Process Capability (Cp) and Performance (Cpk)

Learn how to determine whether your process is meeting its full potential—and see opportunities for improvement.

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How do you use Cp and Cpk?

Although statistical process control (SPC) charts can reveal whether a process is stable, they do not indicate whether the process is capable of producing acceptable output—and whether the process is performing to potential capability.

Capability (Cp) and performance (Cpk) indices go beyond elemental quality control to illustrate a process’s ability to meet specifications. Using information from these statistics, you can better understand which processes need improvement, where you have opportunities for improved productivity, and how to prioritize improvement activities.

Let’s take a look at the difference between Cp and Cpk.

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What Is the Process Capability Ratio (Cp)?

Process capability analysis with the Cp ratio shows how well the process spread (expressed as six standard deviations) fits into the specification range. This measurement is determined by dividing the specification limit (voice of the customer) by the process spread (voice of the process).

To calculate Cp, subtract the lower specification limit from the upper specification limit, then divide by six standard deviations.

What Is the Process Performance Ratio (Cpk)?

The Cpk ratio shows the relationship of the process spread to the specification limits while taking into account the centering of the process compared to the specification limits. Cpk represents the lowest value of the capability against the upper or lower specification, showing where, within the specification limits, the process is producing.

To calculate Cpk, compare the average of the data to both the upper and lower specification limit. An off-centered process will have a greater risk of fallout to the specification limit closest to the process mean. The reported Cpk will be the one that measures the highest risk.

Evaluating the Relationship Between Cp and Cpk

Before relying on the Cp and Cpk values:

Verify that process variability is stable, i.e. no out-of-control patterns on the control charts.
Review individual data values on a histogram chart to verify that the distribution is normal (or close to normal).
Verify that engineering tolerances are known.
Verify that the estimated standard deviation of the process is known.

Never attempt to interpret numerical summaries of capability without also looking at a histogram of the data plotted against specification limits. Capability studies should also include analysis of control charts and capability indices.

Easily Determine Process Capability & Performance

When you use SPC software from InfinityQS, determining capability becomes easier than ever. See how to turn Cp and Cpk values into actionable information.

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What is a Pareto Chart?

Pareto charts display defect codes and causes in a simple, easy-to-understand bar chart. But don’t let their simplicity fool you—these charts can be useful statistical process control (SPC) analysis controls.

A traditional use of a Pareto chart like the one shown here would be to count and categorize the types of potential defects that result from a visual inspection of an engine. You can see from this example that the defect “Incorrect Torque” is most prevalent.

Multilevel Pareto Charts

InfinityQS^® software takes this chart technology to the next level by supporting multilevel Pareto charts—up to 10 levels deep.

InfinityQS has turned the pedestrian Pareto chart into a robust, sophisticated analysis tool that allows sorting and display of defect codes any way you want—by shift, customer code, employee, lot number, part, time, and more. Any information associated with defect data can be sorted, sliced, and diced.

The two-level Pareto chart shown here includes the same defects as the previous chart but re-sorts the data by engine serial number (yellow bars), then by defect code (blue bars). Clearly the most prevalent defect is “Incorrect Torque,” but the re-sorting reveals additional information including:

The engine serial number where the most defects were found
The total number of defects for each engine
The type of defects found on each individual engine serial number
The fact that not all engines include “Incorrect Torque” defects

In our free webinar Box Plots and Pareto Charts, you’ll learn how to gain the greatest benefit from these tools. You’ll learn best practices, how to easily analyze data, and how to use weighting to monetize quality issues.

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See the Pareto Chart in Action

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Statistical Process Control 101

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The Problem with Tampering

When a process is centered on target and is in state of statistical control, any adjustments to the process only increase variation. Adjusting a process that is in control is referred to as tampering.

The Funnel Experiment and Deming’s Four Rules

The classic analysis of the effects of tampering is Deming’s Funnel Experiment. In this experiment, participants drop marbles through a funnel suspended over a target. The funnel represents the process, the marble drop location is the feature being produced, and the target is the customer specification.

Deming described four approaches—also referred to as rules—that encompass the typical ways in which the experiment participants tamper with the funnel (Out of Crisis, 1986, p. 328).

Rule 1: No adjustment

The optimal approach is to leave the funnel fixed and aimed at the target, without making any adjustments. When a process is stable, centered, and shows only the inherent variation, there is no reason to make an adjustment.

