There are are two managed layers (square and triangle) and one unmanaged layer (star).
The Z-index determines the rendering order; with {square: 1, triangle: 0, star: unmanaged} indices, the rendering order is triangle, square and star on top.

Z-index layer ordering example

Example of ordering layers using Z-index.

layer, ordering, z-index
<!DOCTYPE html>
<html>
<head>
<title>Z-index layer ordering example</title>
<script src="https://code.jquery.com/jquery-1.11.2.min.js"></script>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css">
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/js/bootstrap.min.js"></script>
<link rel="stylesheet" href="http://openlayers.org/en/v3.9.0/css/ol.css" type="text/css">
<script src="http://openlayers.org/en/v3.9.0/build/ol.js"></script>

</head>
<body>
<div class="container-fluid">

<div class="row-fluid">
  <div class="span12">
    <div id="map" class="map"></div>
  </div>
</div>
<div>
  There are are two managed layers (square and triangle) and one unmanaged layer (star).</br>
  The Z-index determines the rendering order; with {square: 1, triangle: 0, star: unmanaged} indices, the rendering order is triangle, square and star on top.
</div>
<div>
  <label for="idx1">
    <input type="number" id="idx1"></input>
    Square layer Z-index
  </label></br>

  <label for="idx2">
    <input type="number" id="idx2"></input>
    Triangle layer Z-index
  </label>
</div>

</div>
<script>
var stroke = new ol.style.Stroke({color: 'black', width: 1});

var styles = {
  'square': [new ol.style.Style({
    image: new ol.style.RegularShape({
      fill: new ol.style.Fill({color: 'blue'}),
      stroke: stroke,
      points: 4,
      radius: 80,
      angle: Math.PI / 4
    })
  })],
  'triangle': [new ol.style.Style({
    image: new ol.style.RegularShape({
      fill: new ol.style.Fill({color: 'red'}),
      stroke: stroke,
      points: 3,
      radius: 80,
      rotation: Math.PI / 4,
      angle: 0
    })
  })],
  'star': [new ol.style.Style({
    image: new ol.style.RegularShape({
      fill: new ol.style.Fill({color: 'green'}),
      stroke: stroke,
      points: 5,
      radius: 80,
      radius2: 4,
      angle: 0
    })
  })]
};


function createLayer(coordinates, styles, zIndex) {
  var feature = new ol.Feature(new ol.geom.Point(coordinates));
  feature.setStyle(styles);

  var source = new ol.source.Vector({
    features: [feature]
  });

  var vectorLayer = new ol.layer.Vector({
    source: source
  });
  vectorLayer.setZIndex(zIndex);

  return vectorLayer;
}

var layer0 = createLayer([40, 40], styles['star'], 0);
var layer1 = createLayer([0, 0], styles['square'], 1);
var layer2 = createLayer([0, 40], styles['triangle'], 0);

var layers = [];
layers.push(layer1);
layers.push(layer2);

var map = new ol.Map({
  layers: layers,
  target: 'map',
  view: new ol.View({
    center: [0, 0],
    zoom: 18
  })
});

layer0.setMap(map);


function bindInputs(id, layer) {
  var idxInput = $('#idx' + id);
  idxInput.on('input change', function() {
    layer.setZIndex(parseInt(this.value, 10) || 0);
  });
  idxInput.val(String(layer.getZIndex()));
}
bindInputs(1, layer1);
bindInputs(2, layer2);

</script>
</body>
</html>