cp and cpk

There’s a great thread on Cp and CpK here:https://www.isixsigma.com/forum/showmessage.asp?messageID=2035

The formulas given by the first person that reply to this message are correct. Both indexes need the specifications. The difference between them is that Cp is a “process potential index” because assumes that the process is centered between the specs or that can be centered. Cpk is a process capability index that measures the proportion of natural tolerances between the center of the process and the nearest spec.
 

cp is a one time measuring process
ex:  measuring 150 item at one time
whereby Cpk required to take measurment at specific time frame
ie.: every 1 hr

I don’t know your specific case, but ussually is not that Ppk is required OVER Cpk, but some oranizations do not accept the result of a Cpk based on a few consecutive sample from the trial run (what usually happens in a short study for the initial submition) just because in such a short time there is no oportunity to prove stability, what is a prerequisite of Cpk. I support this possition. That’s the same reason (I think) why a Ppk of 1.66 (instead of a Cpk of 1.33) is required (it is a safety margin due the low confidence in such a study). Note that, in such a case, if you dont reach a Ppk of 1.66 you will be allowed to supply anyway, but it will be requested that you take some containment action for the potential non conforming parts while you implement the corrections to reach to a Cpk of 1.33. All that is if your process is a new one. If you have your process already working and with history recorded to show, a Cpk of 1.33 based on those records will be probably accepted. That’s at least my experience.
This topic was widely (and wildly) discussed also in the following threads:
Cp, Cpk, Pp and Ppk 
Cp & Cpk against Pp & Ppk

Rich,
     USL and LSL are Upper Specification Limit and Lower Specification Limit.  They are not claculated.  They are determined by your customer (internal or external).
     UCL and LCL on the other hand are your Upper Control Limit and Lower Control Limit on Control charts.  These are calculated Using different methods depending on the specific type of chart you use.
     A good quick reference to use for these is “The Memory Jogger II” from GOAL/QPC.  You can contact them at 1-800-643-4316.
 
I am not now nor have I ever been associated with GOAL/QPC in any way. 

Flatness is critical to a part my company uses. I have flatness specification of 0-.010″. I need to assess capability of the supplier providing the part within that range. How is the best way I can chart my measurement results? I will be taking 3 measurements lengthwise and two widthwise for each part.  Since I have a one sided specification, where I want the curve skewed towards the lower side, what is the appropiate way to determine capability. I could always use .005 +/- 0, but that might lead to incorrect analysis results.

USL and LSL are the upper and lower SPECIFICATION limits used in Cp and Cpk.  And they are the Achilles heel of this whole metric.   Often they are “American style” limits, which tend to be simply 10% of nominal.  Useless in many cases, but common.  So Cp and Cpk can be >5 for example in computerized testing, but parts can cause field failures if distribution shifts by many sigmas and are still “in spec.”  I recommend no Cpk > 3 allowed!  Guardband to that value or tighter to assure that your test system catch big shifts.  Your SPC systems can warn at 3 sigma, but are often ignored for containment.  Japan used TARGETS for inline SPC and CONTROL limits (calculated from the data, not given by engineers as economically sound guesses).  And they used Cpm which does not require SPEC limits, just target and deviations from that. 

Can the cpk ever be greater than the cp?

Cp = (USL-LSL)/6(sigma) = Design_Tolerance/Process_Capability
From the above formula, Cp ONLY tells us whether we have enough tolerance in our design to accomodate imperfection in the manufacturing process. Product design engineers control the numerator while process design engineers control the denominator. Cp DOES NOT tell us if the process is centered within the Design_Tolerance. Thus the need for Cpk which compares the average to the Target Center as shown by the formula below
Cpk = Cp * (1-k)
where k = (Target – Process Average)/[(USL-LSL)/2]
Cpk is the ACTUAL capability index. It takes into account the actual location of the process mean relative to the specification target.
Ideally k = 0, meaning process is centered at target. Thus it follows that ideally, Cpk = Cp. Now as to the question on whether Cpk can be greater than Cp, i think YES because if you look closely at the formula, k can assume a negative value if Target < Process Average – meaning the process (distribution) is shifted right from the target. I am coming from the assumption that k formula is not enclosed in absolute value operator.
Thus, if k can go negative, we can say that ideally Cpk should be slightly less or slightly more than Cp. We know that process has shifted left or right from target depending on whether Cpk is less than or greater than Cp.
Now i go back to my assumption, and ask anyone to please confirm if –
 k = ABSOLUTE VALUE of (Target – Process average)/[(USL-LSL)/2] ? 
 

