Originally developed by Bell Laboratories about a century ago, Statistical Process Control (SPC for short) is a quality control method which employs statistical methods that monitor and control a process to ensure it can meet specifications. We created a quick video for those in the food & beverage industry that want a high-level overview of SPC. In particular, it covers what SPC is, and how using specific metrics like Ppk, SPC, Cpk, Control Limits, Spec Limits, and Run Rules can help users understand and manage variability in a process.

There are many benefits to companies using SPC. It allows food and beverage — and even Consumer Product Goods (CPG) — companies to operate more efficiently, achieve high conformance with specifications, and reduce waste, including rework or scrap. In addition, SPC can help ensure product safety, reduce overall costs, and help satisfy regulatory requirements from FDA, FSMA, USDA, and others. Most of all, it ensures your processes are running well, and provides you with a proven methodology that allows you to communicate that confidence to management and customers.#### Quick - to the Bell Curve!

To begin, 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 very typical bell curve, also known as a normal distribution curve, and walks you all the way through what Statistical Process Controls are and why they are needed in the food and beverage industries. 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) tells you how well your bell curve fits within your spec limits and how well your production run conforms to your specification. To begin, consider this diagram (also located at 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, which means that 99.99% of all materials are within specification limits.

Here is the mathematical formula for the Process Performance Index (Ppk):**Ppk = Min (Mean - LSL / 3**σ**) or (USL - Mean /3**σ**)**

#### Xbar-R and Xbar-S Charts

Since we typically can’t test every unit, we take periodic samples in a “Sample Set”. From those samples, we plot the data on two basic types of charts to graphically represent what’s going on through time. First, we develop the Mean Chart which plots the average values of the sample set. This is also referred to as the “XBar” chart. The second is the Variation Chart, which plots the spread of data in the sample set.

When your sample set is using 2 to 9 data points, the Variation Chart is also called the “Range” or “R” Chart. When you collect 10 or more samples, the Variation Chart can then be called the “Sigma” or “S” chart. In food manufacturing, the two common 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” which are the upper and lower boundaries of expected values. The control limits are completely independent of the specification limits. It simply provides a standard of how the process is expected to perform based on how it has performed historically.

This means that control limits are dependent on the process and equipment, so the same product may very well have different control limits on different lines or even vary somewhat between shifts.

#### Run Rules

When a process is running with a normal variable distribution within the control limits, it is referred to as “Stable.” But often that same process will sooner or later start to drift, and that is an indication that the process is no longer stable. There are a lot of reasons why drift can happen, including changes as equipment warms up, changes as parts start to wear out, variation of materials prior to the monitoring of the step, etc.

To identify a drift away from a stable process we use a set of rules, called “Run Rules”. These rules provide a method to warn operators when a process might be starting to drift, and allows them to take action needed to restore stability. Run rules can be applied 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. Of note — this is the part of the entire process of math and charting that gives SPC the “control” part of its name. Here is a listing of those typical run rules employed at food and beverage manufacturers.

- 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 rule 9 has you scratching your head, you’re paying attention. A lot of points within the first sigma look great, right? But statistics show us that everything is working too perfectly and that 13 consecutive points may mean something is actually wrong in the processing, or that the process is performing much better than should be expected— based on historical performance.

#### Process Capability Index (Cpk)

Not to be confused with Ppk, one final concept to understand for SPC is Cpk. Cpk answers the question “am I capable of meeting my specification?” and is more forward-looking in nature. The formula for Cpk looks at the estimated standard deviation, instead of the standard deviation like Ppk does. The formula looks like this:

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

The Process Capability Index is a measure of whether your process is __capable__ of meeting your specification given the variations that have historically occurred.

Putting it Together

- Cpk provides a method to establish if your process is capable of meeting your specification
- Xbar-R and XBar-S charts provide a way to track your progress at each testing step in your operation
- Run Rules provide a means to alert operators when a process may be drifting, and action is needed to stay in conformance
- Finally, Ppk provides a way to measure how well your process actually performed given the specification limits.

#### See it in Action

To see how SafetyChain develops SPC, with Xbar-R and Xbar-S charting for the food and beverage industry, learn more about our Production Manager Solution.