Many business owners are assessing the current quality and efficiency of their product development processes. Process capability analysis is a tool these businesses can use to determine the current condition of their product development processes—to help assess how well their product development process meets a set of predetermined specifications. This analysis can also help business stakeholders develop quality improvement initiatives.

To use an example for the remainder of this guide, let’s say Bobby is the owner of Bobby’s Bats. He wants to assess how well his bats meet the length standards for Major League Baseball (MLB). He’ll use process capability analysis to determine if his process can meet the standards and the extent to which his production is centered between the specification limits. Bobby can then use the results of this analysis to measure and control the variation of his process to stay ahead of the competition.

## What is Process Capability?

Before we discuss the importance of process capability, let’s first define what a process means.

A process can be any combination of tools, resources, or personnel working in tandem to produce a specific product or output. At Bobby’s Bats, these include the staff, the saws, and sanders, the wood and stain used to make the bats—and computer software.

Ideally, this process would run each time consistently, producing a bat cut to the exact MLB specifications. However, we know that it’s more likely there will be some variation in the output of the process. This is where a process capability analysis becomes useful.

Process capability provides two critical pieces of information. First, it provides a measure of the variability in the output of a given process. Second, it compares the capability of a proposed specification and provides critical data that enables production efficiency—while also identifying potential problem areas.

Process capability requires a data set from an in-control process, which means that the output measures the process in question and then creates a normal bell-curve distribution over time. Using standard, in-control data sets is key to the success of process capability analysis.

## Capability vs. Stability

A process is Capable if the outcomes are predictable and meet specifications. If it is solely affected by recurrent sources of variation, it is called stable. The process specifications are not required to assess process stability but are needed to determine capability.

## The Capability Index, CPK

A Process Capability study produces a single statistic that indicates a process's capacity to constantly deliver output that meets the below criterion.

- CPK <1.00 (Poor, incapable)
- 1.00< CPK <1.67 (Fair)
- CPK >1.67 (Excellent, Capable)
- CPK = 2 for a 6δ process (i.e., a six sigma process)

## Formula for OR, CP, CPK, PP and PPK

## What is CPK?

The "Capability Index" is abbreviated as CPK. It is a measure of a process's capability to generate output that is within the process specification limit. The CPK formula uses a sigma estimate to detail a process's ability to meet criteria using the process mean. When CPK = 1, 99.73% of all data points are within the specification boundaries, i.e 99.73% of process outputs are within specification. The definition of CPK =1.

## What is CP?

CP is a measure of a process's ability to produce output that is within upper and lower specification limitations. The CP metric does not account for process centering. While CP may indicate a potential to function within requirements, inadequate centering may skew the actual output, resulting in outputs outside of specification. As a result, using CP alone can be misleading, but it can provide a good idea of process potential.

The dispersion of the process output diminishes as the CP measure grows, which is otherwise considered positive. The process output gets increasingly uniform as variation decreases.

CP typically gets used in line with the CPK measure to understand both centering and spread.

If the CP and CPK values are equal, the process gets centered between the specifications; otherwise, the higher the difference between the two values, the more the shift in the process from the mean to the nominal mean.

## Process Capability (CPK): Assume the Worst Case

CPK determines how well a process is controlled by monitoring its spread/dispersion within certain boundaries.

In metric units:

CPK = {USL – Mean}/3σshort or {Mean – LSL}/3σshort

We pick the worst-case scenario of either CPK = {USL – Mean}/3σshort or {Mean – LSL}/3σshort

If the mean is centered, both aPProaches get the same result. If the mean is close to the Upper Specification Limit (USL), we utilize USL - Mean to determine the worst-case outcome, i.e., the result that produces the highest level of outputs outside of specification.

## What is PPK?

The PPK measure indicates how well a process performs compared to the process parameters. The PPK metric also considers the centering of process outputs versus specifications.

Because PPK employs actual process sigma rather than an estimate of sigma as CPK does, CPK is used to measure future performance and Process Capability. PPK is used to measure actual past performance.

According to CPK, if PPK = 1, 99.73% of all data points will fall within the specified boundaries.

## What is PP?

PP is a measure of a process's actual performance in terms of producing an output within the upper and lower specification limitation (according to CP).

The PP measure does not account for process centering and merely offers a measure of the extent of process dispersion or variation within it.

To determine how a process performs concerning spread/variation and how effectively the process gets centered between specification boundaries. The PP measure should be utilized in conjunction with the measure.

The dispersion of the process output reduces as the PP measure increases.

When the PP and PPK values are equal, the process gets centered between the specifications; when they are unequal, the higher the difference between the two values, the more the shift to the process mean from the nominal mean.

## Difference Between CP, CPK, and PP, PPK

It is essential to understand the differences between the various calculations. The potential capability (CP) is used to measure how capable a process is of making parts within predetermined limits or specification limits. These limits are defined by a lower specification limit (LSL) and an upper specification limit (USL). The spread between the current process and the process capability is measured using six process standard deviation units.

