CPK PPK PROCESS CAPABILITY & PROCESS PERFORMANCE
Process Capability (Cp, Cpk) and
Process Performance (Pp, Ppk) –
What is the Difference?
In the Six Sigma quality methodology, process performance is reported to the organization as a sigma level. The higher the sigma level, the better the process is performing.
Another way to report process capability and process performance is through the statistical measurements of Cp, Cpk, Pp, andPpk. This article will present definitions, interpretations and
calculations for Cpk and Ppk though the use of forum quotations. Thanks to everyone below that helped contributed to this excellent reference.
Jump To The Following Sections:
Definitions
Interpreting Cp, Cpk
Interpreting Pp, Ppk
Differences Between Cpk and Ppk
Calculating Cpk and Ppk
Definitions
Cp= Process Capability. A simple and straightforward indicator of process capability. Cpk= Process Capability Index. Adjustment of Cp for the effect of non-centered distribution. Pp= Process Performance. A simple and straightforward indicator of process performance. Ppk= Process Performance Index. Adjustment of Pp for the effect of non-centered distribution.
Interpreting Cp, Cpk
“Cpk is an index (a simple number) which measures how close a process is running to its specification limits, relative to the natural variability of the process. The larger the index, the less likely it is that any item will be outside the specs.” Neil Polhemus
“If you hunt our shoot targets with bow, darts, or gun try this analogy. If your shots are falling in the same spot forming a good group this is a high Cp, and when the sighting is adjusted so this tight group of shots is landing on the bullseye, you now have a high Cpk.” Tommy
“Cpk measures how close you are to your target and how consistent you are to around your average performance. A person may be performing with minimum variation, but he can be away from his target towards one of the specification limit, which indicates lower Cpk, whereas Cp will be high. On the other hand, a person may be on average exactly at the target, but the variation in performance is high (but still lower than the tolerance band (i.e., specification interval). In such case also Cpk will be lower, but Cp will be high. Cpk will be higher only when you r meeting the target consistently with minimum variation.” Ajit
“You must have a Cpk of 1.33 [4 sigma] or higher to satisfy most customers.” Joe Perito
“Consider a car and a garage. The garage defines the specification limits; the car defines the output of the process. If the car is only a little bit smaller than the garage, you had better park it right in the middle of the garage (center of the specification) if you want to get all of the car in the garage. If the car is wider than the garage, it does not matter if you have it centered; it will not fit. If the car is a lot smaller than the garage (Six Sigma process), it doesn’t matter if you park it exactly in the middle; it will fit and you have plenty of room on either side. If you have a process that is in control and with little variation, you should be able to park the car easily within the garage and thus meet customer
requirements. Cpk tells you the relationship between the size of the car, the size of the garage and how far away from the middle of the garage you parked the car.” Ben
“The value itself can be thought of as the amount the process (car) can widen before hitting the nearest spec limit (garage door edge).
Cpk =1/2 means you’ve crunched nearest the door edge (ouch!)
Cpk =1 means you’re just touching the nearest edge
Cpk =2 means your width can grow 2 times before touching
Cpk =3 means your width can grow 3 times before touching” Larry Seibel
Interpreting Pp, Ppk
“Process Performance Index basically tries to verify if the sample that you have generated from the process is capable to meet Customer CTQs (requirements). It differs from Process Capability in that Process Performance only applies to a specific batch of material. Samples from the batch may need to be quite large to be representative of the variation in the batch. Process Performance is only used when process control cannot be evaluated. An example of this is for a short pre-production run. Process Performance generally uses sample sigma in its calculation; Process capability uses the process sigma value determined from either the Moving Range, Range or Sigma control
charts.” Praneet
Differences Between Cpk and Ppk
“Cpk is for short term, Ppk is for long term.” Sundeep Singh
“Ppk produces an index number (like 1.33) for the process variation. Cpk references the variation to your specification limits. If you just want to know how much variation the process exhibits,
a Ppk measurement is fine. If you want to know how that variation will affect the ability of your process to meet customer requirements (CTQ’s), you should use Cpk.” Michael Whaley
“It could be argued that the use of Ppk and Cpk (with sufficient sample size) are far more valid estimates of long and short term capability of processes since the 1.5 sigma shift has a shaky statistical
foundation.” Eoin
“Cpk tells you what the process is CAPABLE of doing in future, assuming it remains in a state of statistical control. Ppk tells you how the process has performed in the past. You cannot use it predict the future, like with Cpk, because the process is not in a state of control. The values for Cpk and Ppk will converge to almost the same value when the process is in statistical control. that is because sigma and the sample standard deviation will be identical (at least as can be distinguished by an F-test).
