CSSBB Primer Sample Questions – Need Help

[Lori Snetsinger]

Hello there,

I am currently studying for my CSSBB exam, and I am having some trouble with the Primer practice questions in section 7, primarily #s 7 and 33. Question 7 reads: The report Cpk for a process with an average of 28, a spread of 10 units, and USL and LSL of 35 and 15, respectively would be:

a. 1.6
b. 1.4
c. 1.8
d. .714

I have no idea how to estimate the standard deviation given this information, as “spread” isn’t covered anywhere in the Primer section. Please help!

[waardg]

Cpk = MIN [(USL – mu) / 3 sigma)] ; [(mu – LSL)/3 sigma)]
sigma = Rbar / d2
Rbar = 10, d2 comes from a table. (R= Range = Spread)

[Lori Snetsinger]

The problem is that I don’t have the value for n to be able to look up the d2 value.

[Ted Hessing]

Lori, a quick note on this one. I don’t work through questions from other providers’ question banks, the Primer included; for a specific Primer answer, check with the Quality Council of Indiana. The concept, though: when a question gives you only the process spread, read it as the natural process width of 6 sigma, so sigma is the spread divided by 6. Cpk is then the distance from the mean to the nearest specification limit, divided by 3 sigma. With no subgroup size, the d2 table isn’t the intended path. My Process Capability (Cp and Cpk) article walks through worked examples.

[joey1202]

Which d2 should be used using this table since n is unknown?

[Lori Snetsinger]

I found an answer to this on the interwebs, here’s an excerpt, as well as the link:
In the question process spread is given 10 units… And you have taken it as standard deviation directly….
This process spread of 10 units is assumed to be 6 sigma. Thus sigma is 10/6.

• This reply was modified 2 weeks ago by Ted Hessing.

[Ted Hessing]

Hi Lori,

My reply above gave the short version. Here is the fuller one, with the ground rule first: I don’t work through questions from other providers’ question banks, the Primer included. Their authors own those questions and their answer keys, so the best place to confirm a specific Primer answer is the Quality Council of Indiana. I’m happy to explain the concept behind it, though, because “spread” trips up a lot of people.

When a question gives you the process spread and nothing else about variation, read the spread as the natural width of the process: 6 standard deviations, or plus and minus 3 sigma. That is the same 6 sigma that sits in the denominator of Cp. So sigma is the spread divided by 6.

From there, Cpk is the distance from the process mean to the nearest specification limit, divided by 3 sigma. Work out both sides (upper and lower) and keep the smaller one. The side closest to its limit is the one that controls Cpk.

The d2 route (sigma = R-bar / d2) is for a different situation: you’re given an average range from subgroups of a known size. If a question gives you no subgroup size, that’s a clue the d2 table isn’t the intended path.

There’s a full walkthrough with worked examples in my Process Capability (Cp and Cpk) article.

Ted

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