CP, CPK, CM, CMK, CONTROL LIMITS

Home / Six Sigma Study Guide Articles / Process Capability & Performance (Pp, Pchiến tranh, Cp, Cpk)
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Cp, Pp, Ckungfu, và Pchiến tranh are capability and performance indicators for your process. Is a process capable? Is the process acceptable? How is the process actually behaving vs how it theoretically could be behaving? These are questions you can ask during a DMAIC project during both the measure phase (if you have sầu good, existing data) or in the control phase after you have implemented your changes.

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This article deals with an overall examination of Process Capability và Performance (Pp, Pvõ thuật, Cp, Cpk).

If you’d lượt thích more depth including calculations, etc, see these articles:

To begin to answer these questions it all starts with customer requirements and the follow up with what we know mathematically about the variation of the process.

Cp, Cđánh nhau, Pp and Pchiến đấu are all parameters (indices) that can help us khổng lồ understvà how our process is operating relative sầu to lớn the specifications, or in other words, they measure how cchiến bại our process is running khổng lồ its specification limits.

For requirements we measure the process specifications. To determine the answer to lớn those questions we see how wide the process dispersion (spread of values) and how centered the process is relative lớn those specifications.


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Process spread vs centering

On the mathematical side we require the process to lớn follow a normal distribution so we can take advantage of the properties there. Before using these indices to see how capable & acceptable your process is, chạy thử your process for normality. If it’s not normal, see if you can apply a transsize to get it there. If not, you may have sầu lớn use non-normal distributions and methods (not part of the Six Sigma Blachồng Belt curriculum. – See the Master Black Belt guide.)


Cp, Ckungfu, Pp, Pvõ thuật Practice Questions và Z Charts


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Practice makes perfect! Free Cp, Cđánh nhau, Pp, Phành động practice questions.


When to Use Pp, Pđánh nhau, Cp, & Cpk

The main difference between Pp và Cp on one side and Pvõ thuật và Cchiến tranh on the other side is whether we use complete mix of data for calculation (Pp & Ppk) where we calculate real performance of the system, or we use sample (pre-production, batch, logical subgroups) where we calculate capability of the process. In equation for Pp & Phành động we use standard deviation based on studied data (whole population), & in equation for calculation Cp & Cvõ thuật we use sample deviation or deviation mean within rational subgroups


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When to use Pp Pkungfu Cp Cpk

Differences Between Cp và Pp

The biggest difference between Cp & Pp is how the Standard Deviation is determined. Pp we use sampling & have sầu lớn calculate an estimated standard deviation of the sample. In Cp we are assuming a stable process and will likely have enough data lớn calculate a true standard deviation.

What Can Process Capability and Process Performance Tell Us?

Process Capability Analysis tells us how well a process meets a phối of specification limits, based on a sample of data taken from a process. It can be used to lớn establish baseline for the process & measure the future state performance of the process for comparison.

Here we want to lớn use Cp for new processes or Pp for processes that are understatistical control. A good analogy is parking a oto in a garage. If the oto is bigger than the garage, it will not fit within the specification limits & thus is not capable – this case is clear. What about a case when our car is skinnier than the garage you’re trying to lớn park it in (the specification width)? Can we consider our parking process as a capable one? It depends on our specification and the width of the car. Are we satisfied with the probability of 99% that we will park our oto, without hitting the wall? This mean that one in a hundred attempts lớn park our car will hit the wall of the garage!

One way khổng lồ calculate Process Capability is through number of defects per opportunity. This is usually used for discrete data and in manufacturing is usually acceptable number of 3.4 Defects Per Million Opportunities (DPMO)

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The other way to lớn calculate Process Capability is through use of statistical methodology. Processes with normal distribution of data, have restrictions from one or both side of the curve sầu, based on the Specification Limits (USL- Upper Specification Limit và LSL- Lower Specification Limit):


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Shaded areas represent the probability of defects & our goal is to minimize the kích thước of the shaded areas.

Is a Process Capable?

Process capability analysis is the determining if a process can meet specification.

Here we want to use Pp for new processes or Cp for processes that are under statistical control. A good analogy is parking a car in a garage. A process that is capable indicates the car (process) is skinnier than the garage you’re trying lớn park it in (the specification width). If the car is simply much bigger than the garage, it is not enough lớn be capable of fitting within the specification limits và thus is not capable.

See how to lớn calculate Cp.

See how to lớn calculate Pp.


Cp, Ckungfu, Pp, Pchiến tranh Practice Questions & Z Charts


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Practice makes perfect! Free Cp, Chành động, Pp, Pkungfu practice questions.


