Machined shaft diameters
Quality-control measurements of a turned steel shaft at a fictional precision workshop, Ridgeline Components. The specification is 25.00 mm ± 0.05 mm. For each of two lathes (A and B), five consecutive parts were measured every shift for 30 shifts (30 rational subgroups of 5). Lathe B drifts upward in its later subgroups. Built for X̄–R and X̄–S control charts, detecting a process shift, and process capability (Cp, Cpk).
- Rows
- 300
- Columns
- 7
- One row is
- one measured part
- Version
- v1
Data dictionary
| Column | Type | Unit | Summary | Description |
|---|---|---|---|---|
machineMachine | category | 2 levels: A, B | Lathe that produced the part. | |
subgroupSubgroup | integer | mean 15.5, median 15.5, SD 8.67, range 1–30 | Subgroup number (1–30), one per shift, in time order. | |
sampleSample | integer | mean 3, median 3, SD 1.417, range 1–5 | Position of the part within its subgroup (1–5). | |
dateDate | date | Production date. | ||
shiftShift | category | 2 levels: Day, Night | Shift during which the subgroup was taken. | |
operatorOperator | category | 4 levels: OP1, OP2, OP3, OP4 | Operator code. | |
diameter_mmDiameter | number | mm | mean 25, median 25, SD 0.01527, range 24.97–25.06 | Measured shaft diameter (target 25.000, specification 24.950–25.050). |
What it is good for
- Build X̄ and R charts from rational subgroups and read out-of-control signals.
- Detect a sustained process shift with run rules.
- Estimate Cp and Cpk and explain why capability is meaningless for an unstable process.
- Compare two machines' centring and spread.
Methods: X̄–R chart, X̄–S chart, Western Electric rules, process capability (Cp, Cpk), two-sample t-test, F-test for variances.
Data quality notes
- Machine B shifts upward by about 0.022 mm from subgroup 21 onward; its later points approach the upper specification limit.
- Machine A is stable throughout.
- Values are rounded to 0.001 mm, so ties occur.
- No missing values.
Provenance and licence
Diameter = machine mean + subgroup effect (normal, sd 0.003 mm) + part-to-part noise (normal; sd 0.012 mm for A, 0.014 mm for B), rounded to 0.001 mm like a digital micrometer. Machine A is centred at 25.000 mm. Machine B is centred at 25.002 mm for subgroups 1–20 and at 25.024 mm from subgroup 21 (tool wear after a tool change was skipped).
Synthetic data · CC0-1.0 (synthetic data generated by Statistics Quest) · generated deterministically (seed 20241007). It does not describe real people or organisations; any resemblance is coincidental.
Preview
Dataset
Machined shaft diameters
300 rows · one row = one measured part · synthetic data
| Machine | Subgroup | Sample | Date | Shift | Operator | Diameter (mm) |
|---|---|---|---|---|---|---|
| A | 1 | 1 | 2024-09-01 | Day | OP1 | 25.025 |
| A | 1 | 2 | 2024-09-01 | Day | OP1 | 25.007 |
| A | 1 | 3 | 2024-09-01 | Day | OP1 | 24.995 |
| A | 1 | 4 | 2024-09-01 | Day | OP1 | 24.999 |
| A | 1 | 5 | 2024-09-01 | Day | OP1 | 25.019 |
| A | 2 | 1 | 2024-09-01 | Night | OP2 | 25.027 |
| A | 2 | 2 | 2024-09-01 | Night | OP2 | 24.982 |
| A | 2 | 3 | 2024-09-01 | Night | OP2 | 24.991 |
| A | 2 | 4 | 2024-09-01 | Night | OP2 | 25.007 |
| A | 2 | 5 | 2024-09-01 | Night | OP2 | 24.991 |
| A | 3 | 1 | 2024-09-02 | Day | OP1 | 24.986 |
| A | 3 | 2 | 2024-09-02 | Day | OP1 | 24.992 |
Used in
- Statistical process control · Applied Statistics for Professionals
- Process capability · Applied Statistics for Professionals
- Manufacturing quality investigation · Capstone