When out of control, the values will be distinctly different, perhaps by a very wide margin.” Jim Parnella
“Cp and Cpk are for computing the index with respect to the subgrouping of your data (different shifts, machines, operators, etc.), while Pp and Ppk are for the whole process (no subgrouping). For
both Ppk and Cpk the ‘k’ stands for ‘centralizing facteur’ – it assumes the index takes into consideration the fact that your data is maybe not centered (and hence, your index shall be smaller). It is more realistic to use Pp and Ppk than Cp or Cpk as the process variation cannot be tempered with by
inappropriate subgrouping. However, Cp and Cpk can be very useful in order to know if, under the best conditions, the process is capable of fitting into the specs or not.It basically gives you the best case scenario for the existing process.” Chantal
“Cp should always be greater than 2.0 for a good process which is under statistical control. For a good process under statistical control, Cpk should be greater than 1.5.” Ranganadha Kumar
“As for Ppk/Cpk, they mean one or the other and you will find people confusing the definitions and you WILL find books defining them versa and vice versa. You will have to ask the definition the person is using that you are talking to.” Joe Perito
“I just finished up a meeting with a vendor and we had a nice discussion of Cpk vs. Ppk. We had the definitions exactly reversed between us. The outcome was to standardize on definitions and move forward from there. My suggestion to others is that each company have a procedure or document (we do not), which has the definitions of Cpk and Ppk in it. This provides everyone a standard to refer to for WHEN we forget or get confused.” John Adamo
“The Six Sigma community standardized on definitions of Cp, Cpk, Pp, and Ppk from AIAG SPC manual page 80. You can get the manual for about $7.” Gary
Calculating Cpk and Ppk
“Pp = (USL – LSL)/6*Std.dev
Cpl = (Mean – LSL)/3*Std.dev
Cpu = (USL – Mean)/3*Std.dev
Cpk= Min (Cpl, Cpu)” Ranganadha Kumar
“Cpk is calculated using an estimate of the standard deviation calculated using R-bar/d2. Ppk uses the usual form of the standard deviation ie the root of the variance or the square root of the sum of squares divided by n – 1. The R-bar/D2 estimation of the standard deviation has a smoothing effect and the Cpk statistic is less sensitive to points which are further away from the mean than is Ppk.” Eoin “Cpk is calculated using RBar/d2 or SBar/c4 for Sigma in the denominator of you equation. This calculation for Sigma REQUIRES the process to be in a state of statistical control. If not in control, your calculation of Sigma (and hence Cpk) is useless – it is only valid when in-control.” Jim Parnella “You can have a ‘good’ Cpk yet still have data outside the specification, and the process needs to be in control before evaluatingCpk.” Matt
Description
This module discusses the process capability indices that are commonly used as baseline measurements in the MEASURE phase and in the CONTROL phase.
The concept of process capability pertains only to processes that are in statistical control. There are two types of data being analyzed:
CONTINUOUS DATA:
PPM
DPMO
Z-short term and Z-long term scores
VARIABLE DATA:
Cp
Cpk
Pp
Ppk
Cpm
Capability estimates are strongest (but not always required) when:
Process is stable and in statistical control - use
SPC charts
to verify
Data is normally distributed*
If not normal, the data is transformable
Satisfies the Central Limit Theorem and normality assumptions apply*Keep in mind the data does not have to be normally distributed to use control charts. The data does have to fit (or be assumed) a normal distribution to use these capability indices.
