Guide — How to use

The theory

Weibull describes WHEN an item tends to fail over its life — not the cost, not the detection, only the temporal pattern. Two parameters are enough: β gives the SHAPE of the failure (whether it clusters early, is random, or grows with age) and η gives the SCALE (where in time it happens).

R(t) = exp(−(t/η)^β) — the chance of reaching age t alive

β is the SLOPE of the failure rate over time — the derivative of risk. A single number says which of the three regimes the item is in, and each regime calls for a different strategy:

1. 1

   Isolate one failure mode and fix the clock

   Pick ONE failure mode and the right life variable: operating hours, cycles or starts — never calendar hours. All times in the same unit and on the same clock (hour meter/PIMS, not the date).

2. 2

   Build the sample with failures AND suspensions

   Each unit enters with a time and a label: 'failure' for those that failed by that mode; 'suspension' (right censoring) for those still running, replaced for another reason, or removed from the study. Ignoring suspensions underestimates life and distorts β and η.

3. 3

   Assign the cumulative probability (median ranks)

   Order the failure times and estimate F(t) by median rank — Bernard: (i − 0.3)/(n + 0.4) — adjusting the positions when there are suspensions (Johnson's rank). That is what linearizes the data on Weibull paper.

4. 4

   Fit the parameters: regression or MLE

   Plot ln(t) against ln(ln(1/(1−F))): the slope is β and η is the t where F = 63.2%. With few failures or heavy censoring, prefer maximum likelihood (MLE). Software (Weibull++, R `survival`, Python `reliability`) does both and gives confidence intervals.

5. 5

   Validate before deciding

   With fewer than ~8–10 failures the β has large uncertainty — report the confidence interval and do not decide on a knife's edge. A 'knee' in the line usually flags two mixed failure modes: go back to step 1. Without own data, start from the typical β in the collection's note and calibrate η with your plant's average life.

1. 1

   Enter β and η

   β from your fit (or the typical one cited in the failure-mode note); η in hours. The colored chip beside it classifies the regime instantly.

2. 2

   Set the mission time t

   The decision horizon — for example, the interval until the next shutdown. It is the t inside R(t), F(t) and h(t).

3. 3

   Read survival and life

   R(t) = probability of completing the mission without failing; MTTF = mean life to failure; B10 = age by which 10% have failed — the classic criterion for sizing bearings and replacements.

4. 4

   Compare with your interval

   If you replace or inspect every X hours, confront X with the B10 and with R(X). A low R(X), or an X beyond the B10, tell you the interval is optimistic.

5. 5

   Test scenarios

   Increase η (better installation/design) or push β toward 1 (cause control) and see the effect on R(t) and B10 before committing to a plan. The resulting Fw A category feeds the strategy selector.

The theory

For repairable items life is a cycle: operate → fail → repair → operate. Availability measures the fraction of that cycle in which the asset is fit for duty. Inherent availability (Ai) considers only the technical repair; the operational one in the field, which includes logistics and waiting, is always lower.

Ai = MTBF / (MTBF + MTTR)

1. 1

   Fix the window and the item

   Set the period (12–24 months give a stable sample) and the item or function under analysis. Sum the OPERATING hours over the period from the hour meter/PIMS — an asset that ran 60% of the time 'aged' 60%.

2. 2

   Count only functional failures

   MTBF = operating hours ÷ number of failures (loss of function) in the period. Exclude preventive work, process trips and interventions with no failure. And do not miss the 'small' failures operations fix without a work order — they vanish from the CMMS and inflate the MTBF.

3. 3

   Measure MTTR as ACTIVE time

   MTTR = Σ repair times ÷ number of repairs, from start of intervention to fit return. Do not include waiting for spares, travel, clearance or shift change — that is logistic time (part of MDT), a different metric. Mixing the two hides where the bottleneck is.

4. 4

   Separate by failure mode when possible

   Modes with different dynamics (slow wear × sudden failure) in one MTBF become a blind KPI. One MTBF per failure mode points to action; the aggregate is only good for a report.

1. 1

   Enter MTBF and MTTR

   In the same time unit (hours). The λ = 1/MTBF appears alongside — the failure frequency.

2. 2

   Read the inherent availability Ai

   It is the fraction of time fit for duty considering only the technical repair — the design CEILING. The availability you measure in the field will be lower, because it includes logistics and waiting.

3. 3

   Translate into downtime per year

   The annual unavailability (in hours and days/year) is the number that justifies investment to management: how much production this failure+repair pair costs per year.

4. 4

   Pick the right lever

   Compare two scenarios: doubling the MTBF (more reliability) versus halving the MTTR (more maintainability). See which moves Ai more — one of them is almost always far cheaper to achieve.

The theory

A failure is rarely instantaneous: first it gives a detectable signal (point P), then it loses function (point F). This P-F interval is the window in which an inspection can catch it in time. The on-condition task is only effective if the inspection fits inside it — with slack.

inspection ≤ P-F / 2 — at least 2 detection chances (Moubray, ch. 8)

1. 1

   Choose the detection technique first

   The P-F changes with the instrument, not just the failure. For a bearing, ultrasound/acoustic emission sees the defect weeks before vibration, which sees it before temperature, which sees it before audible noise. Decide which technique the route will use before estimating the number.

2. 2

   Measure the P-F in run-to-failure or history

   Ideally a controlled trial; in practice, use the real events that 'escaped' the route: record the time between the FIRST detectable signal (P) and loss of function (F). Collect several — the P-F has spread.

3. 3

   Adopt the smallest plausible P-F

   Size by the pessimistic tail of the distribution, not the mean: if half the cases warn at 4 weeks and the other half at 2, design the route for 2. Conservative is correct here.

4. 4

   No data? Use the technique's literature

   The collection's failure-mode notes carry the typical P-F per technique; adjust to your context (service severity, load, temperature) before settling the interval.

1. 1

   Enter the P-F and the practiced interval

   The P-F in the chosen technique and the route's current periodicity — in the SAME unit in both fields (days, weeks or months).

2. 2

   Check the recommended interval (P-F/2)

   It is the effectiveness ceiling: inspecting every half of the P-F guarantees at least 2 chances to catch the symptom before F.

3. 3

   Read the detection chances and the margin

   The chances tell how many route passes fall inside the window; the margin is the slack between the window and the practiced interval.

4. 4

   Act if the margin is negative

   Negative margin = the route cannot reach the window in time. Three ways out: increase the inspection frequency, switch to a technique with a larger P-F, or reconsider the strategy in Framework B (the on-condition task may not be applicable).