## A Capable Process

In order to understand capability, it is first important to understand the primary goal in SPC and the inherent nature of variability.    We know that all manufacturing processes will produce parts which vary in any given dimension.  This normal variation is called common cause or “system” variation.

Our goal is SPC is to create statistical control charts which are based on this system variation and allow us to visually see when the process changes or shifts.  So create the charts, we must first study the normal process by doing the following:  gather sufficient data for each specified measurement on the product, create a histogram of the data.  This histogram data identifies the range of sizes produced by the normal process.   We previously learned that the peak of the histogram curve represents the center of the data (and the process).  And the range between + 3 sigma and -3 sigma from this peak represents 99.73% of all the possible parts produced under normal production running.  In manufacturing, we calculate the + 3 sigma and -3 sigma values and call them the process upper and lower control limits.

Engineering typically establishes the required dimensions to create a product that fits and functions as desired by the customer.  These dimensions are called the product specification limits.

So, to determine if a process can consistently meet the customer requirements, we can compare the histogram data to the product specification limits.  This comparison determines the Process Capability.  It is a comparison of “what the process actual produces” to “what is needed” for a quality product.

Ideally, a buffer zone will be established between the control limits and the specification limits. This means that the upper specification limit is greater than the upper control limit and the lower specification limit is less than the lower control limit.  Why is this important?  We will use the control limits to construct run charts for manufacturing and rules for adjusting the process.  However, if the specification limits and the control limits are identical, the process could still produce a random part .27% of the time which is an out-of-specification part (100-99.73% = 0.27%).  Also, if the process shifts at all, it will begin making out-of-specification product.  If there is a sufficient buffer zone then small shifts can be identified and corrected BEFORE out-of-specification product is ever produced.  This is what makes Statistical Process Control a PREVENTION TOOL.

The size of the buffer zone is a strong indictor of how capable the process is in producing in-specification parts. The larger the buffer zone, the greater the process capability.  The buffer zone impacts scrap, rework, and sorting for bad material costs (COPQ). The buffer zone and process capability in general also determine equipment and tooling needs.  In addition, as process capability increases inspection frequency can be reduced. to long-term sampling rates.

There are several capability indices commonly used to communicate process capability.  Cp and Cpk are the most common.

To determine Process Capability:

1. Estimate sigma or standard deviation.
2. Calculate the process control limits at +/- 3 sigma.
3. Calculate Cp and Cpk.
4. Evaluate Cp and Cpk to the required goals.

### Calculations:

Cp = (Total Allowed Variation)/ (Actual Process Variation) = (Upper Specification Limit – Lower Specification Limit) / (Upper Control Limit – Lower Control Limit)

• The goal is for CP (and Cpk) to be equal to or greater than 1.33.  However, companies often require these to be > 1.33, 1.67, or 2.
• If they are = 1, there is no buffer zone for process variation over time and therefore SPC cannot be utilized.
• If they are <1, the process is not currently capable and improvements must be made otherwise 100% inspection will be necessary.
• Notice Cp is a just a ratio of how much greater the allowed variation is compared to the actual variation.

Cpk is similar but 2 calculations are required.   Each calculation looks at ½ of the variation.  This helps determine whether the process is centered.

• Cpk (to the USL) = (USL – Average of the Averages)/ (3 sigma—this is the same as ½ of the actual variation) =  (USL – Average of the Averages)/ ((UCL – LCL)/2)
• Cpk (to the LSL) = (Average of the Averages-LSL)/ (3 sigma—this is the same as ½ of the actual variation) =  (Average of the Averages-LSL)/ ((UCL – LCL)/2)

The average of the averages is the peak of the histogram curve.

Again, the goal is for both numbers to be greater than 1.  If one is greater and the other is less than one, then the process is not centered.  It is skewed towards the number which is the smallest.  While technically, the smallest number is what is reported for the Cpk. Knowing both results helps determine if the process is centered and capable of meeting the requirements.

Here is an example to work through:

The specification for the diameter of a pupe is 100mm +/- 1mm. A new study was conducted and the control limits were calculated to be UCL=99.5mm and the LCL=100.7mm. The average of averages is 100.1

To calculate Cp:

• Cp = (101-99) / (100.7-99.5) = 2/1.2 = 1.667

To calculate Cpk:

• Cpk ( to the USL) = (101-100.1) / ((100.7-99.5)/2) = .9/.6 = 1.5
• Cpk ( to the LSL) = (100.1-99) / .6 = 1.1/.6 = 1.833
• The Cpk is reported as 1.5, the smaller number.  However, this shows that the process is not centered and is skewed towards the upper limit.

Is the process currently capable? Yes, all  numbers are greater than 1.33.

Is the process centered? No, not perfectly. It is skewed towards the upper specification.

Watch the video below to learn more about Cp and Cpk and how to interpret those results. Then, it may be beneficial to read this study: Process Capability Improvement of an Engine Connecting Rod Machining Process (2013).

• What does it mean if both Cp is 1?  This means that your process control limits and specification limits are exactly the same.
• Is this ideal?  No, if the process varies a little more or shifts (for instance due to tool wear) then out-of-specification product will be produced
• What is the goal for Cp and Cpk?  Typically >1.33
• Can SPC charts be utilized when Cp is <=1?  NO.  The process has too much variation.
• What does it mean when Cp is Greater than 1, but Cpk is not?  This means that the process could be capable but it is not centered.  Adjust the process mean to produce closer to the nominal specified dimension, this should increase the Cpk value.
• What does it mean if both the Cpk values are less than 1?  The process is not capable.
• What needs to be done?  The normal process has too much variation.  Identify sources of variation and initiate process improvements as needed.
• Cp is a quick check of potential process capability.  Cpk tells you both that your process could be capable and if it is capable.

## Determining Capability

When a process is in control but not capable, first, “center the output of the process on the target value and re-evaluate to see if the output became capable” (Key Performance, 2014). If the process is still not capable, there is a bigger problem. The process needs to be modified in order to reduce variations and increase capability.

## Two Types of Manufacturing Process Capability Studies

Machine capability

• A specific machine or operation is examined, used to qualify a machine for production. Usually, this is a short-term study, with a minimum of 30-50 parts.
• Individual machines are sampled sequentially.

Process capability

• This includes all machines to better understand the combined variation from all sources. This is typically a long-term study (more than 30 days). The parts in this study are randomly sampled from the finished inventory.

## References:

CQE Academy (2021, February 24). Process capability: Explaining Cp, Cpk, Pp, Ppk and how to interpret those results [Video]. YouTube. https://www.youtube.com/watch?v=H6St9mCKWuA

Key Performance (2014, April 14). Process capability and process control: How are they different? Retrieved on August 8 from https://keyperformance.com/2014/04/process-capability-and-process-control-how-are-they-different/ 