## A Capable Process

A capable process should meet the customer’s expectations, reliably producing parts within the specification limits. In order to calculate capability, complete the following steps. First, estimate sigma or standard deviation. Calculate the process control limits. Finally, compare control limits to the specification limits, calculating  and .

Control limits use sigma and the process average (average of the averages). After calculating the process average, identify the and the . Cp compares the control limits to the span specific limits. Cpk is two separate calculations comparing the LCL to the LSL and the UCL to the USL.

There is a buffer zone between the control limits and the specification limits. This determines how capable the process is in producing in-specification parts. The buffer zone impacts scrap, rework, and sorting for bad material costs (COPQ). The buffer zone also determines equipment and tooling needs, in addition to long-term sampling rates.

### 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).

Something to think about: Why are minimum Cp/Cpk values required before using SPC charting?

## 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.

Learn more about analyzing normal and non-normal data with the following video:

## 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/

RealEngineeringExplained (2020, December 23). Process capability analysis [Video]. YouTube. https://www.youtube.com/watch?v=LlMxEo4BP8c

Sharma, G. & Srinivasa Rao, P. (2013). Process capability improvement of an engine connecting rod machining process. Journal of Industrial Engineering International, 9. https://www.econstor.eu/bitstream/10419/147178/1/775205362.pdf 