WEBVTT

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This video takes life data with censored units through Survival Plots in ReliaEn: first the survival curve, then the choice of a distribution.

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The data are the removal ages of 21 control valves.

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In column A, type the ages of the 9 valves that failed: 6, 6, 6, 7, 10, 13, 16, 22 and 23.

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In column B, type the ages of the 12 valves taken out while still working: 6, 9, 10, 11, 17, 19, 20, 25, 32, 32, 34 and 35.

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These ages are censored: each of those valves would have failed later than its age shows.

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ReliaEn counts a censored valve as still at risk up to its age, then lets it leave without a step in the curve.

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Open the Life Data menu and choose Survival Plots…

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The form Survival Plots opens in the left panel.

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Data situation is Exact + right-censored, and Failure times column already shows column A.

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Set Censored column to B.

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Confidence % stays at 95, and Fitted overlay at Best by ranking.

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Press OK — Calculate.

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The INPUT DATA card shows 21 units: 9 failures and 12 censored.

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In RESULTS, the median survival time is 23: at that age the survival curve first falls to one half or below.

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The lower quartile, where survival falls to one quarter, is not reached, because at the last failure 0.4482 of the valves still survive, and ReliaEn does not extrapolate.

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The best-ranked distribution is the lognormal, Lognormal(μ = 3.203, σ = 0.9787), with the lowest AICc, the corrected Akaike information criterion.

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The survival staircase steps down at each failure age.

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The ticks mark the censored valves, the shaded band is the 95% confidence band, and the dashed line is the fitted lognormal.

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Below it, the distribution overview shows the lognormal's density, its cumulative failure with the plotted ages, its survival against the staircase, and its hazard.

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The distribution identification plot draws each distribution's quantiles against the observed ages: the straighter the points lie on the line, the better that distribution describes the data.

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The Kaplan-Meier life table lists each failure age.

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At age 6, 21 valves were at risk, 3 failed, and survival fell to 0.8571.

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The distribution comparison ranks the 7 fitted distributions by AICc: the lognormal first at 86.027, then the exponential at 86.560, the loglogistic at 86.955, the gamma at 87.545 and the 2-parameter Weibull at 87.984.

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The three-parameter Weibull is not fitted (threshold at the data boundary).

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The best rows lie within about 2 of each other, and ReliaEn says so: A close AICc race (within ~2) means the data cannot separate the families — pick by engineering physics, not by the third decimal.

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So the 5 best distributions fit these valve data almost equally well, all within 2 AICc points of the lowest: choose by the failure mechanism, then run that distribution's own analysis for its bounds.

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The next video turns to repairable equipment: the fleet growth curve and the generalised renewal process.