# From Fundamentals to Application: Understanding Statistical Process Control (SPC)

Leveraging data holds the key to driving greater efficiency and transparency. From plant facilities to entire supply chains, costly nonconformances can eat away at profit margins at a time when competition is high. As the global markets grow more complex, it’s crucial for manufacturing organizations to hone processes that access and interpret data in real-time to control variances and target quality.

**What Is the Meaning of SPC?**

Statistical process control (SPC) is a way to use data to improve and control systems and processes. It improves quality by reducing defects. SPC can be used in conjunction with other problem-solving methods like Root Cause Analysis (RCA) to help uncover additional insights and helps answer operational questions that other data approaches may not perfectly target, such as “by how much does the product vary?”

**A Brief History of SPC**

While the concept of SPC has been around since the 1920s, the mathematics driving it are relatively young and cutting edge. In the last hundred years, several people have developed and enhanced key concepts of SPC. Walter Shewart, working at Bell Labs, invents control charts as a way to help discriminate between variation inherent in the process and external factors. We understand these concepts today as common cause versus special cause variation. W. Edwards Deming, an engineer, statistician, and champion of Shewart’s work, traveled to Japan in the 1950s as a management consultant. Deming further developed the concepts Shewart had outlined, resulting in total quality management (TQM). His work on TQM and his 14 quality principles revolutionized the Japanese economy. Later, Taiichi Ohno, while working at Toyota, formalized a system for in-process quality and ongoing improvement. The Toyota Production System later traveled to the US as the basis for lean. In 1986, Motorola created Six Sigma, a formal methodology for improving quality by reducing variation in processes and products. This concept is a measure of process capacity. Six Sigma helped Motorola reduce variation and vastly improve the quality of its products.

Precision, control, and comprehensive visibility are essential in today’s global manufacturing industries. As demands for quality and transparency have grown, SPC has evolved to bridge the gap, enabling manufacturers to meet customer expectations, hit quality targets, and increase profits. The work that Shewart, Deming, Ohno, and others have done has created a robust foundation for data-based processes that have adapted well to the modern world.

**Real-Life Examples—Variability Is Everywhere**

Some amount of process variation is an unavoidable fact. However, too much variation results in waste, rework, additional labor costs, and slower order fill times. SPC provides a means for ensuring that the variation remains within specifications. Moreover, it can help manufacturers identify ways to further reduce variation that may lie within the specification limits. But practically speaking, what does variation look like in the real world?

We can go to our closest grocery store to see variability in person. Check out the gallon jugs of water, and note where the water level is in each jug. Chances are, you’ll be able to observe some variability in water levels, with some clearly not filled, while others may be overfilled, and most are in the “Goldilocks” zone—just right. However, if you were to spill out your bottle of Tylenol pills, you would probably have difficulty locating any oddly-shaped pills, and that’s because the product undergoes a much tighter tolerance for variability. This control leads to a more consistent product.

**What Are SPC and CPK?**

SPC includes the use of several statistical techniques that a facility can use to control a process or production. Like a toolbox, SPC encompasses a suite of procedures that can help an organization differentiate between the two different types of process variation—special cause and common cause variation—and develop solutions for issues.

Cpk is the common abbreviation for a measure of process capability. Using capability indices, Cpk compares in-control process output to the specification limits. If almost all of the measurements occur within the specification limits, then the process or product is considered capable. Cpk measurements can help you understand if you are close to your quality target and illustrate how consistent the process is. The data points will appear as a bell curve.

**The Bell Curve**

The bell curve is the basis for everything we do in statistical process control. In a bell curve, the mean is equal to the median, which is equal to the mode, so the curve is symmetrical. A standard deviation (σ) is a measure of dispersion for a distribution. We can predict the probability that a data point will fall within a standard deviation. A less dispersed distribution will appear as a smaller spread. The greater the standard deviation, the more dispersed the distribution is.

**Applying SPC to Process Capability**

Let’s consider the jug of water again. We want to determine the customer tolerance for maximum and minimum. If the water is too high, it might spill as soon as the customer opens it. Too low, and the customer feels they aren’t getting the product they paid for. In between the two is the “Goldilocks” target. Using the concept of process capability, we can identify how capable the process is the process for meeting customer specifications. As we tighten our distribution, more of the water jugs will fall into the customer specifications, with less spillage and waste and greater customer satisfaction.

**Measuring Process Capability**

There are several methods for measuring process capability, including:

**DPMO:**Defects per million opportunities (DPMO) illustrates how many defects were created per million products.**σ Level:**Observing the σ Level indicates how many σs fall within the limits of the customer specifications.**Cpk and Ppk:**These methods deliver a capability index score**Yield %:**This metric looks at how many good products a facility has produced within specification, divided by the total produced.

**Two Examples of SPC Process Capability**

**Example #1: **Raw rubber material undergoes steam and pressure treatment to become the tires we use on our cars. However, as air escapes during this processing, it passes through vents in the tire. If the vents get too big, they can cause the tire to seal poorly, and air will escape. Using capability analysis, initially, the distribution of data indicated the company was not capable of meeting customer specifications, with numerous outliers and other issues. This analysis showed there was a process problem.

