Process Capability and Performance Overview

Question 1

Process Capability & Performance (Pp, Ppk, Cp, Cpk)

Answer 1

• Cp, Pp, Cpk, and Ppk are capability and performance indicators for your process.
  
  • Is a process capable? Is the process acceptable? How is the process actually behaving vs how it theoretically could be behaving?
    
    • These are questions you can ask during the measure and control phase
• Cp, Cpk, Pp, and Ppk are all parameters (indices) that help us to understand how our process is operating relative to specifications
  
  • In other words, they measure how close our process is running to its specification limits.

Question 2

Process Capability & Performance (Pp, Ppk, Cp, Cpk) Requirements

Answer 2

• For requirements we measure the process specifications. To determine the answer to those questions we see how wide the process dispersion (spread of values) and how centered the process is relative to those specifications
• On the mathematical side, we require the process to follow a normal distribution so we can take advantage of the properties there
  
  • before using indices to see how capable and acceptable your process is, test your process for normality. If it’s not normal, see if you can apply a transform to get it there. If not, you may have to use non-normal distributions and methods

Question 3

How do you know if a process is following an Normal Distribution?

Answer 3

• Visual Normality Tests/Graphical Analysis
• Quantifiable Normality Test

Question 4

Visual Normality Test/Graphical Analysis

Answer 4

• Visual examination. Make a histogram or another bar graph. Only reject normality in the presence of “gross non-normality” - extreme departures from symmetry
• If you see a bell curve, a distribution is approaching normal
• Tall, shin curve = smaller standard deviation
• Fatter, lower curve = larger standard deviation
• You can test using a Normal Probability Plot. The probability plot transforms the data into a normal distribution and plots it as a scatter diagram
  
  • Normal data will follow the trend line
  • Non-normal data will have more points farther from the trend line
• The peak of the normal curve an indication of the average, which is the center of process variation. An average of a group of numbers is an indication of the central tendency.
• Neat interactive graphic here

Question 5

Quantifiable Normality Tests

Answer 5

• Use the Chi Square Goodness of Fit test
• Follow the Anderson-Darling Normality test or Critical Value Method.
  
  • The output includes the Anderson-Darling statistic, A-squared, and both a p-value and critical values for A-squared.
  • “Null hypothesis” is that the data is normal. The “alternative hypothesis” is that the data is non-normal. Reject the Null hypothesis (i.e., accept the alternative) when p<=alpha or A-squared>critical value.
  • if p > alpha then the data is normal.
  • if A-squared < Critical Value, then the data is normal
• Mean is the inverse of the Poisson distribution.
• The smaller the standard deviation, the tighter the grouping of data around the mean.

Question 6

When to use Pp, Ppk, Cp, and Cpk

Answer 6

• The main difference between Pp and Cp on one side and Ppk and Cpk on the other side is whether we use complete set of data for calculation (Pp and Ppk) where we calculate real performance of the system, or we use sample (pre-production, batch, logical subgroups) where we calculate capability of the process
• Pp and Ppk (Process Performance)
  
  • In equation for Pp and Ppk we use standard deviation based on studied date (whole population)
• Cp and Cpk (Process Capability)
  
  • In equation for calculation Cp and Cpk we use sample deviation or deviation mean within rational subgroups

Question 7

Differences Between Cp and Pp

Answer 7

• The biggest difference between Cp and Pp is how the Standard Deviation is determined.
• 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

Question 8

What can Process Capability and Process Performance tell us?

Answer 8

• Process Capability Analysis - tells us how well a process meets a set of specification limits, based on a sample of data taken from a process.
  
  • It can be used to establish baseline for the process and measure the future state performance of the process for comparison.
• Cp are for process that are under statistical control and Pp are for new processes.
  
  • A good analogy is parking a car in a garage.
    
    • If the car is bigger than the garage, it will not fit within the specification limits and thus is not capable - this case is clear
    • What about a case where our car is skinnier than the garage you’re trying to park it in (the specification width)? Can we consider our parking process a capable one?
      
      • It depends on our specification and the width of the car.
      • Are we satisfied with the probability of 99% that we will park our car, without hitting the wall?
        
        • This means that one in a hundred attempts to park our car will hit the wall of the garage!

Question 9

Calculate Process Capability

DPMO

Answer 9

• One way to calculate Process Capability is through number of defects per opportunity.
• This is usually used for discrete data and in manufacturing is usually acceptable number of 3.4 Defects Per Million Opportunities (DPMO)

Question 9

Calculate Process Capability

DPMO

Answer 9

• One way to calculate Process Capability is through number of defects per opportunity.
• This is usually used for discrete data and in manufacturing is usually acceptable number of 3.4 Defects Per Million Opportunities (DPMO)

Question 10

Calculate Process Capability

Statistical Methodology

Answer 10

• The other way to calculate Process Capability is through use of statistical methodology.
• Process with normal distribution of data, have restrictions from one or both side of the curve, base on the Specification Limits (USL - Upper Specification Limit and LSL - Lower Specification Limit)
  
  • Shaded areas represent the probability of defects and our goal is to minimize the size of the shaded area

Question 11

Is a Process Capable?