Hi Ross,
Thanks a lot for your confirmation. Now i understand the other definition/formula of Cpk (i.e. the lesser of USL – Mean/ ..or  Mean – LSL/….).
sam

Cp is calcuated as (USL – LSL)/6*Std.Dev.
Cpl = (Mean – LSL)/3*Std.dev
Cpu=(USL-Mean)/3*Std.dev
Question:
What’s explanation behind the “6” used in Cp and the “3” used in Cpl/Cpu?
Appreciate someone can enlighten me on that.
Cheers and thx!
Rgrds,
Desmond.

Difference between UCL and LCL = 6 standard deviation (total range)
Mean to LCL = 3 standard deviations, lower part of the range (Mean cuts the UCL and the LCL in half if distribution is normal)
Mean to UCL = 3 standard deviations, upper part of the range
I hope this helps.

detais and graphs

pictures speak louder
http://www.et.byu.edu/groups/mfg340/lessons/capability/8rulesforcpk.html

Dear Sir,
Pls. send me the detail of Cp & Cpk.
I am very thanks full to you.
Thanks & Regards
Vishal Bhardwaj
 
 
 
 

Your post describes Cp and Cpk as calculated using stdev. However Pp and Ppk are calculated with stdev, but Cp and Cpk use sigma estimator the average of the ranges over the constant d2 (Rbar/d2). For correctness, your post should read:
Calculating Cpk and PpkCp = (USL – LSL)/6*SigmaEstCpl = (Mean – LSL)/3*SigmaEstCpu = (USL-Mean)/3*SigmaEstCpk = Min(Cpl,Cpu)
Pp = (USL – LSL)/6*Std.DevPpl = (Mean – LSL)/3*Std.devPpu = (USL-Mean)/3*Std.devPpk = Min(Cpl,Cpu)
AIAG standard formulas are available at: http://www.qimacros.com/formulas.html#histogram

When calculating Pp and Ppk for a process capability study, overall standard deviation is typically adjusted by the bias correction factor c4, so there will be a slight difference in the overall standard deviation calculation for the smaller sample sizes.

Before getting wrapped around the axle on this one, consider why you are using it….I am not a big fan of this particular metric…lots of reasons…talk to someone smarter than me to determine if you even want to get into this metric….can be misleading, confusing, and just plain wrong….good luck.

Dear Sir,
hello,
how are you ?
sir first pls explain me cp/cpk value,how to use.
regards!
lokesh
mobile no:9811511103

Cp gives how much process variation is fitting between specification limits. For example Cp=1 indicate that 99.73 % of process variation in fitting between specification limits. 
While Cpk gives closeness of process mean to mean of specification limits in addition to information given by Cp.
For example your Cp=2 and your Cpk=1.5. It indicate that your 99.999998% of variation is fitting between specification limits but your process mean is away for specification mean 1.5 time of Std. deviation.

Cp – can be simply defined as process capability mean how much a process can deliver good results.
Cpk – is process capability indiex.

Dear Mr. Ashok,
By Cp and Cpk we would always try to measure the process capabilities with respect to our specification(standard).
Thats why, always we should consider the standard specifications for the USL and LSL in Cp and Cpk calculation.
In your case standard spec is 700+5% and actual mean is 704 mg, So for Cp and Cpk calculation,
Average = 704 mg(Actual)
USL = 735 mg(standard)
LSL = 665 mg (standard)
Formule for calculation:
Cp=(USL-LSL)/(6*Standard Deviation of mesured values)
Cpk=(USL-Avg)/(3*Standard Deviation of mesured values) or
         (Avg-LSL)/(3*Standard Deviation of mesured values) whatever is lower.
 
Regards,
Bhupendra Nema
Crompton Greaves Ltd.
Bhopal (India)