Ceramic batch defective-piece frequency calculator

Calculate batch observed defect proportions and Wilson95 bounds and pooled observed defect fraction with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use batch observed defect proportions and Wilson95 bounds and pooled observed defect fraction to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Batch defect counts [batch ID,pieces inspected,pieces with any defect]
[["A",100,5],["B",80,8]]
Batch observed defect proportions and Wilson95 bounds
[["A",0.05,0.0215436791544,0.111750469232],["B",0.1,0.0515476155674,0.185106888061]]
Pooled observed defect fraction
0.072222

Try another scenario

Batch defect counts [batch ID,pieces inspected,pieces with any defect]
[["A",100,10],["B",80,12]]
Batch observed defect proportions and Wilson95 bounds
[["A",0.1,0.0552291370607,0.174365661505],["B",0.15,0.0879404050616,0.244132285613]]
Pooled observed defect fraction
0.122222
Calculation method

Calculation method

Batch observed defect proportions and Wilson95 bounds

Use unique defective-piece counts, not sum overlapping defect categories.

Pooled observed defect fraction

Total defective pieces/total inspected.

Symbols and units
a
Batch defect counts [batch ID,pieces inspected,pieces with any defect]

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • Observed defective-piece rate by firing batch, with marginal binomial intervals. Per-category defect frequencies must be supplied separately; multiple defects on a piece must not be double-counted as defective pieces. Quantities are deterministic calculations from supplied observations and assumptions; no external data is fetched. Supported limits: Finite inputs only; numeric fields bounded as labelled. Lists and JSON records are limited to 256 entries unless a stricter tool bound is stated. No automatic design approval, legal conclusion, treatment recommendation or safety certification.
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