The capability indices of Ppk and Cpk use the mean and standard deviation to estimate probability. A target value from historical performance or the customer can be used to estimate the Cpm.
Cp and Pp are measurements that do not account for the mean being centered around the tolerance midpoint. The higher these values means the narrower the spread (more precise) of the process. That spread being centered around the midpoint is part of the Cpk and Ppk calculations.
The midpoint = (USL-LSL) / 2
The addition of "k" quantifies the amount of which a distribution is centered. A perfectly centered process where the mean is the same as the midpoint will have a "k" value of 0.
An estimate for Cpk = Cp(1-k).
and since the maximum value for k is 1.0, then the value for Cpk is always equal to or less than Cp. Cp and Cpk are coined as "within subgroup", "short term", or "potential capability"
measurements of process capability because they use a smoothing estimate for sigma. These indices should measure only inherent variation, that is common cause variation within the subgroup. Plotting subgroup to subgroup data as individuals (I-MR) will likely show an out of control chart and process that is likely in control just showing lot-lot variation, shift-shift variation or day to day variation which is expected. Therefore the SEQUENCE of gathering and measuring is mandatory to have a correct calculation of Cp and Cpk. The subgroups should be the same size and an the highest value is most likely obtained for Cp when the samples are collected with one operator on one shift on one machine with one set of tools, etc.
Most common estimate for Cp and Cpk uses an average of the subgroup ranges, R-bar, in a process with only inherent variation (no special causes) formula that lowers the width of the data distribution (sigma) from the X-bar & R chart. This optimization of sigma reduces its spread and value further increasing the value Cp and Cpk over Pp and Ppk.
Pp and Ppk use an estimate for sigma that takes into account all or total process variation including special causes (should they exist) and this estimate of sigma is the sample standard deviation, s, applies to most all situations. This estimation accounts for "within subgroup" and "between subgroup" variation.
Cp, since it is a short term index and not dependent on centering and uses an optimal smoothed and reduced estimate for sigma, represents the process entitlement. Process entitlement the best a process can be expected to perform in terms of minimal variation under existing conditions.
Cpk value can never exceed Cp. A perfectly centered distribution on the midpoint will have a Cpk = Cp. Any movement either way from the midpoint will have a "k" value of <1.0 and Cpk < Cp.
In Cp and Pp, consider the numerator (USL-LSL) as a constant. As the estimate for standard
deviation (sigma) of a distribution reduces and approaches zero the value of Cp and Pp will increase towards infinity.
Cp and Pp are meaningless if only unilateral tolerances are provided, in other words if only the USL or LSL are provided. Both tolerances (bilateral) must be provided to calculate a meaningful Cp and Pp. A boundary can be used (such as 0 lower limit) but the meaning of Cp to Cpk will differ from the
meaning using bilateral tolerances.
The overall process performance indices, Pp and Ppk, most often uses the sample standard deviation, s, formula as an estimate for sigma. There are other methods available for estimating the overall (total) process sigma.
The Cpk and Ppk will require two calculations, selecting the minimum is the value use as baseline and to compare to customer acceptability level. These can be calculated using unilateral or bilateral tolerances. Shown in the table below is the formula for bilateral tolerances where a LSL and USL are provided. If only one specification is provided (unilateral) then the value used for Cpk and Ppk is provided by the calculation that involves the specification limit provided.
Pp and Ppk are rarely used compared to Cp and Cpk. They should only be used as relative comparisons to their counterparts. Capability indices, Cp and Cpk, should be compared to one another to assess the differences over a period of time. The goal is to have a high Cp, and get the process centered so the Cpk increases and approaches Cp. The same applies for Pp and Ppk. Cpk and Ppk account for centering of the process among the midpoint of the specifications. However, this performance index may not be optimal if the customer wants another point as the target other than the midpoint. The calculation of Cpm accounts for the addition of a target value.
Capability Analysis for VARIABLE data
STEP 1:
Decide on the characteristic being assessed or measured. Such as length, time, radius, ohms, hertz, thickness, hardness, tensile strength, weight, or distance.
