**Cp Cpk and**

Pp Ppk Difference

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

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.

of mean, range and Standard deviation is in below picture

**Standard deviation**

and Process VARIABILITY

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

between Cp & Pp

**we**

__Pp__: –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.

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.

** Process** – It helps in determining that new process

Performance (Pp & Ppk)

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

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?

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?

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?

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?

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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