Four concepts come up repeatedly throughout this menu. Understanding them will help you avoid most mistakes.
Censorship
A piece of data is censored when the product has not yet failed at the end of the observation. All we know is that it lasted at least until then.
⚠️ Ignoring censoring is a classic mistake—and a serious one at that: keeping only the defective products is like looking only at the students who are struggling. The estimated reliability becomes dramatically pessimistic. Censorship conveys information and must be taken into account.
That is why all of Ellistat's data entry formats include a censoring column.
The Weibull Distribution
It is the benchmark law in reliability because its form adapts to the three stages of a product's life cycle. Its parameter β (beta), the form, is interpreted directly:
| β | Diet | Interpretation |
| β < 1 | Early Failures | Infant mortality: manufacturing and assembly defects. The failure rate decreases. |
| β = 1 | Random Failures | Default Rate constant : The law follows an exponential pattern; the failure is accidental. |
| β > 1 | Wear and Tear | The default rate grows : aging, wear and tear, abrasion. |
💡 β is the first number to look at, even before the service life. It identifies the nature of the problem and, therefore, the area for action: a β less than 1 is addressed during production, while a β greater than 1 is addressed during design or preventive maintenance. Choosing the wrong regime means choosing the wrong action plan.
The second parameter, η (eta), the scale, is the time at which 63 % of the population failed. Ellistat proposes Two-parameter Weibull and 3-Parameter Weibull, the third being the estimated position δ, an initial delay, which is useful when no failure is possible before a certain amount of time has elapsed.
R(t), MTTF, and failure rate
- Reliability R(t) : the probability of still being operational at time t. R(0) = 1; R decreases.
- MTTF : the average time to failure.
- Default Rate : the probability of failing in the next instant, given that one has held out until now. This is what β describes.
⚠️ MTTF is a convenient but misleading figure. An MTTF of ten years does not mean that the product will last ten years: with an exponential failure rate, More than one-third of the fleet has already failed after an MTTF. For a contractual commitment, think in terms of R(t) at the maturity date of the guarantee, not in MTTF.
Nevada
This is the natural format for after-sales service data: a triangle values. Each row represents a sales period; the columns show the returns observed over the subsequent periods. Products sold more recently have a shorter track record, which explains the triangular shape.
💡 Nevada contains two distinct pieces of information, which Ellistat can distinguish between: diagonally We look at the shelf life (of products of the same age), in columns We can see the seasonal patterns (what happens at the same time of year, regardless of age).