Life data analysis is the easiest analysis in this knowledgebase to run and one of the easiest to run wrongly, because the software always returns a β and an η and neither of them looks suspicious.
| Pitfall | What it looks like | The guard |
|---|---|---|
| An MTBF read as a life | A quoted mean used to set a limit, an interval or a warranty | The mean fixes one number and leaves the behaviour free; ask for β and a B-life |
| Suspensions dropped | Only the failed units in the dataset | Every unit with a known age is data; survivors carry evidence of survival |
| Mixed failure modes | One fit across everything that came off the item | One distribution per mode; a dogleg in the plot is two modes arguing |
| Age measured in the wrong units | Calendar time on an item whose damage accumulates with cycles | Use the clock the damage runs on: hours, cycles, landings, starts |
| Age since when | Time since manufacture used for a repaired item | Time since the last renewal of that mode, or the fit is meaningless |
| Method unstated | A β quoted with no estimator and no sample size | Say which method, how many failures, and how many suspensions |
| Small-sample bias ignored | An MLE β taken at face value on ten failures | Apply the correction, and report the interval as well as the point |
| The three-parameter fit reached for | A location parameter added because it improves r² | Only where a physical reason exists for failure-free life, never to flatter the fit |
| r² read as validation | A fit declared good on r² = 0.99 alone | A straight line through the wrong model is still straight; check the residual shape |
| Extrapolating far past the data | A B1 life quoted from thirteen failures, none of them early | The tails are where the data is thinnest and the confidence widest |
| Confidence intervals omitted | A single β, presented as a fact | On small samples the interval on β routinely spans a factor of two |
| Constant rate assumed forever | An item with β = 4 carried in a model as a fixed λ | A constant rate on a wear-out mode is true at one fleet age and expires |
| Fleet age ignored | A field rate quoted with no statement of the fleet's age profile | The same item gives a different rate on a young fleet and an old one |
| Left truncation missed | Units that entered the record part-worn treated as new | Their early life was never observed, and ignoring that biases the fit |
| Interval censoring flattened | An inspection finding recorded as a failure at the inspection time | It failed somewhere in the interval, and the method for that exists |
| Weibull assumed | The distribution chosen before the data was looked at | Weibull is flexible, not universal; a lognormal repair-time or a bimodal wear pattern is not Weibull |
| A repairable system fitted as lives | A Weibull through the gaps between one machine's successive repairs | Those gaps are not independent lives; a repairable system's arrivals belong to the NHPP models in reliability growth |
| The fit never revisited | β and η from year two, still in the model in year eight | Refit as the fleet ages; the tail is exactly what new data adds |
Six deserve more.
An MTBF does not describe a life. It is the mean of the distribution, and the mean is one number out of a two-parameter family: hold it at 100 hours and the age by which a tenth of the population has failed can be anywhere from about half an hour to eighty hours, depending only on β. The worked example does this with two real datasets, both ten failures in a thousand hours. Neither report was dishonest and neither number was wrong; the mean simply does not carry the information a life limit needs, so asking for it more precisely does not help.
Dropping suspensions is the error the arithmetic punishes hardest. It feels harmless, because the survivors have not done anything yet. What they have done is survive, and an estimator shown only the units that broke sees a sample of the unlucky. The bias has a fixed direction: the estimated life can only come out short, so every interval derived from it comes out short too, and the programme spends money being early.
Mixed modes produce a fit that describes nothing. A bearing that fails from grease breakdown at one age and from cage fatigue at another produces a plot with a bend in it, and a single Weibull through the bend fits neither population. The tell is visual and it is why the plot matters more than the r². Split the data by mode, and if the mode cannot be determined from the record, that is a finding about the FRACAS, not about the bearing.
Successive repairs of one machine are not a sample of lives. This is the misuse that looks most like the method and is furthest from it. Life data analysis needs independent and identically distributed lives, which is what a population of items each running once to failure gives you. Take one repaired machine instead and record the gaps between its failures, and the gaps are neither independent nor identically distributed: each one starts from whatever state the last repair left the machine in. Fitting a Weibull to them returns a β and an η that mean nothing, and the β is routinely misread as wear-out when what it is describing is a system whose failure intensity is drifting. The right model there is a process rather than a distribution, and it lives in reliability growth. The test is one question: are these the lives of different items, or the intervals of one?
A good r² is not a validated model. Rank regression will happily draw a straight line through points that curve gently, and the correlation stays high while the model is wrong in exactly the region a maintenance decision cares about. Look at where the points sit relative to the line, not at the summary statistic, and if the fit has to be defended formally, use a goodness-of-fit test built for estimated parameters or a likelihood comparison against the lognormal. The foundations chapter sets out all three.
The result expires. Every β greater than one says the hazard is a function of age, so the item's failure rate is a function of the fleet's age profile. Quoting it as a constant is legitimate only alongside the age profile it was true at, and only until the fleet moves on. On the worked example the constant everything downstream carried was 55 failures per million hours; averaging the fitted hazard across the ages the fleet actually has gives 401, and nothing about the hardware changed.