# Formulas to be able to answer these Run Chart questions

#### leaning

##### 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.

Calculate:
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?

Regards,
leaning

#### Miner

##### Forum Moderator
Minitab's online help has some good information on the methods and formulas they use.

S

#### suraj.singh

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.

#### leaning

##### Involved In Discussions
suraj.singh,

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!

Regards,
leaning

#### JeantheBigone

##### 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?

#### Attachments

• Runs Test.JPG
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#### optomist1

##### A Sea of Statistics
Super Moderator
Amen, have used Minitab.....and very valuable resource

#### David-D

##### 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.

David

#### David-D

##### Involved In Discussions
A random web app seems to say the standard deviation is a bit more than 4 do control limits would be 3.xxx and 20.yyy so none of the run points would be rejected.

David