DQM Common Units
Statistical Quality Control cheat sheet
Every chapter's key points, formulas and definitions on one page, for the last week before the exam. Each heading links to the chapter that explains it.
Sampling and collecting data
- A population is the complete set of items a study is interested in and a sample is the subset actually observed; a statistic calculated from the sample is used to estimate a population parameter.
- Probability methods (simple random, systematic, stratified, cluster) need a full list of the population to sample from; convenience or judgmental sampling is quicker but cannot support statistically valid inference back to the whole population.
- Yamane's formula, n = N / (1 + N·e²), sets the sample size from a known population N and an acceptable margin of error e.
- The standard error of the mean, SE = s / √n, falls as the sample grows, so a larger sample gives a more reliable estimate.
- Accuracy is how close a measurement is to the true value and precision is how close repeated measurements are to each other; quality control aims for both together.
Key terms
- Population
- The complete set of items or observations a study is interested in.
- Sample
- A subset of the population actually observed or measured.
- Parameter
- A numerical characteristic of the population (e.g. the true population mean).
- Statistic
- A numerical characteristic calculated from a sample, used to estimate a parameter.
- Variable
- A characteristic that can take different values across the units observed.
- Simple random sampling
- Every unit has an equal chance of selection.
- Systematic sampling
- Units are selected at a fixed interval from a randomly chosen start.
- Stratified sampling
- The population is divided into groups (strata) and a sample is drawn from each.
- Cluster sampling
- The population is divided into clusters, and whole clusters are sampled.
- Convenience/judgmental sampling
- Units are selected for ease of access or the sampler's judgement, not randomly.
- 90% confidence level
- z ≈ 1.645; a wider acceptable margin of error, a smaller required sample.
- 95% confidence level
- z ≈ 1.96; the most commonly used standard in quality work.
- 99% confidence level
- z ≈ 2.576; a narrower margin of error, requiring a larger sample.
- Sampling error
- The natural difference between a sample statistic and the true population parameter, purely because a sample, not the whole population, was observed.
- Non-sampling error
- Errors from sources other than sampling itself, faulty measuring instruments, data entry mistakes, or a poorly worded questionnaire.
- Accuracy
- How close a measurement is to the true value, a systematic property (bias).
- Precision
- How close repeated measurements are to each other, regardless of whether they are close to the true value.
- Sampling
- Examining a representative subset of the population.
- Census
- Examining every single unit in the population, no sampling error, but far costlier.
- Qualitative (categorical) data
- Describes a quality or category, e.g. defect type, colour grade.
- Quantitative (numerical) data
- Describes a measurable quantity, e.g. weight, length, count of defects.
- Discrete data
- Countable, whole-number values only, e.g. number of defects per batch.
- Continuous data
- Can take any value within a range, e.g. weight, dimension, temperature.
The rest of the sheet covers
- Coding and presenting data
- Analysing data
- Statistical tools in quality control
- Worked examples
- Exam technique and revision
- Glossary