# Cp Cpk Pp and Ppk difference

## 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.**

Formula 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 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

**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.

### Process Capability Vs 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.

** 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 6σ range of a process’s total variation (common causes + Special Causes), here σ (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 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- *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 |

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 6σ 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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