Process Capability (Cp & Cpk) (Pp & PpK) Process capability is the ability of process to meet the requirement's set for the process i.e. to do particular work without producing or producing less defects Cp and Cpk are called Process Capability. Pp and Ppk are called Process Performance. In both cases we want to try to verify if the process can meet to meet Customer CTQs (requirements) Process capability  – Cp :  This is defined as the tolerance width divided by the total spread of process (6 Sigma) Cp indicates the spread of variation present in a process Process capability is the ability of process to meet the requirement's set for the process i.e. to do particular work without producing or producing less defects One way to determine process capability is to calculate capability indices. Capability indices are used for continuous data and are unit less statistics or metrics Cp :- It is the potential capability indicating how well a process could be if it were centered on target. This is not necessarily its actual performance because it does not consider the location of the process, only the spread. It doesn't take into account the closeness of the estimated process mean to the specification limits. Cp indices recognize the fact that your samples represent rational subgroups, which indicate how the process would perform if the shift and drift between subgroups could be eliminated. Therefore, it calculates the process spread using within-subgroup variation Cpk :-Measures of potential process capability, calculated with data from the subgroups in your study. They measure the distance between the process average and the specification limits, compared to the process spread: CPL measures how close the process mean is running to the lower specification limit CPU measures how close the process mean is running to the upper specification limit Cpk equals the lesser of CPU and CPL Process is centered – Cp Process is not centered - Cpk How to calculate Cpk? How to calculate Cpk using Z value ? Cpk can be determined by dividing the Z score by three. A z score is the same as a standard score; the number of standard deviations above the mean. How to read Z table How to calculate Cpk using Z value ? What are Good Values for Cpk? Remember the Car parking in the garage analogy? Cpk = Negative number: Your process will regularly crash the car into the wall Cpk =0.5: You have a good chance hitting the  wall on entry Cpk =1:  Your car may be just touching the nearest edge of the entry Cpk =2: Great! You have great clearance. You could double the width of your car before you hit the side of the garage Cpk =3: Excellent!  You have excellent clearance. You could triple the width of your car before you hit the side of the garage The Cp index is calculated using specification limits and the standard deviation only. This index indicates, in general, whether the process is capable of producing products to specifications. No information on the ability

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Quality Journey
Process Capability (Cp & Cpk) (Pp & PpK)

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What Process Capability ?
• Process capability is the ability of process to meet the requirement's set for the process i.e. to do particular
work without producing or producing less defects
• Cp and Cpk are called Process Capability. Pp and Ppk are called Process Performance. In both cases we want to
try to verify if the process can meet to meet Customer CTQs (requirements)
Stable Process
Under statistical
Control
Unstable process
Not under statistical
control
Process is centred Cp Pp
Process is not centred Cpk Ppk
Cp,Cpk v/s Pp,Ppk :-
High Cp /Low Cpk High Cp /High Cpk
Note :- The ‘k’ stands for ‘centralizing factor.’ The index takes
into consideration the fact that your data is maybe not centered.

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What Process Capability ?
• Process capability is the ability of process to meet the requirement's set for the process i.e. to do particular
work without producing or producing less defects
• One way to determine process capability is to calculate capability indices. Capability indices are used for
continuous data and are unit less statistics or metrics
Process capability – Cp : This is defined as the tolerance width
divided by the total spread of process (6 Sigma)
Cp indicates the spread of variation present in a process

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Cp & Cpk
Cp :- It is the potential capability indicating how well a process could be if it were centered on target. This is not necessarily
its actual performance because it does not consider the location of the process, only the spread. It doesn't take into account
the closeness of the estimated process mean to the specification limits.
Cp indices recognize the fact that your samples represent rational subgroups, which indicate how the process would perform
if the shift and drift between subgroups could be eliminated. Therefore, it calculates the process spread using within-
subgroup variation
Cpk :-Measures of potential process capability, calculated with data from the subgroups in your study. They measure the
distance between the process average and the specification limits, compared to the process spread:
o CPL measures how close the process mean is running to the lower specification limit
o CPU measures how close the process mean is running to the upper specification limit
o Cpk equals the lesser of CPU and CPL
Process is centered – Cp
Process is not centered - Cpk

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e.g. to understand Cpk
The Parking a Car in the Garage Analogy
• If you think of the walls of your garage – where you have to fit your car in – they become the customer specification
limits. If you go past those limits, you will crash, and the customer will not be happy!
• If your process has a lot of variation, that means the process average is all over the place. Not good for parking a car,
and not good for any other process. To give your parking process the best chance of success you should work on
reducing variation and centering.
• If the car is too wide for the garage, nothing you do to center the process will help. You have to change the dispersion
of the process (make the car smaller.)
• If the car is a lot smaller than the garage, it doesn’t matter if you park it exactly in the middle; it will fit and you have
plenty of room on either side. That’s one of the reasons the six sigma philosophy focuses on removing variation in a
process.
• 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.”

