Quality control and total quality
A plan that inspects 50 units and accepts the lot with one defect rejects 9 % of good lots and accepts 28 % of bad ones. With 200 units and up to 5 defects, those risks drop to 1.6 % and 6.2 %.
01What quality is
For Juran, quality is fitness for use; for Crosby, conformance to requirements. The two views complement each other: a product has to meet its specifications and, in addition, the specifications have to reflect what the customer needs. The way of ensuring it changed over time: at first the finished product was inspected to separate the bad; then the process was statistically controlled so that it would not produce the bad; today quality is managed throughout the organization.
02Inspection and acceptance sampling
Inspecting every unit is expensive and, if the test is destructive, impossible. In acceptance sampling a sample of \( n \) units is inspected from each lot and the lot is accepted if \( c \) or fewer defective units appear. The probability of accepting a lot with a defective fraction \( p \) is the operating characteristic curve of the plan:
The probability of accepting the lot as a function of its defective fraction. An acceptable quality of 1 % defective is taken (green line) and a limiting quality of 5 % (red line).
03Statistical process control
Acceptance sampling improves nothing: it only separates. Statistical process control, which Shewhart invented in the 1920s, monitors the process while it produces by means of control charts, with limits at three standard deviations from the mean: a point outside, or a suspicious run, indicates an assignable cause that has to be found and eliminated. The capability of the process against the tolerances is measured with the Cp and Cpk indices, which were covered in measurement automation. Ishikawa popularized the seven basic tools: check sheet, histogram, Pareto chart, cause-and-effect diagram, scatter diagram, stratification and control chart.
04Total quality
Total quality management extends responsibility for quality to the whole organization, with customer focus, data-based decisions and continuous improvement according to the PDCA cycle —plan, do, check, act— popularized by Deming. The costs of quality are classified into prevention and appraisal, which are chosen, and internal and external failures, which are suffered: investing in the former usually reduces the latter far more. Six Sigma aims at processes so capable that they produce about 3.4 defects per million opportunities. The ISO 9001 standard sets out the requirements of a quality management system that an external body can certify.
05In the laboratory
Classify the faults found when testing the boards assembled in the course and build the Pareto chart.
Build the Ishikawa diagram of the most frequent defect with the categories of method, machine, material, manpower, measurement and environment.
Look up in a sampling table the plan for a lot of 2000 resistors with an AQL of 1 % and compare its curve with the lab.
06Common mistakes
- Believing that inspecting improves quality. It only separates; quality is built into the process.
- Expecting a sampling plan to be infallible. There is always a risk of accepting bad lots and rejecting good ones.
- Confusing control limits with tolerances. The former are set by the process; the latter, by the customer.
- Taking ISO 9001 certification as a guarantee of a good product. It certifies a management system, not each product.
07Self-assessment
With n = 50 and c = 1, what is the probability of accepting a lot with 2 % defective?
73.6 %.
What is the producer’s risk?
The probability of rejecting a lot that has the acceptable quality.
What happens to the curve when n is increased while keeping the ratio c/n?
It becomes steeper: it discriminates better between good and bad lots.
What do the letters of the PDCA cycle stand for?
Plan, do, check and act.
08Further reading
- Douglas C. Montgomery. Introduction to Statistical Quality Control. Wiley. (Spanish edition: “Control estadístico de la calidad”, Limusa Wiley.) Control charts, capability and acceptance sampling.
- Kaoru Ishikawa. What Is Total Quality Control? The Japanese Way. Prentice-Hall, 1985. (Spanish edition: “¿Qué es el control total de calidad? La modalidad japonesa”, Norma.) Total quality told by one of its creators.
- W. Edwards Deming. Out of the Crisis. MIT Press, 1986. (Spanish edition: “Calidad, productividad y competitividad: la salida de la crisis”, Díaz de Santos.) Deming’s fourteen points and his critique of inspection.