Cpk Calculation - Tolerance to maintain 1.33 & 1.67 Cpk respectively

[bobdoering]

Re: Cpk Calculation

1) confirm that you have a capable measurement system for this characteristic
2) run a process trial to understand the variability of this characteristic
3) confirm stability, normality, remove outliers
4) calculate the standard deviation
5) calculate what dimension tolerance you should have if Cpk had to be 1.33 or 1.67

I would clarify this a bit:

1) confirm that you have a capable measurement system for this characteristic (GRR at 5% of tolerance or 10% of control limit for 1.66, minimum, 7% of tolerance or 10% of control limit for 1.33 minimum)
2) run a process trial to understand the variability of this characteristic
3) confirm stability, correct distribution (normal only if it is a normal process - if it is normal and it should be non-normal, then you may have too much measurement error, etc.), remove outliers if identifiable as special causes
4) calculate the standard deviation (if a normal distribution or similar - not necessary for uniform distribution)
5) calculate what dimension tolerance you should have if Cpk had to be 1.33 or 1.67 based on the appropriate statistics for the distribution

 

[brahmaiah]

Re: Cpk Calculation

To start a new X-R control chart here is a guide to fix provisional control limits.which should be replaced after the first trial batch.:
V.J.Brahmaiah

 

[gianni]

Thank you all for your responses. Basically using the CP formula and calculating the sigma (assuming process is centered) I can determine that to achieve 1.33 & 1.67 I will use 75% and 60% of the tolerance respectively. Once I conduct actual trials I can adjust from there.

 

[tahirawan11]

Hi all,

I have a similar situation as well; my customer is interested to know how much of the allowable tolerance he can use in order to achieve a Cpk of 1.33, assuming that the process is centred and under control. The specification limits which cannot be changed are (USL = 170 and LSL = 100, total tolerance = 70) and the current std. deviation of the process is 14.2.

Using the formula given by Miner I calculated the total tolerance = 113.3, which is more than the total tolerance limit, can anyone tell me why is that so and does it mean the std. deviation must be reduced to get a Cpk of 1.33 and if so then how much?

Cp = USL - LSL / 6 StdDev

USL - LSL = Total Tolerance = Cp * 6 StdDev

Total Tolerance = 1.33 * 6 * 14.2

Total Tolerance = 113.3

 

[bobdoering]

My customer is interested to know how much of the allowable tolerance he can use in order to achieve a Cpk of 1.33, assuming that the process is centered and under control. The specification limits which cannot be changed are (USL = 170 and LSL = 100, total tolerance = 70) and the current std. deviation of the process is 14.2.

Using the formula given by Miner I calculated the total tolerance = 113.3, which is more than the total tolerance limit, can anyone tell me why is that so and does it mean the std. deviation must be reduced to get a Cpk of 1.33 and if so then how much?

Cp = USL - LSL / 6 StdDev

USL - LSL = Total Tolerance = Cp * 6 StdDev

Total Tolerance = 1.33 * 6 * 14.2

Total Tolerance = 113.3

Your problem is your standard deviation is too large to be able to meet 1.33 Cp wit the specification cited. Also, you might be mixing up process tolerance and customer specification. If your customer specification can not change, your process tolerance (Upper process spec-lower process spec) will be less than the customer specification to meet the Cp. I have attached an excel file that you can plug in your specs, your Cp and it will back calculate your starting Upper process spec and Lower process spec (assuming centered and assuming NORMAL), which also gives you your require standard deviation to meet the Cp. You can also plug in the Cp.

Do not use this approach for precision machining, as the normality assumption is invalid if controlled correctly.

 

[Stijloor]

Friends,

Process capability indices (Cp, Cpk, Pp, Ppk, etc.) are the pixie dust of process controls.
Easy to calculate, easy to impress an ignorant customer, and it provides instant gratification.
I call it the vending machine mentality; a few numbers in, out come instant results.
Everybody happy.

Stijloor.

 

[tahirawan11]

so i guess now i know what i need to do

Step 1, Reduce the std, deviation to 8.77

Step 2, the maximum allowable process tolerance can be 161 - 108 which will take us to 4-sigma so everyone can live happily ever after.

 

[bobdoering]

so i guess now i know what i need to do

Step 1, Reduce the std, deviation to 8.77

Step 2, the maximum allowable process tolerance can be 161 - 108 which will take us to 4-sigma so everyone can live happily ever after.

Yep...that is how it works! One way I explain it is this: The customer (and final inspection, which is the surrogate of the customer) are the only ones that "own" the customer spec. The process does not, thanks to total variation, including sampling error, measurement error, and much, much more. Some folks in production hate to hear that, they say "Hey, you cut our tolerance 75%!" Unfortunately, it is the "our tolerance" they are getting wrong.

Have fun!