Ask an engineer why the pump is overhauled every nine thousand hours and you will usually be told: because it always has been. Ask where nine thousand came from and the room goes quiet.
The number came from an assumption — that equipment wears out, that failure probability climbs with age, and that replacing a component before the climb steepens is therefore prudent. For a bicycle chain this is true. For most of what runs on your plant floor, it is not.
The number that should have ended calendar maintenance
Fewer than twenty per cent of failures are age-related. Roughly eighty per cent are random with respect to operating time.
This is not a new finding. It emerged from a study commissioned by the United States Department of Defense and carried out by United Airlines, published in 1978 by Nowlan and Heap. Its conclusions became MSG-3, which the world’s civil aviation fleet still uses to build maintenance programmes. Every RCM course teaches it in the first hour.
And still, most plants overhaul on a calendar.
What Weibull actually tells you
The Weibull distribution has a shape parameter, usually written beta. It is the whole argument in one number.
- Beta below 1 — failure rate is decreasing. Infant mortality. The component is most likely to fail when it is new. Scheduled replacement makes things worse: every overhaul resets the clock to the most dangerous point.
- Beta near 1 — failure rate is constant. Random. Age carries no information. Scheduled replacement is pure cost with no reliability benefit.
- Beta above 1 — failure rate is increasing. Wear-out. Here, and only here, does a replacement interval make sense — and the distribution tells you where to set it.
Fitting a distribution to failure history is now a single line of code. The analysis that once served as the entry barrier to the profession takes seconds. Which means the barrier is no longer statistical competence. It is having failure history worth fitting.
Where it goes wrong
Three failure modes of the analysis itself, in order of how often we see them.
Mixed populations
Fitting one distribution across pumps that operate in different services, at different duties, with different fluids. The fit will converge. It will describe nothing.
Suspended data ignored
The units that have not failed carry information — often more than the ones that have. Discard them and beta rises spuriously, manufacturing a wear-out pattern that does not exist. Then you buy an overhaul programme to prevent it.
Preventive replacements counted as failures
The most common error, and the most self-fulfilling. Every scheduled overhaul enters the CMMS as an event. Fit that history and you will discover, with high confidence, that the component fails at exactly the interval at which you replace it.
The task that remains
The machine fits the distribution. It cannot tell you that the three pumps in the dataset serve different processes. It cannot tell you that the technician logs an overhaul under the same code as a breakdown. It cannot tell you that beta came out at 3.1 because someone was gaming the completion metric.
Garbage in, danger out. The arithmetic was never the hard part.