**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
Cause**

**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
level.

Refer 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.

**Mean:-
**The mean is a measure of central tendency. It is the arithmetic average
of the data values (*x*1, *x*2, *x*3…..
*xi*).

**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
deviation.

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

**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 distribution.

- 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.

**Differences
between Cp & Pp**

**we use sampling and have to calculate an**

__Pp__: -__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 6Ïƒ range of a process’s inherent variation (Variation due to common causes), for statistically stable processes only, here Ïƒ (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.

** Process
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 6Ïƒ range of a process’s total variation (common causes +
Special Causes), here Ïƒ (S.D) is usually estimated by s, the sample standard
deviation.

- 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 acceptability.

**Control limit Vs Specification
Limit**

- 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
Capability**, 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 6Ïƒ.
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 (6Ïƒ). 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-
*k***)**,
Where *k *factor quantifies the amount by which the process is off center. With
below table you can understand relation between Cp & Cpk:-

Cp |
Cpk |
Remarks |

OK |
OK |
Process is Capable |

OK |
NG |
Process has potential Capability, need improvement |

NG |
NG |
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.

Cpk |
Ppk |
Remarks |

OK |
OK |
Process is Capable & Performing |

OK |
NG |
Process has Capability, but
not performing |

NG |
NG |
Process is neither Capable nor performing |

__Conclusion__

- 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 stabled)
- Cp is process capability which defined ability of a process to satisfy customer expectations (Meeting specification limit).
- Pp is 6Ïƒ range
of a process’s total variation (common causes + Special Causes), here Ïƒ (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

Hope you like this post. If you found this informative. Please support by following on below social media icon.

Difference between Significant characteristic and Critical Characteristics

IATF16949 Clause 7-Support In Automotive

## 0 Comments

Thank You for comment, will reply you soon...