Is the Process Acceptable?

A capable process does not necessarily mean it is acceptable. Using the garage example, the car may have crashed into the side of the garage, or may have missed it completely. This point reflects how centered a process. We can measure this using Pvõ thuật or Cđánh nhau.

See how to lớn calculate Cchiến đấu.

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See how khổng lồ calculate Phành động.

A lưu ý on a Process Being Both Capable & Acceptable

A process is said to lớn be capable & acceptable when it meets customer requirements. Having zero defects is usually unrealistic and not usually a part of customer requirements. A process could be capable, but not acceptable because it is poorly centered and ends up outside the spec limits (ex oto could fit in the garage, but the process for parking it is could have it just as easily end up in your front door as where it should be).

Six Sigma Process Capability và Performance Limits

According lớn Six Sigma philosophy, Cp or Pp và Cđại chiến or Pkungfu should be greater than 1.50. From a technical standpoint, Six Sigma deems a process being acceptable only after achieving a maximum defect rate of 3.4 parts per million opportunities. There is a direct correlation between Cđánh nhau or Phành động and parts per million defects because only Cps or Pps & Cpks or Ppks that are greater than 1.50 are achieving this goal (3.4 Defects per million).

Control Limits, Specification Limits và Process Capability


Keeping a process in control limits is not sufficient lớn achieve sầu good unique. Quality is always dictated by the user. For that we use specification limits when assessing process capability. The process specifications used in process capability are the voice of the customer và control limits of Statistical Process Control are the voice of the process.

It is very possible to have great process control (indicated on a control chart) yet have poor process capability. That would be a mismatch of where the process is centered versus where the customer wants it khổng lồ be centered. Either that or the process has more variability than the customer desires.


Pp vs Cp (Capability Indices)

Both Cp và Pp are a monitoring indices for the spread of your process compared khổng lồ the specification spread.

Cp is used when a process is under statistical control. Pp is used when a process is initially starting out.

Uses for Cp & Pp

Used to see if a process is capable.Neither are concerned with centering. Cp or Pp takes inlớn tài khoản dispersion, NOT centering. Since Cp does not consider process centering so it cannot be used to lớn determine if a process is acceptable.Cchiến tranh & Pchiến tranh both take centering into lớn trương mục, so they can be used to see if a process is acceptableCp và Pp are NOT concerned with the control of a process. The term “control” infers an element of time and Cp or Pp is merely a snapshot of the process variation at a given point in time.For example, a Cp of Can never be 0.If Cp or Pp >1, Tolerance is > spread, Process has potential lớn be capable (depending on centering).A CPhường. of >1 doesn’t mean unique One could have a Cp of 400 và be producing 100% defects, because the process was not centered within the specification limits.If Cp or Pp tolerance, và the variation will never fit và the process will never be capable.A Cp of If 0Ex. Cp 0.70 = 70%. A Cp of 0.70 means the specifications are 70% of the process.

Ppk vs Cchiến tranh (Acceptable Performance)

Cpk & Pchiến tranh are ways to measure the capability of a process because they are monitoring indices for process centering.

Uses for Cp và Pp: Is The Process Acceptable?

Cvõ thuật or Ppk takes inkhổng lồ trương mục centering and thus can be use to determine if a process is acceptable.

Ways to lớn measure the capability of a process.Reflect the actual performance of the process.Both Chành động & Pkungfu can be a negative sầu numbers.It means that, on average, the process is not meeting customer requirements.

Can Cđánh nhau or Pkungfu be Negative? What does a negative Cđại chiến or Pkungfu Indicate?

Yes, it is possible for Ckungfu và Pvõ thuật khổng lồ be negative. Let’s look at the equation – for simplithành phố we will use the Ppk.

Pđánh nhau = < USL – x(bar) > / 3 s

It is impossible lớn have a standard deviation be negative so that would mean that x(bar) was larger that the Specification Limit. In other words, the process average is out of specification.

This could be an indication that the process mean has drifted over either the upper specification or the lower one. This is not good because it means that the process is not meeting customer requirements.

Pp, Phành động vs Cp, CPK

Cp và Cchiến tranh use an estimate for the standard deviation using the R Bar / d2 method.Pp, Phành động are more liberal where Cp, CPK are more conservative.Use Pp & Ppk when you are initially setting up your process.Use Cp & Cvõ thuật once the process is in a state of statistical control.Cchiến tranh or Ppk is less than CPhường or Pp.

Interesting đoạn Clip on assessing Pđại chiến and Cvõ thuật in Minitab.