicted from a stable control chart as R-bar/d2. R-bar is the average of ranges in the data. d2 is a constant based on the sub-group size. The standard deviation calculated thus, can be used to predict the Capability of the process if it runs stable in the future.

The root mean square std dev leads to the Capability Indices of Pp & Ppk which have an anecdotal value , whereas the R-bar/d2 std dev leads to the Capability Indices of Cp & Cpk which have a predictive value. Wheeler highlights the fact that the two types of Capability Indices serve different purposes, and each needs to be used accordingly.