Attribute control charts

Method

• Data: one row per subgroup, in time order, with the count and the subgroup size (units inspected). Columns are found by their header names (Defectives, Defects, Count…; Size, Inspected, Sample size…; Lot, Date…), otherwise the two rightmost number columns are Count and Size. Without a Size column, type one size for every subgroup. Counts must be whole numbers of 0 or more; for defectives the size must be a whole number and at least the count.
• Which chart: defectives (each unit passes or fails) → P (proportion) or NP (number, best with equal sizes); defects (nonconformities counted, several possible per unit) → C (same opportunity in every subgroup) or U (defects per unit, any size). Laney P′ and U′ are for large subgroups, where the P and U charts flag many points only because the subgroups vary more than the binomial or Poisson model allows.
• P chart: p̄ = Σd / Σn, limits p̄ ± 3√(p̄(1 − p̄)/nᵢ). NP: center nᵢp̄, limits nᵢp̄ ± 3√(nᵢp̄(1 − p̄)). C: c̄ = mean count, limits c̄ ± 3√c̄. U: ū = Σc / Σn, limits ū ± 3√(ū / nᵢ). Unequal sizes give limits that vary from subgroup to subgroup (and an NP center line that varies too). A lower limit below 0 is set to 0, an upper limit above the largest possible value (1 for P, nᵢ for NP) is set to it. These are Montgomery's textbook formulas and Minitab's defaults.
• Laney P′ and U′ (D. B. Laney, Quality Engineering 2002): zᵢ = (pᵢ − p̄) / σpᵢ with the P (or U) chart's σ of each subgroup; σZ = average moving range of the zᵢ / d2(2), d2(2) = 2/√π ≈ 1.128; limits p̄ ± 3 σpᵢ σZ. σZ near 1 means the P (or U) chart is right; above 1 the data is overdispersed and the limits widen; below 1 they narrow. Minitab's default estimate (average moving range) is used.
• Phase I and Phase II: in Phase I p̄, ū or c̄ (and σZ) come from the data shown. In Phase II they are typed in from earlier stable data, and new subgroups are judged against fixed limits. Freeze limits takes them from the first N subgroups (25 by default) or all data so far and switches to Phase II; the values are saved in the settings file. Changing them, the chart type or going back to Phase I ends the freeze.
• Tests 1–4 (Minitab's attribute-chart tests and fixed parameters): 1 point more than 3σ from the center line; 9 in a row on one side; 6 in a row all rising or all falling; 14 in a row alternating up and down. Minitab's default is test 1 only. They run on the standardized values (xᵢ − center) / σᵢ: for equal sizes the signals are the same as on the plotted values; for unequal sizes a count that grows only because the subgroup grew is not counted as a trend. Runs do not cross an empty row. The point that completes a pattern is flagged, and every later point of the same run that still fits it.
• Live monitoring (Chrome and Edge, File System Access API) reads a file that an inspection station appends rows to, or a folder where every new file (matching a pattern such as *.csv) adds its rows, with the same columns as above; the new rows are added to the data in the columns already there. A file is read only after its size and time stayed the same for two checks; every file read is remembered and never read twice. Rows found when watching starts are history; a new signal afterwards shows a banner, “(!)” in the page title and, if chosen, a short sound. The page must stay open; files are only read, never changed; sub-folders are not watched. This offline file does not remember the choice: choose the file or folder again each time you open it. Nothing is sent anywhere.
• Conclusion: “In control” when no enabled test fires, otherwise the number of signals. Limits estimated from fewer than 20 subgroups are unreliable.
• Files: CSV, TSV and TXT are read as if pasted (UTF-8, UTF-16, otherwise Windows-1257). XLSX: choose the sheet and the columns or a cell range; formula cells use the value Excel last saved, dates are kept as text. Files up to 20 MB are read in this browser only and never uploaded.
• XLSX files are read with SheetJS Community Edition 0.20.3, Apache License 2.0 (license text at the end of this file).