Statistical process control (SPC) charts are used in quality-focused facilities to monitor process output on a continual basis and alert process operators, managers and the support staff in real-time when the process is shifting towards an undesirable condition. This rapid response provides a cost-effective approach to defect detection, and many cases defect prevention, to keep orders on-time and within cost estimates. SPC charts are essential tools for implementing lean just-in-time, since low or no inventory requires the predictability that a capable, statistically controlled process can reliably deliver.

When disruptions are detected in the process, it’s critical that process operators have the tools available to them to quickly diagnose and correct the issues. Most SPC software has features built-in to accommodate these needs, so it’s not surprising that the paper-based systems of the past have been replaced by modern, almost futuristic systems that can monitor the process with minimal input needed from process operators. Data can be electronically submitted via serial ports or seamlessly linked from coordinate measurement machines (CMM) or other measurement systems.

Troubleshooting procedures, drawings and recommendations can be version-controlled and directly linked to the monitoring charts so they are quickly available for review when needed. Likewise, when support personnel such as process supervisors or manufacturing engineers are automatically alerted via email or text messages, they can provide real-time hands-on problem solving. Yet, diagnosing special causes is often not trivial, and sometimes requires more information.

One quick source of information for troubleshooting is data stratification. Usually, data entry includes not just the measurement data but one or more traceability fields associated with each data value. These can include items such as the current manufacturing order number, as well as traceability back to the supplier, such as supplier lot number. Stratifying by source, such as shown in Figure 1, makes it easy to identify the potential cause of the process shift when relevant traceability data is included. In this case, the Supplier Lot PY167, represented by the blue circles, is coincident with the process shift. Returning to use of the earlier Supplier Lot F182, represented by the green squares, coincides with the return of the process to its original operating level, suggesting the influence of a deviant supplier lot.

**Figure 2.** In analyzing the process data in Figure 2, the process personnel realized the chart contained subgroups for two types of parts from the same part family.

Sometimes stratification effects will be more subtle and appear as the random variation between the control limits, also known as common cause variation. In analyzing the process data in Figure 2, the process personnel realized the chart contained subgroups for two types of parts from the same part family. Type C and Type D parts are similar in most details, so the quality team thought a single chart of both types would be acceptable. Sometimes that is a reasonable approach, and the chart verifies that the variation between the two types (Type C as blue squares; Type D as orange triangles) is small relative to the control limits. Curiously, the subgroups for the Type C parts were all below the process centerline, while those for Type D were above the centerline. With a couple clicks of the mouse, the analyst quickly created charts filtered by part type, and sees that the chart for Type D shows a process whose capability index Cp is 1.5 with a Cpk of 1.0, indicating that the capability of this process can be improved to 1.5 by centering the process at the midpoint of the specifications. Re-centering the process is usually one of the easier improvements, sometimes simply a matter of changing a backstop or a fixture adjustment. The Type C process shows similar levels of Cp and Cpk of 1.2, so process centering is not the issue. Instead, the overall variation of the process for Type C parts is excessive. This usually requires more involved process redesign; a designed experiment would likely be helpful to identify the process factors contributing to the excessive variation. [Note: The charts use a subgroup size of three, so a typical rule of thumb would require 50 subgroups to establish statistically valid control limits. We used less groups in this case for ease of display, although statistically valid limits based on less groups would be wider and not impact our analysis appreciably].

**Figure 3.** This data could be from a multi-head filling machine such as used in beverage or cosmetic bottling; the multiple cavities of an injection molding machine; the multiple parts placed on a magnetic chuck in a CNC grinding machine; or any number of similar processes.

In some cases, the simpler stratification techniques seen here won’t show anything that stands out because of the effect of interactions. For example, if the differences between the Type C and Type D parts were only evident when the parts were run on a specific machine, then that would indicate an interaction between the machine and the part types. Sometimes you can pick this up with a multiple regression of the process data in Excel or Minitab, in which case you’d have a suspicion about the interaction that can be confirmed with a designed experiment. Bottom line is that the more advanced tools of regression, and the simpler tools of stratification, when used to mine process data should be validated with a designed experiment.