The takeaway: Before attempting any process adjustment, you must gather enough data to make sure you understand the normal behavior of the process. Use a control chart to track variations, and then adjust the process only when special variations occur.

Rule 2: Adjustment from last position

Sometimes referred to as the “human nature” approach, some participants move the funnel after each drop, to try and compensate for the previous drop’s variation. In this approach, the funnel is moved the exact negative distance of the drop. Compensating for the “error” of the drop, might improve the on-target average but doubles the variation.

The takeaway: When participants compensate for error, the variation doubles—and remember, variation is the true issue. This problem is prevalent in gauge calibration when manufacturers adjust a gauge after taking one standard measurement.

Rule 3: Adjustment from target

Participants trying to take a “logical” approach also move the funnel to try to compensate for the previous drop. But in this instance, the funnel is moved not based on its last location, but on its distance from the target. For example, if the measurement of the previous drop was 5 units above the target, participants move the funnel 5 units below the target.

The takeaway: Although this approach seems logical, it results in an oscillating process.

Rule 4: Adjustment from last drop

In this approach, participants move the funnel to point at the previous drop rather than the target. In other words, at drop n, they set the funnel over the location of the n-1 drop. As you might expect, this approach creates a pattern that moves steadily away from the target.

The takeaway: Believe it or not, this approach occurs in calibration scenarios when one product is used to set up for the next production. This issue is typical in workplaces where on-the-job training is prevalent.

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Statistical Process Control (SPC) Implementation

Statistical process control is certainly not the only technique used to improve processes. But for our purposes here, we will focus on two of the tools used most in SPC:

Histograms
Control charts

LEARN MORE: SPC TOOLS FOR ANALYSIS

Histogram

Histograms can provide a quick view of process variation and are used to plot frequency distributions.

Control chart

Control charts are the best-known tools associated with SPC.

Control charts are used to determine whether a process is stable or unstable. There are many types of control charts that can be used to fit the nature of different types of data streams and sampling methods.

Below are examples of the most commonly used control charts:

Variable data
- Xbar-S: Xbar and standard deviation
- Xbar–R: Xbar and range chart
- IX–MR: Individual X and moving range chart
Attribute data
- c: Defect count
- u: Defect count, normalized to sample size
- p: Proportion defective
- np: Proportion defective multiplied by sample size

Control charts are discussed further in the Process Behavior and SPC Control Charts section as well as in our Definitive Guide to SPC Charts.

LEARN MORE: DEFINITIVE GUIDE TO SPC CHARTS

Although SPC charts are revealing, today’s manufacturers increasingly recognize the benefits of moving away from manual SPC—conducted by recording data on paper and then running analysis via offline spreadsheets or statistical software—and instead using real-time SPC software.

SPC Software

Quality control software for manufacturing offers multiple benefits:

Surface relevant information more quickly
Filter data according to role (e.g., operator, quality manager) and location (e.g., the lines being worked on that day)
Faster, focused, and more detailed analysis
Additional means of evaluating data (e.g., grading and stream summary)
Directed alerts and notifications
Mobile, enterprise-wide visibility into operations

InfinityQS is the leading provider of SPC software and services for manufacturers, providing quality intelligence solutions that work in the cloud or on-premises, across the globe.

LEARN MORE: SPC SOFTWARE FOR MANUFACTURING

Remember: Using statistical process control just to “put out fires”—finding an out-of-control point on a control chart and then determining and removing the assignable cause—is not the same as creating continuous improvement. SPC can be fully realized only when you use it to improve processes and reduce variation.

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Statistical Process Control FAQs

Still have questions about statistical process control (SPC)? Click the links below to locate information about popular topics.

What is SPC (statistical process control)?

Statistical Process Control (SPC) is a scientific, data-driven methodology for quality analysis and improvement. In manufacturing, SPC is an industry-standard methodology for measuring and controlling quality during the manufacturing process.

LEARN MORE: WHAT IS SPC?

What are the origins of SPC?

Dr. Walter A. Shewhart (1891–1967), a specialist in the use of statistical methods, was responsible for the application of statistical methods to process control. Up until Shewhart, quality control methods were focused on inspecting finished goods and sorting out the nonconforming product. As an alternative to inspection, Shewhart introduced the concept of continuous inspection during production and plotting the results on a time-ordered graph that we now know as a control chart.

LEARN MORE: SPC 101

How does SPC relate to quality control in manufacturing?

