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Process Capability and Performance (Cp, Cpk, Pp, Ppk)
What is Process Capability Analysis?
In simple terms is an analysis of a process to measure how “capable” (process capability) and how well a process actually “performs” (process performance) to meet the customer requirements also known as product or design specifications.
Both the process capability and performance are essentially a ratio of the customer requirement (specification) and the expected/actual process variation.
Process capability/performance = Voice of the customer (specifications) / Voice of the process (process variation)
A process with normally distributed data (data when plotted will appear to look like a “bell-shaped” curve as shown below in blue), may have restrictions from one or both side of the curve, based on the Specifications, the upper is known as Upper Specification Limit (USL) and lower is known as Lower Specification Limit (LSL) represented by the red dash lines.
The shaded areas beyond these limits represent non-conforming product produced by the process.
In a manufacturing setting this is typically marked by a “scrap” or “reprocess” event, which essentially leads to an overall “yield-loss” leading to increases in manufacturing costs.
When the data is collected is a subset in time (typically 30datapoints collected over 30-60days), we get a measure of the process capability, represented by the terms Cp, Cpk, where the “C” stands for Capability.
When all the data collected is utilized (typically a quarter or in some cases the entire year), we get a measure of the “actual” process performance, represented by the terms Pp, Ppk, where the “P” stands for Performance.
Which one to use Cp, Pp or Cpk, Ppk?
A process is considered in a state-of-control when it is “centered” and has “spread” less than the width of the specifications. To better illustrate this concept, consider the output of a shooting range shown in the figure below made by four shooters.
The best shooter being “1” who was closest to target on every attempt. As you can see his output is both centered and the spread of each shot is within the boundaries.
The Cp, Pp terms measure only measure the spread of the process compared to the width of the specifications, while the Cpk, Ppk terms measures both the spread of the process relative to the specification width as well as how centered the process is within those limits.
In the figure above notice both the “blue-bell” curves namely “a” and “b” are identical in shape, which would mean their Cp and Pp are the same. On closer inspection we can see that the “b” curve’s mean (aka center) is shift towards the USL, creating a shaded area beyond the specifications. This means non-conforming product.
If we relied on the Cp, Pp terms we would have incorrectly deemed the process to be highly capable and performing. So, for the purpose of reporting, it is good practice to report on Cpk and Ppk and the remainder of this article will focus on these terms only.
What Cpk or Ppk value should you aim for and why?
When the Cpk or Ppk calculation is a high number (general industry guideline is 1.33 or higher), then it is a good indication the process is statistically in control.
In general, the higher the Cpk, the better. A Cpk value less than 1.0 is considered poor, and the process is not capable. A value between 1.0 and 1.33 is considered barely capable, a value greater than 1.33 is considered capable and a value of 2.00 is considered state-of-the-art. The same applies to Ppk.
The main purpose of these indices is to predict how much product is going to fall beyond the specifications. The higher the Cpk, the more the curve falls within the specifications, leading to less non-conforming product. But what does that mean in reality?
To understand this, we introduce a commonly used term DPM or DPMO, which stands for Defects per Million Opportunities, this DPMO value is related to the material falling beyond the specifications.
Looking at the figure above a Cpk = 0.7 will lead to some products falling outside the limits indicated by the red squares. Without going into too much detail, we can calculate the percentage area under the curve inside the limits (also known as process yield) and derive the DPMO for the process.
The table below gives the relation between Cpk, Area-under-normal curve (Yield) and DPMO.
Cpk Value | Area under the curve within specifications (Yield) | Defective units per million units produced (DPMO) |
---|---|---|
0.70 | 72.600000% | 274,253 |
1.00 (3-sigma) | 93.300000% | 66,807 |
1.33 (4-sigma) | 99.400000% | 6210 |
1.67 (5-sigma) | 99.980000% | 233 |
2.00 (6-sigma) | 99.999660% | 2 |
Based on the table a process with Cpk = 0.7 will produce 274253 non-conforming units for every 1million units produced.
Now if we are to manufacture 1000 units with the process, we can expect a minimum 274 non-conforming units with a resultant yield of 72.60%.
This is an important metric for production planners and continuous improvement agents, as it helps them determine how much more to produce at a minimum to meet the demand, and helps justify and drive process improvement projects.
Difference between Capability (Cpk) and Performance Indices (Ppk) and why they are both equally important?
Process capability, Cpk, is important because it indicates whether a process potentially can meet a specification in the short term, like during initial setup of the process.
Process performance, Ppk, is a measure of the process ability to consistently produce output within specifications over long period.
Process Capability (Cpk) | Process Performance (Ppk) |
---|---|
Potential of a process to meet a specification in the short term. | Measures how the process "actually" did in long term. |
Uses estimated standard deviation to calculate process deviation | Uses the actual standard deviation to calculate the process variation |
Typically used while processing in the ideal conditions to identify if the process can meet the specifications | Typically used to gauge real process state because it does not cut out real data |
It is important to note that a process that is “capable”, may or may not perform well in the long run.
The term “mature process" is generally used to indicate that the process has both the capability and performance to meet specifications over time. In scenarios like these typically the Cpk and the Ppk will converge.
If the two terms are considerably different, even though the Cpk value may be acceptable, this is an indication that the process is not in statistical control because there are more data points that have been evaluated in actual process conditions.
Long term, it is not clear that consistent parts are being produced. Even though they may be within the specification limits, the parts could be at the low or high end of the specification. If a process cannot handle that variation well, this could cause all sorts of issues such as installation challenges, performance issues, and other quality issues, leading to loss of time, money and product reputation.
How to calculate the Capability (Cpk) and Performance Indices (Ppk)?
The formulas for Cpk and Ppk are based on data being normally distributed and are given below. We can see they are nearly identical and the major difference being how the process variation is determined.
The Cpk is calculated using the WITHIN standard deviation, while Ppk uses the OVERALL standard deviation. Without going into details, the within standard deviation is the average of the sub-group standard deviations, while the overall is the standard deviation of all individual data.
The sentient X-bar chart below shows the process Cpk=1.40 which is based on the sigma (within) = 0.5318 which is the standard deviations of the averages plotted in the chart.
The Ppk=0.91 is based on the sigma (overall) = 0.70 which is standard deviation of all the individual data.
It is important to note that for the same specifications the process is not performing less than its capability.
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Abeer Singhal
Abeer has over a decade of experience in semiconductor processing and advanced manufacturing. He is co-inventor on U.S. patents in the field of semiconductor manufacturing and has extensive experience implementing advanced manufacturing systems for high volume and complexity products. Prior to his role at Sentient, Abeer has worked as an equipment technician, process engineer, advanced process control systems engineer, and manufacturing systems architect. He has a degree in Microelectronic Engineering.