pattern of events was not unique, the Step 2-Optimization found an offset with no slack, as expected; this case is addressed further in the discussion section。 Case 5 and 6 were infeasible as expected。 The multiple runs in Case 7 all had feasible solutions, with slack decreasing as more events were added。 Case 8 was similar to Case 7, however events were randomly removed from the CVR and FDR lists and still all solutions were feasible as expected。 Case 9 presented a set of events where the timebase of the CVR was other than one; this simulates the case were the CVR was either recorded or played back such that 1 second equaled 1。00125 seconds。 Given the total duration from the first event to the last event was over 4000 seconds, the drift in events was such that an infeasible outcome was created。 Case 9 is addressed in the  discussion。

Discussion

Through TDD and linear programming, a model has been created to align and optimize CVR and FDR timelines。 The process is completed in two steps, first matching the events between recordings and then optimiz- ing the alignment。

Step 1 – Matching

Step 1 presented a robust ability to match events。 While robust, Step 1 requires analyst review to ensure the solution produced is in fact unique since there is a possibility that a

Table 2

Step 2 Optimization Test Cases and  Summary

Case Description Outcome

1 7 perfectly aligned events。 Expected outcome: feasible, no slack。 Feasible solution; S 5 4000 ¡ 0。

2 Same as case 1, with one missing CVR event。 Expected outcome: feasible, no slack。 Feasible solution; S 5 4000 ¡ 0。

3 6 randomly perturbed CVR events, and 7 FDR events (one CVR event missing)。 All CVR events have perturbations added。 Expected outcome: infeasible solution。

Infeasible solution。

4 3 events, non-unique in pattern。 Expected outcome: feasible, no slack。 Feasible solution; S 5 4000 ¡ 0。

5 7 CVR events and 6 FDR events with no relationship in patterns。 Expected outcome: infeasible solution。

Infeasible solution。

6 Similar to case 3。 Expected outcome: infeasible solution。 Infeasible solution。

7 Perfectly perturbed events。 Starting with one event, adds a perfectly perturbed event until a total  of 8 events are tested。 Expected outcome: all solutions feasible, with decreasing slack per  case。

8 Multiple cases: 8 total events。 Each sub-case removed a random event from CVR and/or FDR event list。 Expected outcome: feasible solutions with less slack as more  points。

9 Perfectly perturbed events, however, a linear trend of 。125% is added to the base rate of the CVR。 Expected outcome: infeasible solution。

10 Perfectly aligned events, similar to case 1, except S will be negative。 Expected outcome: match all points, trial S negative。

Feasible solution of decreasing slack。 See graph in Figure 8。

Feasible solution with less slack with more cases。

Infeasible solution。

Feasible solution, no slack, S , 0。

non-unique pattern of events may exist between the CVR and FDR。 The analyst can use Step 1 as a tool to quickly discover a likely match, and then review other parts of the CVR to verify event alignment, such as crew callouts related to altitude, heading, and airspeed, or aural alerts all of which may have corresponding FDR  events。