Cp Cpk and
Pp Ppk Difference

  • Cp & Cpk are capability indices
  • Pp & Ppk are performance indices

Before going direct onto Cp & Cpk, we have to understand
some terminology and definition.

Common cause Vs Special

Chronic problems (Common cause) exist when
the process is at a long-term unacceptable operating level; solution to chronic
problems is a change in
the normal operating level of the process
. Chronic problems often
involve extensive investigation time and resources.

Sporadic problems (special cause)
are defined as unexpected changes in the normal operating level of a process.
With sporadic problems the corrective action is to bring the process back to the normal operating

below picture for more understanding.

With the help of
Process control charting techniques, we can monitor the process stability and
identify the existence of both chronic and sporadic problems in the process.

Let’s say we
have specification limit of 25±2 (Min=23, Max=27). On collecting measurement
data over a period, we plot it on control chart. 

Let’s understand some Sample
statics- Mean/Range/Standard Deviation/Median.

The mean is a measure of central tendency. It is the arithmetic average
of the data values (
x1, x2, x3…..

Range: Range is a statistic that describes data
dispersion. It is simply the difference between the highest and lowest value of
a set of data.

Standard deviation: is a statistic that
quantifies the dispersion of data. Here dispersion means- variation of set of values
from mean. Dispersion of data not only measure by standard deviation but can
also be measured by Range, Variance. Here variance is square of standard

  • Low standard
    deviation mean- The value is close to the mean (Expected value)
  • High standard
    deviation mean- The values are spread over wider range.

of mean, range and Standard deviation is in below picture

Standard deviation
and Process VARIABILITY 

When a data
have a bell-shaped distribution (i.e., are normally distributed), approximately
68.26% of the data is expected to be within a plus or minus one standard
deviation range around the mean.

Above picture
shows that case 2 has more variability than case 1, which will cause more
uncertainty in any estimated population parameter mean.

Now let’s move to Cp & Cpk. —>

Cp, Cpk, Pp and Ppk are all parameters (indices) that can
help us to understand how our process is operating relative to the
specifications, or in other words, they measure how close our process is
running to its specification limits. We required the process to follow normal

  • For Pp & Ppk we use complete set of data for
    calculation, in which we calculate real performance of the system.
  • For Cp & Cpk we use sample (pre-production, batch,
    logical subgroups) where we calculate capability of the process.

between Cp & Pp

Pp: – we
use sampling and have to calculate an estimated standard deviation of
the sample.

Cp: – we
are assuming a stable process and will likely have enough data to calculate a true
standard deviation

Definition of Process
Capability and Process performance

Process capability (Cp & Cpk) – How well a process meets
a set of specification limits. Process capability is broadly defined as the
ability of a process to satisfy customer expectations which is product
specification limit.

It is 6σ range of a
process’s inherent variation (Variation due to common causes), for
statistically stable processes only, here σ (standard deviation) is usually
estimated by R/d2.

  • With Cp & Cpk we try to calculate process capability and
    process acceptability respectively
  • With these indices we assess potential short term capability
    using short term standard deviation
  • In capable process, variation should come within
    specification limit.

Performance (Pp & Ppk)
– It helps in determining that new process
is capable and acceptable by measuring ratios of distribution to spread and
centering. It is 6σ range of a process’s total variation (common causes +
Special Causes), here σ (S.D) is usually estimated by s, the sample standard

  • With these indices we assess long term capability using long
    term standard deviation
  • Process
    acceptability is checked with Cpk & Ppk calculation
  • For better process we need process capability and process

Control limit Vs Specification

  • Control limit is voice of process 
  • Specification limit
    is voice of customer.

Difference between Cp,Pp, Cpk&Ppk can be understand by below picture:-


What is difference
between Cp & Cpk?

Cp & Cpk both are process capability indices. Process capability is represented using
the distance of process average from specification limit in standard deviation
unit. Capability in SPC is total spread of 6sigma or ±3 Sigma.

Cp= Process
, Indicate spread of variation present in a process. It is
defined as tolerance width divided by total spread of process. Tolerance width
will be USL (Upper specification Limit)-LSL (Lower specification Limit). Total
spread is 6σ.
Cp talks about process capability.

Cpk= Process Capability Index, it indicates
shifting of process from target value or mean value. It is defined as minimum
of Cpk upper and Cpk Lower. While Cpk upper/lower is scaled distance between the process mean and the closest specification limit to
half the total process spread (6σ). Cpk talks about process acceptability.

With below picture you can easily understand difference between
these two indices:- 

What is relation between Cp & Cpk?

Mathematical Relation to Cp & Cpk; Cpk= Cp (1-
factor quantifies the amount by which the process is off center. With
below table you can understand relation between Cp & Cpk:-






Process is Capable



Process has potential Capability, need improvement



Process is not Capable

What is process width
in SPC?

It is difference
between UCL (Upper control limit) – LCL (Lower control Limit). Process
variations within this range represent voice of process. Process with is range,
you can understand better by below picture.

UCL, LCL is used in X-bar and R chart and is calculated by
following formula:-

What is difference
between Pp & Ppk?

Pp & Ppk are process performance indices. Definition and
calculation formula are similar to Cp & Cpk respectively. Difference
between these indices has been explained in table above attached.

What is difference
between Cpk & Ppk?

Cpk talks about process capability index, while Ppk talk
about process performance index. Difference between these two can be understood
by below table.






Process is Capable & Performing



Process has  Capability, but
not performing



Process is neither Capable nor performing


  • Cp & Pp- Process capability
  • Cpk & Ppk- Process capability
    and process performance (Acceptable performance)
  • Cpk or Ppk is less than CP or Pp.
  • Use Cp & Cpk once the process
    is in a state of statistical control
  • Use Pp & Ppk when you are
    initially setting up your process, in new development
  • Pp, Ppk  are more liberal (Because
    process is not yet set) where Cp, CPK are more conservative(Here process is
  • Cp is process capability which
    defined ability of a process to satisfy customer
    expectations (Meeting specification limit).
  • Pp is range
    of a process’s total variation (common causes + Special Causes), here σ (S.D)
    is usually estimated by
    s, the sample standard deviation (Long term standard deviation)
  • Cp can never be zero while Cpk can be negative

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