Reliability and inverse reliability functions
Smallest extreme value
- Reliability
-
- Inverse reliability
-
where
| Term | Description |
|---|---|
| t | time |
| μ | location parameter |
| σ | scale parameter |
| Φsev(t) | CDF of the smallest extreme value distribution |
| Φ-1sev(t) | inverse CDF of the smallest extreme value distribution |
Weibull
- Reliability
-
- Inverse reliability
-
| Term | Description |
|---|---|
| t | time |
| p | probability |
| β | shape parameter |
| θ | scale parameter |
Exponential
- Reliability
-
- Inverse reliability
-
| Term | Description |
|---|---|
| t | time |
| p | probability |
| θ | mean parameter |
Normal
- Reliability
-
- Inverse reliability
-
| Term | Description |
|---|---|
| t | time |
| μ | location parameter |
| σ | scale parameter |
| Φnor(t) | CDF of the normal distribution |
| Φ-1nor(t) | inverse CDF of the normal distribution |
Lognormal
- Reliability
-
- Inverse reliability
-
| Term | Description |
|---|---|
| t | time |
| μ | location parameter |
| σ | scale parameter |
| Φnor(t) | CDF of the normal distribution |
| Φ-1nor(t) | inverse CDF of the normal distribution |
Logistic
- Reliability
-
- Inverse reliability
-
| Term | Description |
|---|---|
| t | time |
| μ | location parameter |
| σ | scale parameter |
| Φlogis(t) | CDF of the logistic distribution |
| Φ-1logis(t) | inverse CDF of the logistic distribution |
Loglogistic
- Reliability
-
- Inverse reliability
-
| Term | Description |
|---|---|
| t | time |
| μ | location parameter |
| σ | scale parameter |
| Φlogis(t) | CDF of the logistic distribution |
| Φ-1logis(t) | inverse CDF of the logistic distribution |
Equation
The equation for an m-failure test plan is as follows:
Notation
| Term | Description |
|---|---|
| α | alpha (which equals 1 – the confidence level) |
| R | reliability or survival function at time t |
| N | minimum numbef of units to be tested |