By using statistical process control, manufacturers can move from a detection approach to a prevention approach, reducing or eliminating the need to rely on sorting or inspection. SPC can increase productivity, reduce waste, and reduce the risk of shipping nonconforming products.

LEARN MORE: WHY USE SPC IN MANUFACTURING?

How can I implement an SPC measurement system?

Control charts are used to determine whether a process is stable or unstable. However, using statistical process control just to “put out fires”—finding an out-of-control point on a control chart and then determining and removing the assignable cause—is not the same as creating continuous improvement. SPC can be fully realized only when you use it to improve processes and reduce variation.

LEARN MORE: STATISTICAL PROCESS CONTROL IMPLEMENTATION

What are statistical process control limits?

Control limits are calculated from the process itself. Because control limits show how the process is performing, they are also referred to as the “voice of the process.” Control limits show how the process is expected to perform; they show the variation within the system or the range of the product that the process creates.

LEARN MORE: SPECIFICATION AND CONTROL LIMITS

What are specification limits?

Specification limits are boundaries set by a customer, engineering, or management to designate where the product must perform. Specification limits are also referred to as the “voice of the customer” because they represent the results that the customer requires. If a product is out of specification, it is nonconforming and unacceptable to the customer.

LEARN MORE: SPECIFICATION AND CONTROL LIMITS

What are Shewhart statistical process control charts?

All control charts have three common elements:

Plot points: Plot points usually represent individual measurements, averages, standard deviations, or ranges.
Centerline: The centerline is usually (but not always) the average of the points plotted on the chart.
Control limits: Control limits represent the amount of variability in the process.

There are four foundational guidelines to Shewhart statistical process control charts.

LEARN MORE: SPC CONTROL CHARTS

What’s the best use of SPC control charts?

LEARN MORE: STATISTICAL PROCESS CONTROL (SPC) IMPLEMENTATION

How should I use SPC charts to determine process capability?

Capability is calculated from existing data but can be used as a prediction of future performance. However, the capability results must come from an in-control process if the results are to be used to predict the process’s behavior in the future. The most commonly used measures of capability are Cp, Cpk, Pp, and Ppk.

LEARN MORE: PROCESS CAPABILITY

Why do SPC initiatives fail, and how can I help ours succeed?

Statistical process control can help manufacturers achieve continuous process improvement—when it is implemented properly. Watch out for obstacles that can sideline your SPC efforts.

LEARN MORE: OVERCOMING OBSTACLES TO EFFECTIVE SPC

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Why Use SPC in Manufacturing?

Today’s consumers expect the best quality products at the lowest price. Why do manufacturers use SPC? Because statistical process control can help you meet both these demands.

By using statistical process control, manufacturers can move from a detection approach to a prevention approach, reducing or eliminating the need to rely on sorting or inspection. SPC can increase productivity, reduce waste, and reduce the risk of shipping nonconforming products.

Statistical Process Control Reduces Scrap

For many years, the term quality control meant inspecting to remove nonconforming products. Products are produced, then inspected to determine whether they are fit to be shipped to the customer. Products that aren’t acceptable are either scrapped or reworked. Sorting products is not only expensive—you’re basically paying one employee to make the product and another to make sure that the product is right—it’s also not very accurate. Studies have shown that 100% inspection is approximately 80% effective.

Statistical process control helps manufacturers escape this inefficient cycle. SPC leads to a system of preventing nonconforming product during the production process instead of waiting until products are complete to determine whether they are acceptable. This reduces waste, increases productivity, makes product quality more consistent, and reduces the risk of shipping non-conforming products.

When statistical process control is properly implemented, manufacturers foster an environment in which operators are empowered to make decisions about processes. In this way, processes—and product quality—can be continuously improved.

SPC is a powerful tool—but success depends on regular and proper application. Management must support its implementation through trust and education of employees and a commitment to supply the necessary resources.

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Histogram

Identify variations in process data at a glance.

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What is a Histogram?

A histogram is a graphical frequency distribution of raw data values. Histograms reveal the distribution of data values, compare them with specification limits, and generate useful metrics and statistics that describe the data set in detail.

When analyzing data, histograms are often used with statistical process control (SPC) control charts. That is, the same data used to create control charts can be used to create histograms. While control charts display data in time sequence, histograms do not. Instead, histograms show individual data values summarized and compared to engineering specifications.