In Bobby’s case, the LSL and USL would specify how short or long the bats should meet MLB specifications, respectively.

The actual capability during production (CPK) measures whether the process is centered between the previously determined specification limits. The k is the factor that centralizes the data. If you picture a bell curve, the CPK measures how centered the curve is between the LSL and USL limits of the curve.

Both the CP and CPK measurements assume that the sampling comes from a normal distribution of a large (more than 50 measurements), randomly selected sample.

The preliminary process capability (PP) and its respective preliminary process capability index (PPK) are used more commonly to evaluate new processes that haven’t been established yet or processes that don’t come from a normal distribution of data.

In Bobby’s case, he may want to calculate a PP and PPK if he decides to change his process to accommodate a higher production volume.

## Advantages of a Capable Process

- A process must produce outputs that meet standards. A capable process will meet specification requirements regularly and reliably.
- A capable process with a low amount of spread will provide extremely uniform outputs.
- With a reliable, low variability process, in-process and final inspection and testing can decrease, saving time and money.
- Defect rates will be minimal or even non-existent. A capable process will have low scrap, rework, and repair levels.
- A capable process, well-centered and with a modest spread, will allow for the revision of specification limitations.

Customer requirements and expectations must get addressed in the specs. It will necessitate ongoing communication with the customer.

## How to Measure and Calculate Process Capability

There are several steps one should follow when performing a capability analysis. The first step is to determine the upper and lower specification limits for the process. The customer, client, or personnel involved in the production of the product can define these limits.

The second step is to collect a sampling of the current production process to determine the mean and standard deviation of the existing product output. In this step, obtaining a large sample size (typically 50 or more measurements) and collecting samples over a long period in one production run is vital to ensure robust and accurate sampling.

Potential capability is calculated by dividing the specification width by the process.

Because potential capability is calculated using six standard deviations, Bobby will multiply six times the standard deviation he calculated from his sample to get the process width. He’ll also subtract the LSL from the USL to get the specification width, which looks like this:

CP=USL-LSL6σ

Bobby is looking for a process capability that is greater than one (1). If this is the case, it means that his process has the potential to be capable of producing the specifications required, depending on the way the process centers. To determine process centering, we need to calculate the actual capability during production (CPK).

The CPK is a measurement of how centered the process is between the specifications. This is determined by calculating the process capability of both the lower specification (CPl) and the upper specification (CPU):

CPl=(Process Mean-LSL)(3s)

CPu=(USL-Process Mean)(3s)

Once those are calculated, we take the smallest value of the CPl or CPU, which can be calculated as follows:

CPK=Min(CPl, CPu)

If the minimum value is lower than one (1), the process can’t be accepted and won’t meet the required specifications. While a minimum of one (1) could be considered acceptable, numbers closer to two (2) and three (3) are more desirable. Note that a CPK higher than 1.33 is the standard most companies require as a satisfactory process capability.

If Bobby’s actual capability during production is just below this capability, he’ll need to make some changes if he wants to produce more volume going into the summer. To accomplish this, he could work toward a more robust reduction in the process’s variability or towards centering the midpoint of the process output.

## Process Capability for Non-Normal Data

Calculating a preliminary process capability should only be used when a new process is being established and has not yet reached statistical control. The critical difference between a preliminary process capability index (PPK) and the actual process capability index (CPK) is that PPK can only assess information from the past due to the lack of current data on the process. Unfortunately, this calculation can’t be used to predict future process outcomes reliably.

It’s also important to note that CPK and PPK values will vary greatly when the process is not under statistical control. Understanding these differences will ensure that you’ll choose the capability analysis most appropriate for your data set.

The importance of process capability lies in its ability to inform businesses both what they’re doing well and where they can afford to improve.

## Interpreting the Capability Index

Capability index > 2.0 Excellent. At the six sigma level.

Capability index of 1.34 – 2.0 Good

Capability index of 1.00-1.33 Need Control

Capability index < 1.00 Not Capable

## Factors Influencing Process Capability

- Machine and equipment condition
- The type of operation and the operational conditions
- Raw material kind
- Operator and Inspector Competence
- The method of measurement
- The state of the gauges and instruments

## Tools for Process Capability Estimation

- Histogram
- Control diagrams
- Variance Analysis
- Create a run chart

## Practical Concerns When Conducting Capability Studies

Capability estimates have both good and negative features. CP and CPK estimations, for example, are very sensitive to the assumption that one is sampling from a normal distribution—that is, the majority of the data points are concentrated around the average (mean), generating a bell-shaped curve.

In addition, sampling from a stable system is necessary to obtain meaningful predictions of process performance for future output.

Many quality practitioners only report numerical assessments of competence. Others point out that capability estimates are only statistics or point estimates of the true capability of a process.

Other ways for obtaining meaningful capability estimates may be appropriate for sampling from stable but non-normal distributions, such as:

- Transforming the data to be approximately well described by a Normal distribution.
- Applying a different probability distribution, such as the Weibull or lognormal distributions.

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