A different type of stratification can also impact the estimate of common cause variation represented by the chart’s control limits. For the familiar X-Bar/Range chart, the control limits on the X-Bar chart are calculated using the average range within each subgroup. The control chart works because if the process is stable, then the short-term variation seen in each subgroup should be a good predictor of the longer-term variation seen from subgroup to subgroup. Figure 3 shows a control chart whose subgroups are all well within the control limits, so the process would appear at first glance to be in control. Yet, if these control limits were realistic, we should expect to see the subgroups relative position between the control limits resemble the bell-shaped curve of the normal distribution: Most (approximately 68% over the long term) within +-1 sigma (i.e. a third of the way between the centerline and the control limit on each side); a small number of groups beyond +-2 sigma (about 5% total on both sides); and the remaining groups between the 1 and 2 sigma levels.

We’ve included the zone lines on this chart so it’s clear that all the groups are within the +-1 sigma zone. Fortunately, software can easily look for these types of non-random behavior, and since this chart shows many of the groups within the small band about the centerline, these groups are flagged automatically as suspicious. The circles indicate a run test violation, notably Run Test 7: fifteen successive groups within 1 sigma of the centerline. What’s the cause of this behavior, and why is it a concern?

**Figure 4.** Figure 4 shows the batch means chart for this process data. Figures from SPC-PC IV Explorer by Quality America. Used by permission

This data in Figure 3 could be from a multi-head filling machine such as used in beverage or cosmetic bottling; the multiple cavities of an injection molding machine; the multiple parts placed on a magnetic chuck in a CNC grinding machine; or any number of similar processes. In each case, you’ve assembled your subgroup using a single sample from each stream of a multiple stream process. The control chart is not testing if the short-term variation is a good predictor of the longer-term variation but is instead testing if the variation between the multiple streams (i.e. between each head of the filling machine) is a good predictor of the variation over time. In statistical terms, we would say that is not a rational subgroup, which lies at the heart of a control chart: It is not reasonable to expect the variation between the filling heads to predict the variation over time, and the run test violations have detected that as an issue. In that case, you could look at each head individually, or alternatively use a special case version of the X-Bar chart: the batch means chart. Figure 4 shows the batch means chart for this process data. The range chart at the bottom plots the variation between the filling heads, while the averages chart at top plots the average of the heads over time. The difference from the standard X-Bar chart is that the control limits on the averages chart are calculated based on the moving range between the subgroup averages. As such, they provide a better predictor of the process variation over time, while the range chart shows if the differences between the heads are consistent over time. **Q**

Paul Keller is president of Quality America, a publisher of software and training for Six Sigma Quality Improvement. He has written several books, including SPC Demystified (McGraw Hill, 2011) and the third, fourth and fifth editions of The Six Sigma Handbook (McGraw Hill, 2009, 2013, 2018). For more information, email pkeller@qualityamerica.com or visit www.qualityamerica.com.

## FAQs

### What are the four key steps to statistical process control? ›

Statistical Process Control technique steps include **detection, study, prioritization, illumination and then charting**. Before using quality control software, it's critical to collect proper data for analysis.

**How can statistical process control be improved? ›**

**Seven Steps to Improving Your SPC Program**

- Focus on the Right Characteristics to Control. ...
- Ensure Adequate Measurement Systems are Used. ...
- Select the Right Chart for the Application. ...
- Employ Effective Sampling Strategies. ...
- Select the Right Sample Size. ...
- Empower Operators to Seek Improvements.

**How do you calculate statistical process control limits? ›**

Control limits are calculated by: **Estimating the standard deviation, σ, of the sample data**. **Multiplying that number by three**. **Adding (3 x σ to the average) for the UCL and subtracting (3 x σ from the average) for the LCL**.

**What is an example of statistical process control? ›**

SPC can be applied to any process where the "conforming product" (product meeting specifications) output can be measured. Key tools used in SPC include run charts, control charts, a focus on continuous improvement, and the design of experiments. An example of a process where SPC is applied is **manufacturing lines**.

**What is statistical control example? ›**

statistical control Statistical techniques for excluding the influence of specified variables in an analysis. For example, **if the data from a sample survey showed a strong association between unemployment and clinical depression, one might want to control for the effect of social class**.

**How do you know if a process is statistical control? ›**

...

**Three characteristics of a process that is in control are:**

- Most points are near the average.
- A few points are near the control limits.
- No points are beyond the control limits.

**What is the main focus of statistical process control? ›**

The main objective of SPC is **to prevent the special causes of variation occurring**. If it achieves this objective, then the process remains statistically in control, that is, process variation is due to common causes only.

