Introduction to SPC

Quality management tools and techniques

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What is statistical process control (SPC)?

What are quality tools and techniques?

Quality management tools and techniques are the means to analyse the processes comprising your quality management system. Generally, data analysis techniques can be subdivided into two groups; mathematical statistical tools, and logical tools/non-statistical tools.

Statistical tools and techniques

The analysis of the data can be undertaken using statistical techniques to help break down the information and present it in a format that allows a determination to be made of whether actions are needed to improve performance.

Statistical techniques assist in identifying, measuring, analyzing, interpreting and modelling variability to maintain or improve effectiveness and efficiency.

Techniques use mathematical concepts and statistical methods to interrogate and make sense of the data collected from quality management system outputs to facilitate better use of available data to assist in decision making.

Statistical techniques used for establishing, controlling, and verifying process capability and product characteristics should be done in accordance with customer requirements. Statistical Process Control (SPC) is a mathematical tool employed to control processes, and to aid in establishing and verifying process capabilities, and are expressed by the following formats:

Control charts

  • Control charts are used when taking samples of a process in order to detect possibility of the process being out of control. Quality data is collected in the form of product or process measurements or readings from various machines or instrumentation.
  • The data is collected and used to evaluate, monitor and control a process. Sample sizes may be informed by process risk assessments or a statistical rationale based upon defined Acceptance Quality Limits (AQL), Unacceptable Quality Level (UQL).
  • A sampling plan defines the product type, features, characteristics, batch/lot size, sample size, inspection levels, type of inspection, and the need for qualifying measurement systems analysis (Gage R&R).
  • Gage Repeatability and Reproducibility (R&R) is a statistical tool that measures the amount of variation in the measurement system arising from the measurement device and the people taking the measurement.
  • Measurement uncertainty is the concept of evaluating uncertainty is fairly straightforward. It requires a detailed knowledge of the nature of the items being measured and of the measurement method, rather than an in-depth understanding of statistics.


  • Histograms chart how often something happens and therefore highlights its likelihood, and are usually used to present frequency data.
  • Used to show distributions of variables, while bar charts are used to compare variables, histograms provide an easy way to evaluate the distribution of data over different categories.

Scatter diagrams

  • Scatter diagrams can be used to verify a cause-and-effect relationship and find the correlation between two variables – dependent and independent.
  • Good for demonstrating correlations between values and showing trends for value changes.

Run charts

  • Run charts organise data to represent changes in measurement over time, or through a sequence of events; they help to define the avarage character of the data.

Pareto analysis

  • Pareto analysis helps to evaluate the importance of items where resources may be best focused. Pareto Charts are used to apply the 80/20 rule of Joseph Juran which states that 80% of the problems are the result of 20% of the problems. A Pareto Chart can be used to identify that 20% root-causes of problem.
  • Product characteristics include drawings or specifications that define dimensions, tolerances, assembly interfaces, surface contours or shapes, materials, requirements for materials that would be an exception to an identified material specification, processes, surface preparations, etc.
  • Significant Product Characteristic (SPC) are those product characteristics that if not controlled within specified limits will negatively affect form, fit, function, safety, performance, agency approvals, or any governmental regulations.
  • Critical Product Characteristic (CPC) are those product characteristics that if not controlled within the specified limits, may have an unacceptable affect to form, fit, function, safety, performance, agency approvals, or any governmental regulations.

Tools and techniques you can download for free...

SPC - This site is run by a team of volunteers with over 24 years experience working in manufacturing, quality and product development.

Free SPC templates and guidance
Determination of Calibration Intervals.pdf Guidelines for the determination of calibration intervals of measuring instruments
Use of Data From Control Charts.pdf Use of Data from Control Charts for the Estimation of Measurement Uncertainty
Validation of Excel Spreadsheets.pdf Validation of Computerised Systems - Annex 1 – Validation of Excel Spreadsheets
Capability Study Template.xlsx Conduct a process capability study to determine the extent to which a process can meet expectations
Statistical Process Control Chart.xlsx Includes X-bar chart, range chart, histogram and probability plot

Control charts, an introduction for non-mathematicians

Understanding standard deviation

All processes vary and the the aim of SPC is to minimize this variation. Variation is expressed as 'sample standard deviations' (SD) and SD is a mathematical term, based on probability theory. Click the links to download copies of a Capability Study Template and Statistical Process Control Chart.

Consider the process of driving a car along a dry, straight, level road; look at your hands on the steering wheel - they move as you make slight adjustments. Why are the adjustments necessary? Because the road is not totally flat, there's some play in car's suspension, etc.

If you draw a graph of the movements you will have a 'normal distribution curve'. In a normal distribution, most of the time your hands are in the middle. (In the secret language of SPC the 'middle' is called the 'average' or 'mean' or 'x-bar')

But sometimes your hands are a little to the left, at other times they're a little to the right, and on rare occasions they're on the extreme left or extreme right.

Normal Distribution Curve

How to apply statistical process control

Using the sample standard deviation (SD), you can then calculate and chart the usual extremes of a process under a given set of conditions. This variation is 'normal' and we cannot reduce the variation without making fundamental changes to the process (e.g. going on an advanced drivers course, buying sports suspension, etc.)

Because of the properties of the normal distribution it is usual in SPC or quality control applications to multiply the standard deviation by three and then add that to and take it away from the average which gives a confidence level which encompasses 99.73% of the observations or 'population'.

For example: 

average = 20

1 SD = 1.3

3 SD = 3.9

average + 3 SD = 23.9

average - 3 SD = 16.1

therefore 99.73% of all that we see will be between 16.1 and 23.9

Back in the car... 

A child runs out in front of you and you swerve to avoid him. The chart now shows a blip which is outside the normal curve. This indicates that something unusual has happened.

Non-normal Distribution Curve

In SPC applications it is often useful to recognize what is normal and what is non-normal. This case is clearly non-normal. In some situations also helps to know when things happen. Therefore, an SPC control charts also has a time axis.

Statistical process control chart

We can then apply these concepts in an SPC chart for monitoring customer complaints.

Control Chart

Having collected the basic information we can then add the average and +/- 3 SD markers.

Control Chart

What we are saying is:

  1. Given the normal variation of the process we will always have a level of complaints. There is nothing we can do without making fundamental changes to the process.
  2. As long as the individual plots are between the red lines then the process is exhibiting normal variation.
  3. BUT clearly something unusual (non-normal) happened in March - we had far more complaints than usual. We need to investigate and find out why.
  4. THIS IS THE CLEVER BIT - February's low result is equally unusual. We need to find why it happened and build that in to the process. Do it often enough and the average line will go down, and eventually become zero.

To help the investigation, use appropriate problem solving tools.

The problem with traditional SPC

Most SPC control chart techniques are based around the +/- 3 SD method, which covers 99.73% of a population. 99.73% sounds good until you realize that this means that 0.27% are not accounted for, there is 1/4 percent chance of something slipping through the net. 

If you are trying to control critical processes or very high volume (e.g. aerospace, building nuclear reactors, making silicon chips, etc.) then you will get it wrong once in every 370 attempts. 

Such critical industries tend to use Six Sigma (+/- 6 SD) methods as it gives a 99.9997% (3 in a million failures) confidence level. Three in a million sounds much better than one in three hundred and seventy.

To learn more, we recommend reading the articles from SPC Press & Statistical Process Controls, INC

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