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When defects, breakdowns or accidents are rare, what you monitor is the interval between them: how many parts, days or hours pass until the next one, and whether that interval is getting shorter.
Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.
Each point is the interval up to the event. Center line = median; limits from the 0.135% and 99.865% percentiles. Red points fail a test; the number above is the test (B = Benneyan).
Event count against cumulative exposure, with the line expected from the estimated rate and the 90% Poisson band. The curve above the band is deterioration; below, improvement.
Histogram of the intervals with the count expected from the fitted distribution; the vertical lines mark the center line and the UCL.
Points on the line: the chosen distribution describes the intervals well, and the limits can be trusted.
Points that fail a test, with the percentile of the interval in the fitted distribution.
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When the event is rare: defects in PPM, machine breakdowns, accidents, contaminations. A P or U chart would have almost every point at zero and meaningless limits; the G or T chart tracks the interval between events, which changes visibly when the frequency changes.
The G chart counts discrete units between events: parts, cycles, lots or whole days. The T chart measures continuous time (hours, fractional days) and uses the Weibull or exponential. With breakdown dates and times, use T; with the number of parts between defects, use G.
Because intervals between rare events are very skewed: many short and a few very long. The mean is pulled up by the long ones; the median shows the typical interval. The limits are also percentiles (0.135% and 99.865%) rather than mean ± 3σ.
No: on these charts, up is good. A point above the UCL is an unusually long interval without events, a sign of improvement worth understanding. Deterioration shows as low points, usually via test 2 (9 in a row below the center line) or the Benneyan test.
It is the G chart’s own test: it signals when several intervals in a row are zero, that is, events on the same part or the same day. The number of zeros needed depends on p̂; with p̂ = 0.1 it is 3 zeros in a row.
Paste the column of dates (and times) in event order; the page accepts 06/01/2026 07:30, 2026-06-01 07:30 or the Excel date serial number. On the G chart with dates, events on the same day become a zero interval.
β near 1: random breakdowns, unrelated to time since the last repair. β above 1: wear-out, risk grows with time, and preventive maintenance helps. β below 1: breakdowns right after repair, a sign of poor repair work or a bad spare part.
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