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How to calculate Cpk?
• Cpk is a measure to show how many standard deviations the specification limits are from the center of the process.
On some processes you can do this visually. Others require an equation.
• To find Cpk you need to calculate a Z score for the upper specification limit (called Z USL) and a Z score for the lower
specification limit (called Z LSL).
• Since we are trying to measure how many standard deviations fit between the center line and the specification
limit you should not be surprised that the value of those limits, the process mean, and the standard deviation are all
components of the Z calculation.
Cpl = (Process Mean – LSL)/(3*Standard Deviation)
Cpu = (USL – Process Mean)/(3*Standard Deviation)
Cpk is merely the smallest value of the Cpl or Cpu denoted: Cpk= Min (Cpl, Cpu)
Note :- We know that any specification limit has an upper bound and a lower bound. Because you know that 6 sigmas –
or 6 standard deviations account for nearly all eventualities on a process (assuming normal distribution) you shouldn’t
be surprised to see the “/ 3” because we are looking at only one side of the distribution.

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How to calculate Cpk using Z value ?
Cpk can be determined by dividing the Z score by three.
A z score is the same as a standard score; the number of standard deviations above the mean.
Z = x – mean of the population / standard deviation.
Example 1: Longer than
Hospital stays for admitted patients at a certain hospital are measured in hours and were found to be normally
distributed with an average of 200 hours and a standard deviation of 75 hours. How many of these stays can be
expected to last for longer than 300 hours?
x=300 x̅ = 200 s=75
Z= x- x̅/s =300-200/75= 100/75= 1.33 ---- Z score from the table for 1.33 = 0.9082

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How to read Z table

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How to calculate Cpk using Z value ?
Example 2: Less than
Hospital stays, for admitted patients at a certain hospital are measured in hours and were found to be normally
distributed with an average of 200 hours and a standard deviation of 75 hours. How many of these stays can be
expected to last less than 75 hours?
x=75 x̅ = 200 s=75
Z= x- x̅/s =75-200/75= -125/75= -1.667 ---- Z score from the table for -1.667 = 0.0475

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What are Good Values for Cpk?
Remember the Car parking in the garage analogy?
Cpk = Negative number: Your process will regularly crash the car into the wall
Cpk =0.5: You have a good chance hitting the wall on entry
Cpk =1: Your car may be just touching the nearest edge of the entry
Cpk =2: Great! You have great clearance. You could double the width of your car before you hit the side of the garage
Cpk =3: Excellent! You have excellent clearance. You could triple the width of your car before you hit the side of the
garage

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How to calculate Cp?
The Cp index is calculated using specification limits and the standard deviation only. This index indicates, in
general, whether the process is capable of producing products to specifications. No information on the ability of
the process to adhere to the target value is included in this index.
Example :
Food served at a restaurant should be between 38°C and 49°C when it is delivered to the customer. The process used to
keep the food at the correct temperature has a process standard deviation of 2°C and the mean value for these
temperature is 40. What is the process capability of the process?
USL (Upper Specification Limit) =49°C LSL (Lower Specification Limit) =39°C Standard Deviation =2°C Mean = 40
Process Capability = (49-39)/(6*2) = 0.833

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Application of Cp and CpK ?
The following conditions must be met before Cp and CpK can be successfully used to evaluate the ability of a process:
 the sample size must be adequate (large enough)
 the data should be tested for normality
 the process being analyzed should be under statistical control
Caution: Only after a process is under statistical control, can one safely assume that the mean and standard deviation
to have a stable values over time
Cpk is more widely used than Cp, since it takes into account the mean and the standard deviation in its calculation. Please
note that the difference between Cp and Cpk is an indicator of how far the average of the process is from the target
specification. When the average of the process approaches the target value, the gap between Cpk and Cp closes. When
the average of the specification is equal to the target value, then Cpk is equal to Cp. Cpk can never exceed Cp.
Both Cp and Cpk can be calculated with the generation of descriptive statistic views and histograms.

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Pp, Ppk vs Cp, CPK
• Cp & Cpk use an estimate for the standard deviation using the R Bar / d2 method.
• Pp, Ppk are more liberal where Cp, CPK are more conservative.
• Use Pp & Ppk when you are initially setting up your process.
• Use Cp & Cpk once the process is in a state of statistical control.
• Cpk or Ppk is less than CP or Pp
Cpk = Minimum (Cpu, Cpl)
Cpu=(USL-X)/3σ
Cpl=(X-LSL)/3σ
Ppk = Minimum (Ppu, Ppl)
Ppu=(USL-X)/3s
Ppl=(X-LSL)/3s

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