**Example #2:** A pizza company wants to create a contract with a pepperoni vendor. They decided to specify that packs of pepperoni must have 13 slices, with a variability of +/- 2 slices. The hope was that the contract would protect the company. However, the vendor had greater process capability than the pizza company and was able to consistently package and sell 12 slices of pepperoni for the price of 13 slices. At a multinational pizza company, the vendor was able to go on the offensive and benefit from utilizing a more efficient process capability without violating the contract.

**How Is SPC Calculated?**

To understand how facilities can calculate SPC, it’s essential to understand more about what control charts are, what information they can identify or predict, and how to use them to reduce variation and target quality. While control charts can and do work without normal distribution, they need some data spread or dispersion measurement. This data spread can be a range, a mean, or a standard deviation.

**Control Charts and Process Capability**

Let’s revisit the water jugs yet again. Now, let’s examine the individual observations on a timeline. Using control charts, the points are no longer specification limits. Instead, these points become measures of standard deviations. If a point falls two standard deviations away, an outlying point will be part of the normal distribution five percent of the time. But the other 95 percent of the time, it needs to fall within the specification limits. If it falls outside the specification limits, we determine that it indicates something we should investigate. This process is special cause variation versus the common cause variation of process capability. Something external is influencing our processes, and we need to track the issue down.

Other uses for control charts include:

**Defects**—weight per unit or defects per 5,000 units**Productivity**—the time between batches**Quality**—cold chain temperature

Control charts are also a great way to look at trends in your data. Trend reporting can show whether the operation is moving one way or another and whether that movement is good or bad.

**Types of SPC Control Charts**

SPC control charts are handy tools that can help to identify issues quickly, leading to prompt resolution. They also function as predictive tools, assisting facilities in determining the anticipated range of an outcome. All processes, no matter how improved, will show some variation. But this variation can be nearly impossible to spot without the use of control charts. Control charts can be either “variable” or “attribute.”

Variable control charts include:

**Range (R) charts:**R charts are best suited for smaller sample sizes and indicate the variability in a process.**X bar control (X-bar) charts:**The X bar control chart illustrates the mean or average for a set of samples and whether the mean changes over time.**Standard deviation (S) control charts:**S charts are helpful when you need to monitor variable data and when the sample size is large.

Attribute control charts monitor data in one of two ways—either as pass/fail or conforming/non-conforming, or for count data (i.e., 1, 2, 3, 4, etc.). Attribute control charts include:

**C (count) charts:**C charts monitor and control count data when there can be some number of defects and the samples remain constant within the count period.**U charts:**Similar to C charts, U charts take into account that the sampling may be a variable.**P charts:**If your data is pass/fail, you can use subgroups to calculate a proportion (P) of defects per group.**NP charts:**Similar to P charts, NP charts rely on the sample size remaining constant throughout the sampling period, and it delivers the non-conforming number rather than the fraction.

**More on P Charts:** The drawback to looking at quality through a P chart is that it is output-driven rather than process-driven. This method looks at a product into which a facility has put energy and value, only to reject a portion of it. P charts typically produce binary data: the answer is either a yes or a no. To view it through the lens of SPC, many facilities will parse the data to determine a proportion to create a meaningful control chart. By changing the subgroups, a facility can achieve tighter tolerances and become more sensitive to changes in the process as it observes more data. More data creates a better sampling.

**Excel and Control Charts**

While Excel is a fantastic tool, it can make working with control charts challenging. It can be very time-consuming to create and update control charts within Excel. It can also make reading the signals difficult. One solution is to control charts without charts. With whatever signal you want to create, you can look at whether the response is above the upper specification limit or below the lower specification limit. When you detect that signal, you can code it as LOW or HIGH. Using simple formulas in Excel, you can capture the number of HIGH or LOW signals.

**Solving Special Cause with Root Cause Analysis**

Special cause alerts us to something other than the process and invites us to identify the root cause—some factor that has created an issue and needs to be eliminated. Root cause analysis isn’t any one single approach but instead comprises a range of techniques. Two techniques to try are:

**The 5 Whys Method:** Developed by Sakichi Toyoda for Toyota, this tool helps you work back from the initial symptom or pain point to determine the root cause and methods you can employ to prevent the issue from arising again. The technique is simple—work back from the symptom to the root cause by asking ‘why’ five times.

**Fault Tree Analysis:** The benefit of constructing a fault tree analysis is that users can determine why high-level failures happened by identifying the lower-level failures that contributed to the high-level failure. A fault tree analysis can be an excellent tool when multiple nonconformances may have contributed to the failure in question.

**Methods for Solving Common Cause Variation**

We can increase capability by shifting the average of our processes. This method is a systems-based improvement. In this case, there’s no “smoking gun.” Another option is to decrease variation. This method is also a systems-based improvement. The mean remains the same, but the variation between data is much tighter.

It’s crucial to prioritize systems solutions. It’s far easier to improve variation first.

**Calculating SPC with Software**

While it is possible to calculate SPC process capability manually or with Excel, many organizations are transitioning to software programs for greater efficiency and inclusion. Using SPC software can involve more employees from the enterprise level down in the continuous improvement process, helping everyone become more invested in hitting quality targets. With instant control chart visibility and user-friendly dashboards, everyone can be a part of statistical process control even if they are unfamiliar with the mathematical calculations. This inclusiveness can positively contribute to a more robust Lean workplace culture while also reducing costly variation.