**What are the methods of statistical quality control? ›**

There are seven basic techniques employed for SQC. These basic techniques are **(i) check sheets, (ii) histograms, (iii) Pareto analysis, (iv) control chart, (v) cause and effect diagram, (vi) stratification, and (vii) scatter diagram**.

**Which is the most successful tool used for statistical process control? ›**

The most successful tool used for Statistics Process Control (SPC) is **Control Chart**.

**Why Statistical process control is important? ›**

SPC **helps reduce scrap, waste, defects, and rework, improve product quality, eliminate variation in processes, and maintain compliance with regulatory and customer requirements**.

### What is statistical quality control and why is it important? ›

Statistical analysis in quality control is **where statistical methods are used to measure, monitor and maintain the overall quality of products**. Over time, the results help processes, such as manufacturing, ensure that the procedures will produce more specification-conforming products, therefore creating less waste.

**What are statistical control limits? ›**

Control limits, also known as natural process limits, are **horizontal lines drawn on a statistical process control chart, usually at a distance of ±3 standard deviations of the plotted statistic's mean, used to judge the stability of a process**.

**What is Six Sigma statistical process control? ›**

What is Statistical Process Control (SPC) Six Sigma? Six Sigma is **a set of tools used by businesses for quality control and process improvement**. The Six Sigma method is often used to remove defects and optimize processes by monitoring operations and then analyzing the data and statistics collected.

**What are the 3 variables in process control? ›**

There are three broad categories for any given system: **inputs, outputs, and constants or parameters**. Inputs are any factors that change with time that affect the system's output. The output refers to the desired controlled variable.

**What are the 5 steps of the statistical process? ›**

- Step 1: Write your hypotheses and plan your research design. ...
- Step 2: Collect data from a sample. ...
- Step 3: Summarize your data with descriptive statistics. ...
- Step 4: Test hypotheses or make estimates with inferential statistics. ...
- Step 5: Interpret your results.

**What are the 5 statistical process? ›**

The Statistical Process has five steps: **Design the study, Collect the data, Describe the data, Make inferences, Take action**.

**What are the seven tools of statistical process control? ›**

These seven basic quality control tools, which introduced by Dr. Ishikawa, are : **1) Check sheets; 2) Graphs (Trend Analysis); 3) Histograms; 4) Pareto charts; 5) Cause-and-effect diagrams; 6) Scatter diagrams; 7) Control charts**.

**What does statistically control mean? ›**

**If a process produces a set of data under what are essentially the same conditions and the internal variations are found to be random**, then the process is said to be statistically under control.

**What does it mean to control for in statistics? ›**

“Controlling for a variable” means **measuring extraneous variables and accounting for them statistically to remove their effects on other variables**. Researchers often model control variable data along with independent and dependent variable data in regression analyses and ANCOVAs.

**How do you determine if the process is capable? ›**

**The Cp index is a fundamental indication of process capability**. The Cp value is calculated using the specification limits and the standard deviation of the process. Most companies require that the process Cp = 1.33 or greater.

### What are the two main statistical methods? ›

Two main statistical methods are used in data analysis: **descriptive statistics, which summarizes data using indexes such as mean and median and another is inferential statistics**, which draw conclusions from data using statistical tests such as student's t-test.

**What are statistical quality control tools? ›**

Histogram and its application. Statistical Quality Control (SQC) is the term used to describe the set of statistical tools used by quality professionals. SQC is used to analyze the quality problems and solve them.

**What are the 5 common statistical tools? ›**

...

- Mean: ...
- Standard deviation: ...
- Regression: ...
- Hypothesis testing: ...
- Sample Size Determination:

**What statistical tool is used for effectiveness? ›**

The most well known Statistical tools are the mean, the arithmetical average of numbers, median and mode, Range, dispersion , standard deviation, inter quartile range, coefficient of variation, etc. There are also software packages like **SAS and SPSS** which are useful in interpreting the results for large sample size.

**What are the five statistical tools? ›**

**The Top 7 Statistical Tools You Need to Make Your Data Shine**

- SPSS (IBM) ...
- R (R Foundation for Statistical Computing) ...
- MATLAB (The Mathworks) ...
- Microsoft Excel. ...
- SAS (Statistical Analysis Software) ...
- GraphPad Prism. ...
- Minitab.