Using Histograms

Histograms communicate the central tendency and spread of a data set. When compared with specification limits, histograms reveal how close the average of the data is to the engineering target. In the histogram below, the average (represented by the black vertical line) falls to the right of the target value. This indicates that the process is not centered. This fact is also indicated by the yellow bars, which show that most of the data values fall to the right of the target.

Histograms also allow users to compare individual data values to both upper and lower engineering specification limits. This allows quality professionals to access a variety of different statistics and improvement metrics.

This histogram represents the measurements of a feature, “Location C,” from a specific part, revealing the following important information:

The mean value is larger than the target value.
Data values are “bunching up” against the upper specification limit.
The yellow bars do not seem to match the normal curve fit.
No data value falls below the lower specification limit.
If unchanged, the process is expected to generate a loss of about 4.8% above the upper specification limit.

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See the Histogram in Action

Histograms can be combined with other SPC tools and control charts to reveal important quality information and opportunities for improvement at a plant—and even across sites.

Modern SPC software solutions make these complex analyses possible. When data is centralized and standardized in a unified data repository, SPC software provides instant access to quality information, ensuring immediate attention to your greatest quality challenges.

See how InfinityQS^® reveals valuable quality information and makes SPC easy.

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SPC Control Charts

All control charts have three common elements:

Plot points: Plot points usually represent individual measurements, averages, standard deviations, or ranges.
Centerline: The centerline is usually (but not always) the average of the points plotted on the chart.
Control limits: Control limits represent the amount of variability in the process.

The Four Foundations of Shewhart’s Control Charts

There are four foundational guidelines to Shewhart statistical process control charts:

Shewhart statistical process control charts always use control limits that are set to 3 sigma units on either side of the central line. These 3-sigma limits are always based on the chart’s data and define when action should be taken on the process. Control limits are never based on any calculation using the specification limits. Specification limits are the customer requirements and define how to treat the product, not the process.
Always use an average dispersion statistic or a median dispersion statistic when computing 3-sigma control limits. Using the average or median of several dispersion statistics increases the robustness of the chart.
The conceptual foundation of Shewhart’s charts is the notion of rational sampling and subgrouping.
Control charts are effective only to the extent that the organization can effectively use the knowledge gained to take action.

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Process Capability

Process capability is calculated from existing data but can be used as a prediction of future performance. However, the process capability analysis results must come from an in-control process if they are to be used to predict the process’s behavior in the future. The most commonly used measures of capability are Cp, Cpk, Pp, and Ppk.

Remember, in-control means that the process is showing primarily common cause variation and so is both stable and predictable. Also remember, a process can be within control limits and still be outside product specification limits.

What is Process Capability? Hearing Two Voices

As mentioned earlier, a 6-sigma range (+3 standard deviations) is the voice of the process and show only the expected variability of the process itself. Specification limits are the voice of the customer and represent what the customer expects. The graphic below shows a process that is consistently making product that is out of specification.

SPC Cp Index

The SPC Cp index shows how well the 6-sigma range fits into the specification range. This measurement is determined by dividing the specification limit (voice of the customer) by the control limit (voice of the process).

Formula for Cp calculation

To calculate Cp, use the following equation:

For example: A Cp value of 1 means that the process variation equals the specification limit range. The process is thus capable (but just barely) of meeting the customer’s criteria.

The Cp index does not consider how well (or how badly) the process is centered relative to the specification limit target. Therefore, the Cp is a measure of optimum capability (i.e., what the process is capable of if it were centered, not what the process might be doing).

SPC Cpk Index

Like the Cp index, the Cpk calculation shows the relationship of the 6-sigma spread to the specification limits, however, the Cpk considers the centering of the process. There are two Cpk values calculated, one that considers the upper specification limit and another that considers the lower specification limit. The reported Cpk, however, represents the lowest value of the capability against the upper or lower specification. Cpk shows where within the specification limits the process is currently producing, not what the process is capable of producing. To determine whether the process is capable, you must measure Cp.

Cp Versus Cpk

When the process is centered, the Cp and Cpk calculate to be the same number. However, as the process output deviates from the target value, so do the Cp and Cpk ratios. Some observations to consider looking at the graphic below:

The Cp value remains the same because the width of the distribution is constant.
Cpk = 0 when the process mean equals one of the specification limits.
Cpk < 0 when the process mean exceeds one of the specification limits.

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