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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

Process Capability Indices

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. The minimum value of "k" is 0 and the maximum is 1.0.

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

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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

Process Capability Indices

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. The minimum value of "k" is 0 and the maximum is 1.0.

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

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