<?php

// We have an array of incident domain objects
$downPeriods = array();
foreach ($incidents as $incident) {
    $start = strtotime($incident->getCreatedTimestamp());
    $end = strtotime($incident->getStableTimestamp());  // that doesn't exist but imagine it

    $found = false;
    foreach ($downPeriods as $startDown => $endDown) {
        if ($startDown > $start) { // new down period previous to the rest
            $downPeriods[$start] = $end;
            $found = true;
            break;
        }

        if ($endDown > $start) { // belongs to this period
            if ($end > $endDown) {
                $endDown = $end;
            }
            $downPeriods[$startDown] = $endDown;
            $found = true;
            break;
        }
    }

    if (!$found) {
        $downPeriods[$start] = $end;
    }

    ksort($downPeriods);
}

$mtbf = getMtbf($startPeriod, $endPeriod, $downPeriods);

function getMtbf($startPeriod, $endPeriod, array $downPeriods) {
    $totalTimeDown = 0;

    $previousEnd = null;
    foreach ($downPeriods as $start => $end) {
        if ($previousEnd === null) { // first up period
            $totalTimeDown += $start - strtotime($startPeriod);
        } else {
            $totalTimeDown += $start - $previousEnd;
        }
        $previousEnd = $end;
    }
    $totalTimeDown += strtotime($endPeriod) - $previousEnd;

    return $totalTimeDown / (count($downPeriods) + 2);
}