Three people, three questions
A pallet of brackets arrives from a supplier. The goods-in inspector needs to decide whether to accept it without measuring every part. On the press line, the setter wants to know whether the hole positions are drifting. And the quality engineer preparing a customer approval wants to show that the process can hold the tolerance over a full production run.
All three use statistics, and all three work in what is called statistical quality control. But they are asking different questions, and each question has its own method.
What statistical quality control is
Statistical quality control is a collective name for statistical methods that are used to measure, monitor, control and improve quality. The common idea is that you cannot measure everything, and that variation is always present. Statistics lets you draw reliable conclusions about a whole lot or a whole process from a sample, and tells you how confident you can be in them.
The term goes back to the work of Walter Shewhart and colleagues at Bell Telephone Laboratories in the 1920s, which produced both the control chart and early acceptance sampling plans.
Question 1: can the lot be accepted?
Acceptance sampling takes a random sample from a lot and decides from the result whether to accept or reject the whole lot. Sampling plans state how many parts to inspect and how many defects are allowed. The best-known schemes are ISO 2859-1 for inspection by attributes (pass or fail) and ISO 3951 for inspection by variables (measured values).
Acceptance sampling judges a product that already exists. It cannot make it better; it can only sort it. It also carries a known risk of accepting a bad lot or rejecting a good one, which the plan is designed to balance.
Question 2: is the process stable?
Statistical process control measures small subgroups at regular intervals and plots them on a control chart. Control limits calculated from the process’s own data show what normal variation looks like, and signals show when something has changed. The aim is to find and remove special causes before they create defects, rather than sort the defects out afterwards.
Question 3: can the process meet the requirement?
Process capability analysis compares the spread and centring of a stable process with the tolerance. Indices such as Cp and Cpk summarise how much room the process has. Capability is what a customer usually asks for when approving a new part.
Supporting methods
Around these three sit other methods that are often counted as part of the same toolbox:
- Measurement system analysis, to make sure the data the other methods rely on is trustworthy.
- Design of experiments, to find out which factors affect a result and by how much.
- Basic quality tools such as histograms, Pareto charts and scatter diagrams, for describing data and finding where to start.
How the methods relate
A simple way to think about it: acceptance sampling checks the output, process control watches the process, and capability judges whether the process is good enough. A mature quality system moves effort from the first towards the second and third. If the process is stable and capable, there is less need to inspect lots, because few defects are being made.
Example. The supplier of the brackets runs statistical process control on the hole positions and can show a Cpk well above the customer’s requirement. The customer can then reduce goods-in inspection to an occasional check, instead of sampling every pallet.
Common misunderstandings
- “Sampling proves the lot is good.” It gives a known probability of accepting lots of a given quality; it does not find every defect.
- “A capable process does not need a control chart.” Capability is a snapshot. Without monitoring, nobody notices when the process changes.
- “Statistical quality control and statistical process control are the same.” Process control is one part of the wider field.
In short
Statistical quality control is not one technique but a toolbox. Start from the question you need to answer: accept the lot, control the process or judge its capability, and pick the method that answers it.