STEP 2:
Validate the specification limits and possibly a target value provided by customer. STEP 3:
Collect and record the data in order at even intervals in the Data Collection Plan. If you are taking multiple readings in a group then you have subgroups and will need to get the same amount of readings at each group. If you have a destructive test such as tensile testing, then you will get one reading per part and the subgroup size is one.
To analyze short and long term performance there should be 20-25 rational subgroups. Keep in mind what is practical and economical.
You will have to indicate the subgroup size when analyzing the data using statistical software. STEP 4:
Assess process stability using a control chart such as I-MR, X-bar & R, or other proper control chart. There may be a specific customer required charting method.
STEP 5:
If the process is stable, assess the "normality" of the data. Assuming 95% level of confidence, the p-value should be greater than 0.05. Data must be normal, able to be assumed normal, or transformed in order to proceed.
STEP 6:
Calculate the basic statistics such as the mean, standard deviation, and variance. Calculate the capability indices (Cp, Cpk, Pp, Ppk, Cpm) as applicable.
Verify to the customer requirement for capability where the process is acceptable.
NOTE: This is a SAMPLE analysis. These results are used to make inferences about the POPULATION.
Explaining the Indices
Defining Standard Deviation
In many automotive standards the data is plotted using 125 samples in subgroup sizes of 5 on an X-bar & R chart. The R-X-bar value used in estimation for sigma for Cp and Cpk is the average of each subgroup's range.
The estimation for sigma, s, in Pp and Ppk, is commonly the same formula as the sample standard deviation calculation. It is free from dependency on sequence of sample gathering and is not a function of the subgroup spreads. If the parts being analyzed are being pulled out of carton or pallet randomly and the order of production or subgrouping is unknown then the ONLY estimate is to use the (or one of) "long term" estimate or the "short term" estimate.
It takes into account the total spread of all data points for true performance. However, if the order isn't maintained and measurement plotted vs. time, control charts can't be employed to assess stability and control of the process. Always try to avoid to assessing capability of measurements where process control isn't first understood.
There are many other types of sigma estimates and often statistical software programs allow these choices. There is also much confusion among terminology and the true meaning of the capability indices. The underlying assumptions of control are debatable.
As mentioned before, a control chart of may appear out of control as some of the special cause points may be actual common cause due to inherent operator-operator or shift-shift variability. Therefore (whenever possible) when assessing process capability, Cp and Cpk, of a manufacturing process (the best it can perform) use only one shift with one operator with same lot of material with same tools on the same machine, etc. Maintaining the correct sequence gathering and plotting is required for Cp and Cpk. Since Pp and Ppk measure total observation capability the sequence is not as important.
More importantly, select the calculation for estimating the standard deviation and the capability indices that the team and the customer agree on. Use the same calculations and indices throughout the project.
NOTES:
Processes that are in control should have a process capability that is near the process performance. The more significant the gaps between capability and performance the higher the likelihood of special cause data.
It is possible to have data that falls outside the specification limits (LSL,USL) and still have a capable process. It depends on the performance of the other data, and the customer acceptability levels and any specific rules that may apply from the customer, standard, law, or company.
This is all a part of gathering the Voice of the Customer (VOC), and validating the specifications when using them. Due to the dynamics of customer needs and expectations it is important to continually validate the limits and acceptability levels throughout the project. There could be a long period of time between the SIPOC and the development of theControl Plan and assessing final capability and any changes are better captured sooner than later.
Learn How to Calculate Cp & Cpk -Tutorial, Definition and Example
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Learn How to Calculate Cp & Cpk -Tutorial, Definition and
Example
Process Capability (Cp) Definition:
Process capability is a technique to find out the measurable property of a
process to a specification. Generally, the final solution of the process
capability is specified either in the form of calculations or histograms
Process Capability Index (Cpk) Definition:
Process capability index (cpk) is the measure of process capability. It shows
how closely a process is able to produce the output to its overall
specifications.
Formula :
Where,
USL = Upper Specification Limit, LSL = Lower Specification Limit.