# Define Probability Of Detection (POD) curve for Non-Destructive Inspection (NDI) based on a Log-Normal CDF formulation

### Description

The POD curve in probabilistic damage tolerance analysis is often defined using the formulation of a Log-Normal CDF, with several optional modifying parameters. This function can be used to generate the appropriate POD function for use in the crackRparameters component "pod.func".

### Usage

1 | ```
lognormalPOD(a,median,slope,a.min.detectable=0,poi=1,far=0)
``` |

### Arguments

`a` |
Crack length; the sole input to the POD function generated by this function. |

`median` |
Median detectable crack length. |

`slope` |
Slope parameter (aka sdlog). |

`a.min.detectable` |
Crack size below which detection is assumed to be impossible. Below this size the generated POD curve returns a zero probability. Note the far parameter will override this if far > 0. |

`poi` |
Probability Of Inspection. In practice an analyst may assume that some percentage of scheduled inspections will not occur as planned or will be conducted incorrectly. This can be represented by setting poi less than 1, in which case all detection probabilities are factored down. |

`far` |
Often in Non-Destructive Inspection (NDI) it is assumed there is no false alarm rate. This is most likely untrue. Setting a false alarm rate in this function forces a minimum value of POD that will be returned from the generated function. |

### Note

To define a custom POD function based on another type of curve or
otherwise, the code for `crackRlognormalPOD()`

is a good place to start.

### Author(s)

Keith Halbert <keith.a.halbert@gmail.com>

### References

MIL-HDBK-1823A (Department of Defense, USA) "Nondestructive Evaluation
System Reliability Assessment", Apr 2009

Halbert, K. "Estimation of Probability of Failure for Damage-Tolerant
Aerospace Structures" PhD Thesis, Temple University Department of
Statistics, Philadelphia, PA, Apr 2014

### See Also

`crackRinit`

`inspection`

### Examples

1 2 3 | ```
myPODcurve <- function(a) lognormalPOD(a, median=0.01, slope=0.5, a.min.detectable =
0, poi = 0.95, far = 0.001)
myPODcurve(c(0, 0.005, 0.01, 0.05, 1))
``` |