# Selecting the right control chart

## For real-time monitoring, a control chart is a statistical tool to analyze the past and predict the future. Choosing the wrong one from among hundreds increases the risk of errors. Advice follows on how to choose the right control chart. This is a March Digital Edition Exclusive.

Knowing the right way to look at collected manufacturing or process data turns numbers into valuable information; here's how to choose the right control chart to make real-time control monitoring more valuable.

Would a manufacturer knowingly embark on a fixed-cost job without first understanding the risks of losing money, shipping defective product, missing the delivery schedule, running on incapable equipment, or using unqualified employees? While all these risks are understood because the price quoted for the job includes an allowance for their associated costs, many of these risk items are actually either unknown or not fully defined. Thus, decisions to pursue a job are usually based on history, opinion, and faith alone.

Luckily, the chance of a catastrophic financial hit due to these unknowns is relatively small as long as the profit margins remain high enough after negotiations. However, as margins are squeezed and demands increase, manufacturers must understand these uncertainties better to ensure they avoid the financial breaking point. The good news is that understanding risk and making better business decisions is as simple as applying statistical monitoring and analytics.

**Real-time monitoring, control charts**

Statistics is the science of predicting the future. Industrial statistical methods are the application of statistical methods where the population of "things to measure" is produced in real time. For real-time monitoring, the prescribed statistical tool is a control chart. Academic training introduces students to three types of variables charts (Xbar-R, Xbar-s, and IX-MR) and four types of attribute charts (p, np, u, and c). There are hundreds of control charts from which to choose. Regardless of statistical background, not having the right control chart increases the risk of encountering Type I (false positive) and Type II (false negative) errors. The purpose of a control chart is to describe a process's personality in terms of normal versus abnormal levels of variation. When using control charts for real-time decision making, corrective actions are recommended only when variation levels or patterns exceed the statistically defined levels of what's normal. When inferior sampling strategies are implemented or the wrong control chart is deployed, the risk of making unwise adjustments (Type I error) or missing a signal that warrants attention (Type II error) is elevated.

Why invest time and effort in collecting and analyzing data just to make wrong decisions? Taking the extra step to learn how to pick the right chart could mean the difference between failure and success.

**Ask these questions to choose a control chart **

Fortunately, selecting just the right control chart requires answering only a handful of questions that will pinpoint the perfect chart to use from a pool of 12 potential, standard variables charts.

Basic questions for variables data are:

- What is the sample size?
- Will multiple parts be combined on the same chart?
- Will test characteristics with different target values be combined on the same chart?

To answer these questions properly and ultimately select the correct control chart, a thoughtful sampling strategy is key. In some cases, simple strategies will suffice where a machine is set up to run the same part for weeks or months, and only one or two characteristics are measured to monitor the health of that process. For example, a machine that makes 0.07 mm pencil lead will be busy as long as 0.07 mm mechanical pencils are being used and this particular product is being sold. Of course, there are many contributing factors that will cause a lead machine to misbehave, but as far as a statistical sampling strategy, diameter and length may be all that's monitored. Depending on the historical adjustment frequencies, five leads may need to be collected only once an hour. Though this may be a common case for textbooks, it reflects the real world for only a few industries.

For most manufacturers, machines are used to run many different shapes, sizes, weights, materials, colors, and features. To accomplish this, one machine is designed to accept different programs, tooling, fixtures, speeds, feeds, pressures, temperatures, flow rates, and others. The uncertainties and combinations of things that could go wrong multiply with every added level of machine flexibility. In these cases, one must create customized sampling strategies and pick the best statistical monitoring tool(s) unique to each machine's input and product output complexities.

Items to consider in a sampling strategy include sampling frequency, sample size, test characteristics, measurement devices, and methodologies. These decisions help define the best way to illustrate and update the visual output as new data is captured. Essentially, the data describes the process's personality so it is easier to understand what normal variation one can expect and what constitutes a significant deviation from the norm.

**Variation, different units **

With a strategic sampling strategy in place, it is much easier to answer the questions necessary to use the variable control chart decision tree (see graphic). In addition to a sampling strategy, more complicated scenarios require only two more questions:

- Will within-piece and piece-to-piece variation be monitored?
- Will different types of tests with different units of measure be combined on the same chart?

Adding these two questions expands the list of potential control charts to 48. With each of those 48 charts, one could apply even more refinements, taking the potential number of charts into the hundreds.

Above all, remember that a control chart is the vehicle that will help those involved to remain engaged with the data collected. By engaging with the right data and using the right control chart, no fortune-teller is needed to predict risks and make better business decisions.

- Steve Wise is vice president of statistical methods, InfinityQS International Inc. Edited by Mark T. Hoske, content manager, CFE Media, *Control Engineering*, mhoske@cfemedia.com.

**About the author **

Steve Wise is vice president of statistical methods at InfinityQS International, a provider of manufacturing intelligence and enterprise quality. A Six Sigma Black Belt, Wise focuses on ensuring proper use of statistical techniques within InfinityQS' software offerings and the application of these techniques for the customer base.

**Key considerations **

- Industrial data gathering often means real-time monitoring.
- Selecting the right control chart aids in turning data into information.
- The wrong control chart can provide misleading information leading to wrong decisions.

**Consider this **

If you cannot understand and correctly decide based on data gathered, what use is the data?

**ONLINE **

This article is a *Control Engineering* March 2014 Digital Edition Exclusive.

Link to process details in an InfinityQS International whitepaper, "A Practical Guide to Selecting the Right Control Chart."

See related *Control Engineering* articles below.