Review of Understanding and Applying Statistical Process Control in Manufacturing, Part 2
In my last post, I explained how to implement statistical process control (SPC) in four phases. I introduced the concept of control charts, as a way of studying your SPC process, collecting data, and drawing conclusions as to whether the process variation is consistent. I finished with two basic questions to ask before getting started with SPC.
In this post, we will explore the measurement system evaluation using a gage repeatability and reproducibility study, as well as conducting process potential and process capability studies.
Conducting a gage repeatability and reproducibility study (gage R & R)
One of the keys to successful implementation of SPC is to make sure the measurement system used has only a small amount of variation. The measurement system is the combination of the equipment used to make measurements, the people charged with making the measurements, and the procedure used. The key to a successful gage R and R study is to duplicate the conditions you ultimately want to control. The decisions made as a result of the SPC analysis must be made with confidence that the data collected reflect the actual process performance. So just what are repeatability and reproducibility?
Repeatability: The amount of variability in the measurement system caused by the measurement device.
Reproducibility: The amount of variability in the measurement system caused by differences between operators.
The first step conducting a gage R & R study is to design it by considering the following factors:
- Who should be a part of the study? This must include the operators who will consistently be using the measurement system.
- How many samples should be collected during the study? I recommend that 10 to 15 samples should be collected in order to cover the range of the specifications.
- How many times should each sample be measured? I recommend three times for each sample.
- Must we measure some kind of standard during the study? I always advise that in any MSE, that something with a known value be included in the study.
According to the AIAG1, the guidelines in the table below should be followed.
Percentage of Process Variation
Less than 10 %
The measurement system is acceptable
Between 10% and 30%
The measurement system is acceptable depending on the application, the cost of the measurement device, cost of repair, or other factors.
Greater than 30%
The measurement system is not acceptable and should be improved.
The AIAG also states that the number of distinct categories into which the measurement system divides process output should be greater than or equal to five. Once you have an acceptable measurement system, it is now time to run the process potential study.
Conducting a process potential study
Typically, process variation can be sub-divided into short-term, piece-to-piece variation, and long-term variation, including all potential sources of special cause variation. The process potential study is very useful because it provides a projection of the process capability and it does so by observing data collected over a short period of time.
The process potential study typically consists of 30 individual samples measured by a single operator using product made from a single production run, without making any equipment adjustments. After all data is collected, we then test it to determine if it is normally distributed, which can be accomplished with common software packages such as SQCpack®, Statgraphics®, or Minitab®. Once we know that the data is normally distributed, we know that the process has the potential to meet existing tolerances.
We also test the data for key indicators which measure the process potential indices, Pp and Ppk. Our hope is that the data is normally distributed and that Pp and Ppk are very close to each other and that both are greater than 1.0. We would like these indices to be greater than 1.33, but as a starting point, 1.0 will suffice. If Pp is greater than Ppk, the process needs to be centered before performing the process capability study.
Conducting a process capability study
Whereas the process potential study uses a sample size of one, the process capability study uses sample sizes greater than one. A rational subgroup of samples should be taken under identical conditions (i.e., same operator, same machine setup, and same raw material). By sampling several samples under identical conditions, any observed variation should be due to only common cause variation. Variation within each subgroup is observed on the range chart and is the basis for the X-bar control limits. The subgroup size and sampling frequency is typically a compromise between the cost of each measurement and the sensitivity of the control chart.
Unlike the process potential study, the process capability study represents data collected over an extended period of time. I always recommend at least seven days using a subgroup sample size of four with minimum of 25 subgroups (i.e., 100 measurements). The motive for the extended study is to be able to measure the influence of normal variations associated with the process being measured. These normal variations include things like changes in raw material lots, equipment adjustments, and operator differences.
Just like the process potential study, one of the first things we look at is whether or not the data is normally distributed. If the distribution is not normal, the implication is that special cause variation is present and must be removed. Once we are certain that the data is normally distributed, we then calculate the Cp and Cpk to judge whether or not the process is capable of meeting the specified tolerance. Our goal is to have both Cp and Cpk at the very least at 1.33. If the Cp and Cpk are less than 1.0, then before proceeding we must reduce the variation of the process. If the Cp and Cpk are different from one another, this implies that the process is not centered within the specifications. What we want is for the process average (i.e., X-bar) to be close to the center of the specification.
Coming in the next post
In my next post, I will discuss how to create and implement the process control chart. If you would like to learn more about this topic, check out my recent series, A Practical Guide for Manufacturing Process Improvement.
Until next time,
1 Automotive Industry Action Group (AIAG) (2010). Measurement Systems Analysis Reference Manual, 4th edition. Chrysler, Ford, General Motors Supplier Quality Requirements Task Force
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