Answer 11

• Process capability is the determining if a process can meet specifications
• Pp - use for new processes
• Cp - use for processes that are under statistical control

Question 12

Is the Process Acceptable?

Answer 12

• A capable process does not necessarily mean it is acceptable.
• Using the garage example, the car may have crashed into the side of the garage, or may have missed it completely. This point reflects how centered a process.
  
  • We can measure this using Ppk or Cpk

Question 13

Process being both Capable and Acceptable

Answer 13

• A process is said to be capable and acceptable when it meets customer requirements.
• Having zero defects is usually unrealistic and not usually a part of customer requirements.
• A process could be capable, but not acceptable because it is poorly centered and ends up outside the specs limits (ex car could fit in the garage, but the process for parking it could have it just as easily end up in your front door)

Question 14

Six Sigma Process Capability & Performance Limits

Answer 14

• According to Six Sigma philosophy, Cp or Pp and Cpk or Ppk should be greater than 1.50.
• From a technical standpoint, Six Sigma deems a process being acceptable only after achieving a maximum defect rate of 3.4 parts per million opportunities.
• There is a direct correlation between Cpk or Ppk and parts per million defects because only Cps or Pps and Cpks and Ppks are greater than 1.50 are achieving this goal (3.4 DPMO)

Question 15

Control Limits, Specification Limits, and Process Capability

Answer 15

• Keeping a Process in control limits is not sufficient to achieve good quality. Quality is always dictated by the user.
• For that we use specification limits when assessing process capability.
  
  • The process specifications used in process capability are the voice of the customer and control limits of Statistical Process Control are the voice of the process.
• It is very possible to have great process control (indicated on a control chart) yet have poor process capability.
  
  • That would be a mismatch of where the process is centered versus where the customer wants it to be centered. Either that or the process has more variability than the customer desires

Question 16

Pp vs Cp (Capability Indices)

Answer 16

• Both Cp and Pp are a monitoring indices for the spread of your process compares to the specification spread
• Cp is used when a process is under statistical control
• Pp is used when a process is initially starting out

Question 17

Uses for Cp & Pp

Answer 17

• Used to see if a process is capable
• Neither are concerned with centering. Cp or Pp takes into account dispersion, NOT centering. Since Cp does not consider process centering so it cannot be used to determine if a process is acceptable
  
  • Cpk & Ppk both take centering into account, so they can be used to see if a process is acceptable
• Cp & Pp are NOT concerned with the control of a process. The term “control” infers an element of time and Cp or Pp is merely a snapshot of the process variation at a given point in time.
  
  • For example, a Cp of <1 does NOT indicate a process is out of control.
• Both indices are larger is better quality characteristics
• Can never be 0
• If Cp or Pp >1, Tolerance is > spread, process has potential to be capable (depending on centering)
  
  • A CP of >1 doesn’t mean quality. One could have a Cp of 400 and be producing 100% defects, because the process was not centered within the specification limits.
• If Cp or Pp <1 process spread is > tolerance, and the variation will never fit and the process will never be capable
  
  • A Cp of <1 does NOT indicate a process is out of control. “Control” is controlling variation over a time period.
• If 0< CP <1, then the specifications are that percentage of the process
  
  • Ex. Cp 0.70 = 70%. A Cp of 0.70 means the specifications are 70% of the process

Question 18

Pkp vs Cpk (Acceptable Performance)

Answer 18

• Cpk and Ppk are ways to measure the capability of a process because they are monitoring indices for process centering.

Question 19

Uses for Cp & Pp: Is the Process Acceptable?

Answer 19

• Cpk or Ppk takes into account centering and thus can be used to determine if a process is acceptable.
  
  • Ways to measure the capability of a process
  • Reflect the actual performance of the process
  • Both Cpk and Ppk can be negative numbers
    
    • It means that, on average, the process is not meeting customer requiremetns

Question 20

Can Cpk or Ppk be Negative? What does a negative Cpk or Ppk Indicate?

Answer 20

• Yes, it is possible for Cpk and Ppk to be negative. Let’s look at the equitation - for simplicity we use the Ppk

Ppk = [USL – x(bar)] / 3 s

• It is impossible to have a standard deviation be negative so that would be that x(bar) was larger than the Specification Limit.
  
  • In other words, the process average is out of specification.
  • This could be an indication that the process mean has drifted over either the upper specification or the lower one. This is not good because it means that the process is not meeting customer requirements

Question 21

Pp, Ppk vs Cp, Cpk

Answer 21

• Cp & Cpk use an estimate for the standard deviation using the R Bar / d2 method
• Pp, Ppk are more liberal where Cp, Cpk are more conservation
• Use Pp & Ppk when you are initially setting up your process
• Use Cp & Cpk once the process is in a state of statistical control
• Cpk or Ppk is less than Cp or Pp