# Control chart and sample time

#### Ben-R

##### Registered
Hello,
I try to understand the relation between average run length and sample time of an quality control chart.

I think about the following problem:
I should choose an exponentially weighted control chart with a predefined weighting factor. In the fault free case there should be an average run length of e.g. 371. Now there is a shift in mean which can be detected after e.g. 200 samples. This means, after 200 minutes (with sampling time of 1 minute) the fault will be detected.
So far so good.
My Signal recorded originally with a sample time of 1 second. If I use a sample time of 1 second, the fault will be detected after 200 seconds?
Is it allowed to reduce the sample time to 1 second?

Thanks for Help, Ben

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Usually we talk of average run length based upon the measurements made. Such as I may measure each item produced. However, you have thrown in two factors I would need to know about:
1. You talk of measuring something every time interval. Is this a continuous process and I am measuring something like pH or temperature at certain time increments?
2. You mention an exponentially weighted control chart. That throws in a complication in terms of average run length.

I will say I distrust the exponential weighting, and there are better answers in terms of using a suite of trend rules. For example, the writeup at
6.3.2.4. EWMA Control Charts

states "By the choice of weighting factor, λ, the EWMA control procedure can be made sensitive to a small or gradual drift in the process, whereas the Shewhart control procedure can only react when the last data point is outside a control limit. " Whereas very few applications of SPC utilize ONLY the rule of a single point outside the control limit.

I do not understand your statement: "Now there is a shift in mean which can be detected after e.g. 200 samples." Is this referring to a shift in the process you know about? The average run length relates to detecting a signal when there is no change to the process. what is average run length | WinSPC.com It is related to the alpha error - the false alarm rate.

So if a process is indeed stable, and results are independent from time interval to time interval (regardless of the length of time), and we are not including EWMA, then the average run length has the same meaning whether the samples are 1 second apart or 1 hour apart.

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