## Definitions

**Reliability**:

Reliability is the ability of an entity to perform a required function, under given conditions, during a given time interval.

**Failure:**

Failure is the end of a device's ability to perform a function that was expected. It may be partial (impairment of performance) or total (end of function).

**R(t)**Probability that an entity E is non-faulty over the period [0; t ], assuming that it is not faulty at time t = 0.

**F(t)**F(t) is the cumulative function of failures 猫 F(t) = 1 - R(t)

**Probability density** f(t) represents the failure rate of a product, i.e. the probability that a product will fail over the time interval [t,t+dt].

f(t)=\frac{\text{number of failed elements over time}\Delta t}{\text{number of elements tested}}

**位(t) or failure rate :聽**位(t) represents the failure rate of a product, i.e. the probability that a product will fail over the time interval [t,t+dt] knowing that it did not fail at time t.

\lambda(t)=\frac{\text{number of failed elements over time}\Delta t}{\text{number of failed elements still in test}}

**位(t) decreases**The defect rate decreases over time, and this generally corresponds to early defects. Products with intrinsic defects deteriorate rapidly, whereas other products last much longer.**位(t) constant**The failure rate does not depend on time. There is just as much risk of a product failing at time t, whatever its lifespan. These are intrinsic failures. This is the type of failure often found in electronic products.**位(t) increases**The failure rate increases over time. There is an increasing risk that a product will fail as its lifespan increases. This is the end of the product's life.

**MTTF (Mean Time To Failure)**

**MTBF (Mean Time Between Failure)**

## Weibull's law

To model a product's failure law, you need to be able to model multiple types of failure:

For this reason, Weibull's law is the main one used, as it allows great variability in shape.

Thanks to its great flexibility, Weibull's law can be used to model the behaviour of many types of failure, such as :

- The breaking strength of components or the effort required to fatigue metals
- The failure time of an electronic component
- Failure time for items used outdoors, such as car tyres
- Systems that fail when the weakest component in the system fails

Weibull's law can also be used to model the behaviour of different life situations for the same component

The Weibull distribution function is as follows :

It has 3 parameters:

- \beta shape parameter聽
- \phi聽scale parameter
- \deltadelay parameter

## \beta shape parameter

\beta =1: The failure rate is constant (\lambda constant)

\beta >1: The failure rate increases over time (\lambda increases - end of product life)

\beta <1: Failure rate decreases over time (\lambda decreases - youth defect)

## \phiscale parameter

## \deltadelay parameter

*螔 = 3.6 - 胃 = 100, 未 = 0*

*螔 = 3.6 - 胃 = 100, 未 = 100*

## Here are the modules you can use to model your failures

### Data Analysis

Statistics in 1 click. Use the power of statistics to find out what's behind your production data from the SPC, APC or IQC modules. Thanks to its machine learning algorithms, the Data Analysis module can be used to understand the origin of machine drift or to differentiate suppliers statistically.