# Assignable causes rules clarification

#### rnsvasan

##### Involved In Discussions
In control chart there is a rule that if 7 points continuously falls on either upper or below the average value, then it is assignable causes. Can any one clarify why 7 is taken as a guideline and why not 6, 5 or 4 etc.

#### Johnny Quality

##### Quite Involved in Discussions
The guideline depends on which rules you are using. The chart below is taken from here.

It seems you are using the AIAG rules, someone more experienced with SPC will hopefully post and show you where the numbers come from. I would say the numbers come from the % chance of the phenomenon coming from common causes, as a point beyond UCL or LCL is something like 99.8% from the top of my head.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
“What are the odds of certain patterns occurring simply by chance?”
Many of the rules were deceptively derived through the use of PROBABILITY (Not inferential statistics of any theoretical distributional model, ie the NOT the Normal distribution or the central limit theorem). Some of the probability calculations are exact, some are based loosely on the empirical rule and Tchebycheff’s Theorem. Of course while the Probability calculation can be made exact or precise there is no precise or exact ‘cutoff’ of when to say that a ‘change’ is suspicious enough to warrant investigation. These rules have stood the empirical test of time and are based on the users 'risk' tolerance of a wrong answer. Remember the alarm doesn't mean that an assignable cause has created a change; it means you should investigate to see if a change has occurred. This is subtle but critical.

the calculations can be found at:
Western Electric, "Statistical Quality Control Handbook", 1956, 2nd Edition, 10th Printing, May 1984, Part B, pp. 23-30 and Part F, pp. 149-183 http://www.contesolutions.com/Western_Electric_SQC_Handbook.pdf

Lloyd S. Nelson, "Technical Aids," Journal of Quality Technology vol. 16, no. 4 (October 1984), pp.238-239

The Western Electric Handbook is available for FREE. I strongly recommend it.

#### Mike S.

##### Happy to be Alive
Trusted Information Resource
In "Understanding Variation" Dr. Wheeler states that 8 points above or below the avg is "roughly the same as getting 8 or more heads or tails in succession when tossing a coin" with the odds "commonly cited at less than 1 out of 128".

I suppose 7 points are 1 in 64 odds and for some that is enough to suspect a signal.

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