Six Sigma Process with R
By: Roberto Salazar
Tags: Industrial Engineering, Coding, Six Sigma, Quality Assurance, Programming

Analyzing Process Capability and Sigma Level

Process capability is a statistical measure to asses the ability of a process to meet its specifications. Process capabilities (i.e Cp and Cpk) are usually obtained before and after the implementation of a quality improvement project or initiative to evaluate the level of improvement occurred.

There are two possible scenarios when analyzing processes capabilities: when their mean is aligned with the target value and when it is not. Centered processes are analyzed based on their Cp ratio while non-centered processes are analyzed based on their Cpk index. Let’s analyze both of them using an example in R software for their respective statistical analyses.

Centered Process

Centered processes are those in which the mean of a set of measurement is align to the target. In this scenario, most data points are close to the target, but not necessarily all of them.

For the following example, let’s analyze the capability and obtain the sigma level of a centered process that has a target value of 10, an USL of 13 and a LSL of 7, and from which 100 measures were obtained. Let’s take a look at the R code.

According to the histogram above, the process spread is wider than the specifications spread; thus, it can be stated that the current process is not capable. Even though most of the data points are located within the specification limits, there are nonconforming products exceeding the specification limits. The Cp ratio of 0.5 represents a sigma level of 1.5, which is considered non-competitive.

To deal with this issue, industrial engineers and six sigma practitioners must conduct root-cause analyses to identify causes of special variation. Once identified, they can develop and execute continuous improvement projects and initiatives to reduce the variability of a process and ensure that most of the data points will be located within the specification limits.

After the completion of a continuous improvement project or initiative, the improved process should like like this:

According to the histogram above, the new process spread is equal to the specifications spread; thus, it can be stated that the process is capable with tight control. After the implementation of the six sigma project, all of the new data points ended up located within the specification limits. The Cp ratio of 1 represents a sigma level of 3, which is considered industry average.

However, in order to achieve a sigma level of 6, the process variability must be reduced even more. By achieving this, more data points will be closer to the target and the process spread will be considerably narrower than the specifications spread, reducing the number of nonconforming untis to almost zero.

The histogram below shows the final outcome of the newly improved process, in which its spread is considerably narrower than the specifications spread; thus, it can be stated that the process is highly capable. Now, even more data points are located around the target value. The Cp ratio of 2 represents a sigma level of 6, which is considered world-class.

Non-Centered Process

Non-centered processes are those in which the mean of a set of measurement sis not align to the target; its mean is shifted either to the right or left of the target value. In this scenario, most data points are away from the target.

Since the Cp ratio does not consider the centerness of a process, the Cpk index is used instead to analyze the process capability and obtain its sigma level.

For the following example, let’s analyze the capability and obtain the sigma level of a process that has a target value of 10, an USL of 13 and a LSL of 7, and from which 100 measures were obtained, but from which it is know to not be centered. Let’s take a look at the R code.

According to the histogram above, the process spread is wider than the specifications spread and its mean shifted to the right of the target; thus, it can be stated that the current process is not capable at all. There are nonconforming units exceeding the upper specification limit. The Cpk index of 0.209 represents a sigma level lower than 1, which is considered non-competitive.

Once again, industrial engineers and six sigma practitioners must conduct root-cause analyses to identify causes of special variation and execute continuous improvement projects and initiatives to reduce the variability of the process.

After the completion of a continuous improvement project or initiative, the improved process should like like this:

According to the histogram above, the new process spread has been significantly reduced; thus, it can be stated that the process is highly capable. However, not all of the new data points ended up located within the specification limits, which suggests that the mean of the process needs to be shifted to the left. The Cpk index of 0.685 represents a sigma level of approximately 2, which is still considered non-competitive.

The histogram below shows the final outcome of the newly improved process after the implementation of continuous improvements initiatives and additional efforts focused towards shifting the process mean to the left. In the new process, its mean is (almost) centered with the target value and even more data points are located around it. The Cpk index of 1.81 represents a sigma level of approximately 5.5, which is still considered world-class.

Under perfect conditions, a process with a mean aligned with its target value will yield the same Cp and Cpk values.

Concluding Thoughts

Six Sigma consists in a set of tools, methodologies, frameworks and statistical analyses used to measure and improve a process variability. It is an area of high interest within academics and professionals in multiple fields (e.g. industrial and systems engineers, continuous improvement engineers and quality analysts).

In addition, Lean practices have been merged with Six Sigma, leading to what is known as ‘Lean Six Sigma’, which focuses in reducing process variability and eliminating waste (e.g. transportation, inventory, movement, waiting, over processing, over production, defects, human potential).

This article presented an overall overview of a Six Sigma process with an application in R, a useful free and open source software for statistical purposes with multiple packages focused on Six Sigma (e.g. SixSigma, qcc). In today’s highly competitive world, engineers are highly encouraged to study and understand Six Sigma concepts and pursue professional certifications associated with it to a better competitive advantage and a stronger resume.