# An Introduction to Statistical Process Control (SPC): What Food and Beverage Manufacturers Need to Know

Developed by Bell Laboratories about a century ago, Statistical Process Control (SPC) is a quality control tool employing statistical methods to monitor and control a process, ensuring it meets specifications. We created a quick video for the process manufacturing industry insiders. This high-level overview defines SPC and how using specific metrics like Ppk, SPC, Cpk, control limits, spec limits, and run rules helps users understand and manage variability.

## What Is SPC Used For?

**There are many benefits to ****using SPC****. SPC allows manufacturers, and consumer product goods (CPG) companies to: **

operate more efficiently

achieve high specification conformance

reduce waste, including rework or scrap

**Additionally, SPC helps ensure product safety, reduces overall costs, and helps satisfy regulatory requirements from FDA, ****FSMA****, USDA, and others. Most of all, it ensures processes are running well and provides operators with a proven methodology. **

## Quick—to the Bell Curve!

First, you’ll need a basic understanding of how processes and data build a standard bell curve and represent a fundamental concept of statistics. This video develops an example of a typical bell curve, also known as a normal distribution curve, walking you through what Statistical Process Controls are and why the food and beverage industries need them. We start by learning what a sigma is (one standard deviation away from the mean), how a histogram works within the lower and upper specifications, what a healthy bell curve looks like, and more.

## Process Performance Index (Ppk)

Process Performance Index (Ppk) indicates how well your bell curve fits within spec limits and how well your production run conforms to specification. Start with this diagram (also located around the 6:00 mark in the video). We’ll also cover a simple example of how you can use Ppk to understand your Process Yield. Most food manufacturing companies target a 1.33 Ppk number, meaning 99.99% of all materials are within specification limits.

Here is the mathematical formula for Ppk:

**Ppk = Min (Mean - LSL / 3**σ**) or (USL - Mean /3**σ**)**

## Xbar-R and Xbar-S Charts

We typically can’t test every unit, so we take periodic samples in a *sample set*. Plotting data on two basic charts from those samples graphically represents what’s going on over time. First comes the mean chart, which plots the average values of the sample set. This is also referred to as the “XBar” chart. Next is the variation chart, which plots the spread of data.

When a sample set uses 2 to 9 data points, the variation chart is also called the *range* or “R” chart. When you collect ten or more samples, the variation chart can be called the *sigma* or “S” chart. In food manufacturing, the two standard charting methods are called “Xbar and Range” (XBar-R) or “Xbar and Sigma” (Xbar-S).

## Control Limits

After collecting sample data for a time in a process, we can determine natural statistics’ variability to establish the *control limits*, the upper and lower boundaries of expected values. Control limits are entirely independent of specification limits and provide standards for how operators can expect the process to perform based on historical performance.

Control limits are **dependent** on the process and equipment, so the same product may have different control limits on separate lines or even vary somewhat between shifts.

## Run Rules

When a process runs with a normal variable distribution within the control limits, it’s called *stable*. However, that same process will sooner or later start to drift, indicating the process is no longer stable. There are many reasons why drift happens:

changes as equipment warms up

changes as parts begin to wear out

variation of materials before the monitoring of the step.

To identify a drift away from a stable process, we use *run rules*. These rules provide a method of warning operators when a process might be drifting, allowing operators to take action to restore stability. Operators can apply run rules to both the mean chart and the variation chart. Run rules are typically referred to by a number. Rules 1-9 are the most common in food production. This is the part of the process of math and charting that puts the “control” in SPC. Typical run rules employed at food and beverage manufacturers include:

**Rule 1: Any 1 point above the upper control limit **

**Rule 2: Any 2 of 3 points above the upper 2nd Sigma (2σ)**

**Rule 3: Any 4 or 5 points above the upper 1st Sigma (1σ)**

**Rule 4: 8 Consecutive points above the Mean**

**Rule 5: 8 Consecutive points below the Mean**

**Rule 6: Any 4 or 5 points below the lower 1st Sigma (1σ)**

**Rule 7: Any 2 of 3 points below the lower 2nd Sigma (2σ)**

**Rule 8: Any 1 point above the upper control limit**

**Rule 9: 13 consecutive points in the 1st sigma (1σ)**

If you’re scratching your head because of rule 9, you’re paying attention. Many points within the first sigma look great, right? But statistics show that everything is working too perfectly, and 13 consecutive points may mean something is wrong in the processing or performing much better than expected, based on historical performance.

### Process Capability Index (Cpk)

Often confused with Ppk, one final concept to understand for SPC is Cpk. Cpk looks to the future and answers the question, “am I capable of meeting my specification?” Cpk looks at the estimated standard deviation instead of the standard deviation Ppk uses. Here’s the formula for Cpk:

**Cpk = Min (Mean - LSL / 3*EstStdDev) or (USL - Mean / 3* EstStdDev)**

Cpk measures whether your process is capable of meeting specifications given historically occurring variations.

## What Is SPC Software?

Understanding the importance of SPC and applying mathematics are two different beasts. While operators can deploy charts and monitor processes on paper, tools like SPC software can be the difference-maker that streamlines monitoring and allows for a more flexible and competitive response time. SafetyChain’s SPC software delivers a real-time look at quality by automatically applying the correct charts. Automated reports inform everyone from enterprise-level to operators on the facility floor of any variations. Many facilities also use SPC software to create customized XBar and XBar-R charts or include built-in run rules.

## See it in Action

To see how SafetyChain develops SPC, with Xbar-R and Xbar-S charting for the food and beverage industry, demo the #1 Digital Plant Management Platform.