# inspection: Predict the results of a future scheduled inspection and... In crackR: Probabilistic damage tolerance analysis for fatigue cracking of metallic aerospace structures

## Description

Predict the results of a future scheduled inspection and update the state accordingly. The state prior to inspection is utilized to determine the likelihood of finding each particle, and the state after inspection consists of a combination of missed particles and repaired particles. The Probability of Crack Detection (PCD) results of this inspection are appended to the previously existing PCD results (if any).

## Usage

 ```1 2 3 4 5 6 7``` ```inspection(obj,inspection.type=1) ## S3 method for class 'Sing' inspection(obj,inspection.type=1) ## S3 method for class 'Mult' inspection(obj,inspection.type=1) ## S3 method for class 'CD' inspection(obj,inspection.type=1) ```

## Arguments

 `obj` Object of class crackR `inspection.type` Integer, index of which Probability Of Detection (POD) function from the parameters to utilize for this inspection.

## Details

The likelihood of finding each particle at a future inspection depends only on the crack length at that time and the POD function (as specified by inspection.type). The overall Probability of Crack Detection (PCD) is found by taking a weighted average of the probability of detection for each particle and the importance weights.
Suppose there is a 40% chance of finding a particular particle. That particle will remain in the state, but to reflect the possibility that it was not found, the weight is reduced to 60% of the weight prior to inspection. The remaining weight will be used when generating new repaired particles (by sampling from the repair flaw size distribution). The total weight that is found for all particles is the estimate of PCD for this inspection (optionally partitioned into several crack length ranges using pod.threshold). After inspection, the weight of the repaired particles will sum to PCD, and the weight of the missed particles will sum to (1-PCD). Note also that the set of particles will be re-sampled without replacement to reduce the particle count back to parameters\$Np.

## Value

Object of class crackR.

## Author(s)

Keith Halbert <[email protected]>

## References

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

`crackRinit`
`analyze`
`calcInterval`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```set.seed(327) data(cp7ext) ## initialize crackR object cp7ext.init <- crackRinit(cp7ext) ## advance through time 6000 flights cp7ext.before.insp <- calcInterval(cp7ext.init, interval.flights=6000) ## conduct inspection cp7ext.after.insp <- inspection(cp7ext.before.insp) ## print inspection results cp7ext.after.insp\$results\$pcd ```