3Þ transmission, or if the FDR did not record a   transmission,

。。Si,j zCVRsðk  。{aFDR

。2 ð

eðlÞ 

which can occur for transmissions less than the one second sample rate。

with other overlap areas likewise calculated (not  shown)。

The only constraint is on the binary  SMatch,

ði,jÞ[ðm,nÞ   SMatchi,j ~1 ð4Þ

The test cases used and outcomes observed are summarized in Table 1, all of which are included in the online Appendix。 In Table 1, reference is made to a perturbed sets of events。 This is expanded on in the section

Figure 3。 Permutations of overlap of CVR and FDR  events。

Table 1

Step 1 – Matching Test Cases and  Summary

Case Description Outcome

1 7 perfectly aligned events。 Expected outcome: match all。 All events matched。

2 Same as case 1, with one missing CVR event。 Expected outcome: 6 events   match。 6 events matched。

3 6 randomly perturbed CVR events, and 7 FDR events (one CVR event missing)。 Known to fail step 2。 Expected outcome: 6 events  match。

6 events matched。

4 3 events, non-unique in pattern。 Expected outcome: random  match。 Matched on first event, no warning of non-unique match。

5 7 CVR events and 6 FDR events with no relationship in patterns。 Expected outcome: no events match。 One event matched, all others failed。

6 Similar to case 3。 Expected outcome: all events  match。 All events matched。

7 Perfectly perturbed events。 Starting with one event, adds a perfectly perturbed event until a total  of 8 events are tested。 Expected outcome: all cases should match all events  provided。

8 Multiple cases: 8 total events。 Each sub-case removed a random event from CVR and/or FDR event list。 Expected outcome: all cases should match all events  provided。

9 Perfectly perturbed events, however, a linear trend of 。025% is added to the base rate of the CVR。 Expected outcome: match all points, expect to fail step  2。

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

Each case matched all provided events。

Each case matched all provided events。

All events matched。 All events matched。

explaining Step 2 – Optimization; for the purpose of Step 1

– Matching , it is sufficient to explain perturbation as the introduction of a random offset greater than or equal to 0 and less than 1 to each start and end time of the CVR。 All cases ultimately performed as expected, except cases 4 and

5。 In case 4, the pattern was not unique yet no warning was provided。 In case 5, there was no pattern to be matched, yet one point matched。 These cases are discussed further in the discussion section。

Step 2 – Optimization

The analysis could end with the first step if accuracy to one second is acceptable; however, accident investigations often require the most accurate timeline possible。 To further align the recorded events, the CVR and FDR events are analyzed to determine an optimum offset。 The expected input is shown in Listing 3。 Each row represents the same event recorded by the CVR and FDR。 The first two columns are CVR start and end times (CVRs, CVRe); the next two columns are adjusted FDR start and end times (as explained in Step 1-Matching) (aFDRs, aFDRe); and the last two columns are the raw, sampled FDR start and end times (rFDRs, rFDRe)。 The properly formatted file is a product of Step 1 Matching, though the input file could also be manually created。