While LINGO was used as the programming language for this research, two part methodology is conducive to using any number of computing languages。 Step 1 is fundamentally finding the maximum of the Cartesian product of two arrays。 Step 2 can use the Step 1 trial alignment, S, as the basis of a for-next loop over a range of S9s with a small increment of 0。01。 A range of feasible and non-feasible solutions could quickly be identified over a more than adequate five second span。

Significantly, this model suggests when a feasible solution can be found; an error bound can be reported。 While this is mathematically correct, it may not be ecologically correct。 That is, the qualitative process of determining CVR transmit start and stop times introduces an error that cannot be accounted for by the model   alone。

Limitations

This model is built on the assumption that the CVR and FDR recordings contain overlapping events。 This model will produce no relevant results if a portion of either recording is destroyed and there are no overlapping events。

Further, as mentioned the model assumes r 5 0。

Future Research

The Step 2 model presented herein is essentially a zeroth order regression with constraints。 The zeroth order model can be modified to a first order regression model。 Equation 6 and 7 can be modified as  follows

alignCVRs~Szb m CVRs ð6aÞ

alignCVRe~Szb m CVRe ð7aÞ

The LINGO code listings in the online Appendix present the model in this fashion, however constraints are imposed to force b 5 1。 As stated, by performing first-pass analysis with b constrained to unity, feasible solutions can be expressed with numerical error bounds。

In addition to the first-order regression modification of Equations 6a and 7a, the constraints can be relaxed to permit a feasible solution。 Equations 8 through 11 can be modified

alignCVRs§aFDRs {relaxStart ð8aÞ

alignCVRsƒrFDRszrelaxEnd ð9aÞ

alignCVRe§rFDRezrelaxStart ð10aÞ

alignCVReƒaFDRe{relaxEnd ð11aÞ

where relaxStart and relaxEnd are positive numbers set by the user。

The relaxation parameters allow for discovery of a feasible solution。 The LINGO code listings in the online Appendix present the model in this fashion, with the relaxation parameters set to 0。

Conclusion

The two step solution herein presents a method to align CVR and FDR events producing an error bounded offset result。 The method was developed by using a TDD process。 The optimized offset result can be stated in a consistent and automated format of the form, ‘‘CVR elapsed time was aligned to FDR elapsed time by means of a linear programming model。 8 transmissions from the CVR were aligned with 8 identical transmissions from the FDR。 The resulting 17-decision variable, 48-constraint linear programming model was solved resulting in an offset of 4000。042 seconds ¡ 0。117 seconds’’。 The model provides a first-pass, zeroth order analysis of CVR and FDR events。 When this zeroth order model produces a feasible result, the analyst can gain confidence the timebase of the CVR and FDR were the same while

reporting a quantifiable error bound on the offset  S。

Acknowledge

The authors wish to acknowledge Dr。 Dothang Truong for his critique and support of this paper during his ORMS class。 This work is the authors’ alone and does not reflect the official position of their respective employers。

Appendix

See Appendix online at: https://erau。blackboard。com/ webapps/cmsmain/webui/_xy-38557552_1-t_ggVtZ07h