**What is statistical control in an experiment? ›**

Statistical control refers to **the technique of separating out the effect of one particular independent variable from the effects of the remaining variables on the dependent variable in a multivariate analysis**.

**Is statistical process control a lean technique? ›**

Within Statistical Process Control, data is statistically compared within the context of its occurrence. For example, **factors such as shifts, operators and production events would be included in an SPC study within a lean manufacturing Six Sigma program**.

**What statistical tools are used in Six Sigma? ›**

**Several examples of Six Sigma statistical tools are described below.**

- Capability Analysis. This tool assists in the maintenance of suitable product specifications. ...
- Gauge Repeatability & Reproducibility Studies. ...
- Control Charts. ...
- Accelerated Life Tests. ...
- Variance Components Analysis. ...
- Pareto Analysis.

**What are the 5 most common process variables? ›**

Common process variables include – **level, flow, temperature, density, PH(acidity or alkalinity), mass, conductivity** etc. The SETPOINT is the target value of the process variable that is desired to be maintained. For example, if a process temperature needs to be kept within 5 °C of 100 °C, then the SETPOINT is 100 °C.

**What are the 4 main process variables? ›**

DAC Worldwide's 4-Variable Advanced Process Control Training System (603-000) is a fully functional, industrial-quality fluid process system that provides hands-on training in the measurement and control of four of the most common process variables: **level, pressure, temperature, and flow**.

### What is basic process control? ›

Simply put, process control involves the measurement of a process variable (temperature, flow or pressure, for example), the comparison of that variable against a desired value (called a setpoint), and the generation of a change in the process to adjust the variable to the desired value.

**What are the 7 steps in the statistical process in order? ›**

**1.2 - The 7 Step Process of Statistical Hypothesis Testing**

- Step 1: State the Null Hypothesis. ...
- Step 2: State the Alternative Hypothesis. ...
- Step 3: Set. ...
- Step 4: Collect Data. ...
- Step 5: Calculate a test statistic. ...
- Step 6: Construct Acceptance / Rejection regions. ...
- Step 7: Based on steps 5 and 6, draw a conclusion about.

**How do you calculate UCL and LCL? ›**

**If you're wondering how to calculate the control limits of your process dataset, here are the UCL and LCL formulas below:**

- The upper control limit formula: UCL = x - (-L * σ)
- The lower control limit formula: LCL = x - (L * σ)

**What is the statistical problem solving process? ›**

Consider statistics as a problem-solving process and examine its four components: **asking questions, collecting appropriate data, analyzing the data, and interpreting the results**.

**What are the basic statistical techniques? ›**

Statistical methods involved in carrying out a study include **planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings**.

**What does it mean when a process is in statistical control '? ›**

A process is said to be in control or stable, if it is in statistical control. A process is in statistical control **when all special causes of variation have been removed and only common cause variation remains**.

**What is statistical process control defined? ›**

Statistical process control (SPC) is defined as **the monitoring and analysis of process conditions using statistical techniques to accurately determine process performance and prescribe preventive or corrective actions as required** [440].

**How Process control is achieved? ›**

In Process Control the proportion of defective items in the production process is to be minimized and it is achieved **through the technique of control charts**. Product Control means that controlling the quality of the product by critical examination through sampling inspection plans.

**What are the 3 simple steps to doing statistics? ›**

quality and reliability of the data, sort and classify data, and perform statistical tests and analyze the results.

**What is the most commonly used statistical method for analyzing data? ›**

**Mean or average** mean is one of the most popular methods of statistical analysis. Mean determines the overall trend of the data and is very simple to calculate. Mean is calculated by summing the numbers in the data set together and then dividing it by the number of data points.

### What are the 4 types of control charts? ›

**Types of Control Charts (SPC).**

- X bar control chart. ...
- Range “R” control chart. ...
- Standard Deviation “S” control chart. ...
- Attribute Control Charts: ...
- “u” and “c” control charts. ...
- “p” and “np” control charts. ...
- Pre-control Charts.

**What is control limit in statistics? ›**

Control limits, also known as natural process limits, are **horizontal lines drawn on a statistical process control chart, usually at a distance of ±3 standard deviations of the plotted statistic's mean, used to judge the stability of a process**.

**What is the UCL formula? ›**

**UCL (X-bar) = X-bar-bar + (A2 x R-bar)** Plot the Upper Control Limit on the X-bar chart.