Formulas to be able to answer these Run Chart questions


Involved In Discussions
last one for today:

A run chart has recorded the following values (assume 95% confidence)
10, 8, 6, 14, 16, 14, 18, 20, 8, 10, 10, 10.

a) the actual number of runs
b) the expected number of runs
c) the centerline plotted value
d) would this data pass a runs analysis test?

I can't find any formulas to be able to answer these run chart questions. Can anyone help?



The best way is to put data in Minitab & create a run chart. You can count number of runs by looking at chart. As pointed out minitab documentation has all the detailed formulas for test of randomness.


Involved In Discussions

This is a test question, and during the test, students don't have access to Minitab or the Internet. Just their notes/textbooks. So, they are expected to know it cold just based on experience and what is in front of them.

My problem is that even with my Internet searches, I still wouldn't be able to answer it. Same for the other questions I've posted here.

I will take a look at Minitab's documentation to see if there is anything there that will help.

Thanks for the reply and info, and have a good one!



Quite Involved in Discussions
I've always been an advocate of understanding a concept before turning "responsibility" for a calculation over to any kind of software.

Does this help with the actual vs expected values?


  • Formulas to be able to answer these Run Chart questions
    Runs Test.JPG
    63 KB · Views: 259


Involved In Discussions
Not sure what text book you are using (Montgomery is probably the gold standard) but I'm sure the formulas are readily shown and easy to calculate with a calculator that performs standard deviation. The first three of the four are really understanding questions.

Here's my shot at it w/o looking up anything:
a. 12 (12 data points, each one is a run point)
b. 20 (95% confidence means 1/20 false reject so your Avg Run length is 20 when you use 95% bounds)
c. The centerline of a control chart is just the average of the values. Add the values and divide by 12. (I get 144/12=12 in my head)
d. Determine the actual control limits (avg +2 sd and avg -2 sd) and which/any fall outside (2sd should be a good enough approximation of 95%) I don't have a calculator near me.



Involved In Discussions
A random web app seems to say the standard deviation is a bit more than 4 do control limits would be and 20.yyy so none of the run points would be rejected.

Top Bottom