Q 610. This is a follow up question in relation with the previous one on Capability Stats.

What is the difference between Performance Indices (Pp, Ppk) and Capability Indices (Cp, Cpk)? While doing a DMAIC project, which one should be used and why?

 

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Cp, Cpk, Pp & Ppk are used to see if the process is capable. This concept was widely used in Automobile industry as they had series production (600-700 child parts in day) with functional critical & significant characteristics they realized blindly cannot rely on just 100% Inspection of parts. 100% inspection of all the parts and all the dimensions is not practical for them as numbers were big. So they needed a way to get away with sampling inspection.

 

Cp = A Capability index, Compares the process variation to the maximum allowable variation as indicated by the tolerance. Process variation is derived from within the subgroup range (Sometimes called as short term process capability). Cp Does not consider process location. 

Calculated as follows 

 

Cp = USL-LSL / 6 Sigma

 

Where Sigma = R/D2

R = Mean of all the ranges of each sub group

n = number of samples

D2 = Statistical Constant used in the estimation of Standard deviation from ranges

USL / LSL = Upper and Lower Specification Limits

X = mean of n Samples

 

 

Cpk: A Capability Index, Takes into account process location as well as process variation. Process Variation is derived from the within subgroup range (Sometimes called as short term process capability).

 

Cpk = Minimum [(USL - X) / 3Sigma, (X - LSL) / 3Sigma]

 

Pp = A Process Performance index. Compares the process variation to the maximum allowable variation as indicated by the tolerance. Process variation is derived from process standard deviation (Sometimes referred as overall or long term process capability). Pp does not consider process Location.

 

Pp =  USL-LSL / 6 Sigma

Where Sigma  = Standard deviation

Ppk : A Process Performance index, Takes into account process location as well as process variation. Process Variation is derived from the process standard deviation (Sometimes referred as overall or long term process capability)

 

Ppk = Minimum [(USL - X) / 3Sigma, (X - LSL) / 3Sigma]

 

Note :

a. if you are planning of performing Cp Cpk or Pp Ppk studies, first ensure that MSA has been performed and your measurement system is reliable. Otherwise what ever you do will be of no use.

b. Cpk can never be greater than Cp due to its formulae. In ideal case scenario Cp will be equal to Cpk.  

c. If sub group sample size is 1 then there will not be cp and Cpk values (eg: continuous produced parts) you will have only Pp and Ppk.

 

In Automobile Industry few customers mandate six pack process capability (refer below image) to accept as process is capable during PPAP stage. Only when 6 pack process capability is met, then approval is provided to go for series production.

 

 

 

 

Final Summary 

 

Formulae is same for Cp and Pp, Cpk and Ppk calculation, only difference lies in how standard deviation is calculated. For Cp, Cpk standard deviation is calculated by using within Sub group range. While Pp and Ppk standard deviation is calculated using overall standard deviation. If data is collected at systematic intervals say first 2 parts of every Shift, key dimensions checked in CMM then checking Cp Cpk is preferable. If continuous serialized produced parts (1-30) data is being used then checking Pp, Ppk is preferable. It basically depends on how the data is selected.

 

While doing DMAIC which capability studies can be used.

 

My Opinion

Cp Cpk

a. If data has been systematically time based picked say once in every hour, 5 parts picked. 

b. When you have sub group and sample size is >1.

c. When using historic data say data captured for first and last part inspection at the beginning of every shift and with that data you want to check process capability.

 

Pp Ppk

a. When you do not have historical data all you have is the data that you have produced now.

b. When sub group sample size is 1 

c. When data is of parts from continuous production (eg: serial 1-50)

 

 

Manufacturing process stability is necessary for Cp and CpK but it is not necessary for Pp and PpK.

PpK and Pp represent the actual performance of the process against the theoretical best and Cp, CpK represent the process’s actual best performance when it is stable.

While doing a DMIAC project, it should be used Capability indices. When it comes to DMAIC projects we are mainly focusing on the standard deviation and Cp, CpK also use an estimate for the standard deviation. It clearly measures the ability of the process to meet the specifications while performance indices measures how the actual process performed.  

Process Capability and performance (Pp, Ppk, Cp, Cpk) basically these are indicators of a process relating to process dispersion and process centering.

Process capability is a statistical measurement of a process’s ability to produce parts within specified limits consistently.

 In other way we can say that it is the ability of the process to meet the design specification for a service or a product.

Cp is basically also called as process capability

Pp is basically also called as process performance

 

 

 

 

 

 

 

In the Measure phase the focus is on evaluating the current state of the process and understanding its ability to meet customer needs. In this step, it is recommended to use process capability indices (Cp, Cpk)  to determine the basic capability and identify areas for improvement.

 

 In the Control phase the focus shifts to implementing and maintaining process improvements. Process performance indices (Pp, Ppk) are more important at this stage to monitor ongoing performance and ensure that the process can still meet customer requirements.

Any Manufacturing company should produce product your customers want to pay for. To find out that your process are capable you should use Cp, Cpk,Pp,and Ppk.

 

Capability indices like Cp and Cpk are related to Customer specification whereas Performance Indices are related to Process Specifications.

 

Capability indices are related to engineering specification determined by customer to observed behaviour of process. Capability of process is defined as the ratio of the distance from process center to the nearest specification limit divided by a measure of the process variability. 

 

Cp =a Simple indicator or Process capability.  Cpk= Adjustment of Cp for the effect of non centered distribution.

 

• Cpk measure how close you are to target or specification limit and your consistent around your average performance.  
  • a person may be performing with minimum variation but away from specification limit may have high Cp.
  • Also even if person is performing near specification limit with high variation may have high Cp
  • Cpk will be higher only when you are meeting target or specification limit with minimum variation. As per standard you should have Cpk of 1.33 ( 4 Sigma) to satisfy most of the customers. 

Pp= a simple indicator of Process performance. Ppk=  Adjustment of Pp for the effect of non centered distribution.

 

• Ppk Measures sample generated fro the process is capable to meet customer specification or requirement.
  • Ppk is used when process control can not be evaluated for example pre-production run. 

 

Difference between Cpk and Ppk.

 

• Cpk tells you the process is CAPABLE of doing in future, assuming it remains in state of statistical control. So it is for short term.
• Ppk tells you the how the process has performed in the past. It is more realistic. So it is for Long term.

 

While using DMAIC, it is more realistic to use use Pk and PPk than Cp and Cpk as the process variation can not be tampered with by inappropriate subgrouping.

Cp/Cpk are used to measure the current performance of the process means short range capability of the process. Cp determines the capability of the process but missing center tendency while Cpk confirms the centering of the process. Higher Cp does not mean that the process is centered therefore we need to check both Cp/Cpk values in collected sample data by using below formula’s:

“Cp= specification width / Process width  or  [ ( USL-LSL) / 6*σ ] σ= standard deviation-short term”

“Cpk = (mean- specification) / 3* σ. or (Specification-mean)/3*σ

 

 Pp/Ppk are performance indices measured for overall capability of the process. It is computed with long term standard deviation in place of short-term standard deviation in above formula. Broadly, Pp/Ppk refers to historical process performance to acknowledge that whether was in control or not.

 

While doing the DMAIC project, we check all Cp/Cpk & Pp/Ppk for assimilating the present process status and impact of long period of time but most quite useful is Cp/Cpk which estimate the sigma level of process. Below table for reference and relation among process capability and sigma level.

Interesting thoughts from the respondents. Adil Khan has provided the most appropriate answer to the question and hence has been selected as the winner.

 

Do read Ramdas Jadhav's answer as he provides a very interesting and a different view (contrary to the popular believe).