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mathematics

Quality control

Quality control is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Quality control rather than just read about it. In short: Quality control (QC) is a process by which entities review the quality of all factors involved in production. ISO 9000 defines quality control as "a part of quality management focused on fulfilling quality requirements".

Quality control — main illustration
Quality control — illustration

Key takeaways

  • Quality control belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Quality control to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Quality control from memory before moving on to harder problems.

Reference excerpt

Quality control (QC) is a process by which entities review the quality of all factors involved in production. ISO 9000 defines quality control as "a part of quality management focused on fulfilling quality requirements". This approach places emphasis on three aspects (enshrined in standards such as ISO 9001):

Elements such as controls, job management, defined and well managed processes, performance and integrity criteria, and identification of records Competence, such as knowledge, skills, experience, and qualifications Soft elements, such as personnel, integrity, confidence, organizational culture, motivation, team spirit, and quality relationships. Inspection is a major component of quality control, where physical product is examined visually (or the end results of a service are analyzed). Product inspectors will be provided with lists and descriptions of unacceptable product defects such as cracks or surface blemishes for example.

History and introduction

Early stone tools such as anvils had no holes and were not designed as interchangeable parts. Mass production established processes for the creation of parts and system with identical dimensions and design, but these processes are not uniform and hence some customers were unsatisfied with the result. Quality control separates the act of testing products to uncover defects from the decision to allow or deny product release, which may be determined by fiscal constraints. For contract work, particularly work awarded by government agencies, quality control issues are among the top reasons for not renewing a contract. The simplest form of quality control was a sketch of the desired item. If the item did not match the sketch, the item was rejected, in a simple Go/no go procedure. However, manufacturers soon found it was difficult and costly to make parts be exactly like their depiction; hence around 1840 tolerance limits were introduced, wherein a design would function if its parts were measured to be within the limits. Quality was thus precisely defined using devices such as plug gauges and ring gauges. However, this did not address the problem of defective items; recycling or disposing of the waste adds to the cost of production, as does trying to reduce the defect rate. Various methods have been proposed to prioritize quality control issues and determine whether to leave them unaddressed or use quality assurance techniques to improve and stabilize production.

Notable approaches There is a tendency for individual consultants and organizations to name their own unique approaches to quality control—a few of these have ended up in widespread use:

In project management In project management, quality control requires the project manager and/or the project team to inspect the accomplished work to ensure its alignment with the project scope. In practice, projects typically have a dedicated quality control team which focuses on this area.

See also Analytical quality control Corrective and preventative action (CAPA) Eight dimensions of quality First article inspection (FAI) Good automated manufacturing practice (GAMP) Good manufacturing practice Quality assurance Quality management framework Standard operating procedure (SOP) QA/QC

References

This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 22 January 2022. (in support of MIL-STD-188).

Further reading Radford, George S. (1922), The Control of Quality in Manufacturing, New York: Ronald Press Co., OCLC 1701274, retrieved 16 November 2013 Shewhart, Walter A. (1931), Economic Control of Quality of Manufactured Product, New York: D. Van Nostrand Co., Inc., OCLC 1045408 Juran, Joseph M. (1951), Quality-Control Handbook, New York: McGraw-Hill, OCLC 1220529 Western Electric Company (1956), Statistical Quality Control Handbook (1 ed.), Indianapolis, Indiana: Western Electric Co., OCLC 33858387 Feigenbaum, Armand V. (1961), Total Quality Control, New York: McGraw-Hill, OCLC 567344

External links ASTM quality control standards

Illustrations

Quality control: Quality inspector in a Volkseigener Betrieb sewing machine parts factory in Dresden, East Germany, 1977
Quality inspector in a Volkseigener Betrieb sewing machine parts factory in Dresden, East Germany, 1977
Quality control: Munitions workers inspecting 3-inch mortar bombs, 1943
Munitions workers inspecting 3-inch mortar bombs, 1943

Worked examples

Example 1 — a first encounter with Quality control

Start with the simplest possible case. Write down what Quality control claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Quality control before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Quality control ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Quality control

In research
Quality control appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Quality control in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Quality control is common in secondary-school and first-year university syllabi. It links to neighbouring topics Applied probability, Design for X, Quality control, so understanding it makes those chapters shorter.
In everyday life
Look for Quality control outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Quality control in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Quality control means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Quality control out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Quality control in simple terms?

Quality control (QC) is a process by which entities review the quality of all factors involved in production. ISO 9000 defines quality control as "a part of quality management focused on fulfilling quality requirements".

Why does Quality control matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Quality control?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Quality control.

Tags

  • Applied probability
  • Design for X
  • Quality control
  • Quality management

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