var fruit = ['cherries', 'apples', 'bananas'];

fruit.sort(); // ['apples', 'bananas', 'cherries']

var scores = [1, 10, 2, 21];

scores.sort(); // [1, 10, 2, 21]

// Watch out that 10 comes before 2,

// because '10' comes before '2' in Unicode code point order.

var things = ['word', 'Word', '1 Word', '2 Words'];

things.sort(); // ['1 Word', '2 Words', 'Word', 'word']

// In Unicode, numbers come before upper case letters,

// which come before lower case letters.

// the array to be sorted

var list = ['Delta', 'alpha', 'CHARLIE', 'bravo'];

// temporary array holds objects with position and sort-value

var mapped = list.map(function(el, i) {

  return { index: i, value: el.toLowerCase() };

})

// sorting the mapped array containing the reduced values

mapped.sort(function(a, b) {

  return +(a.value > b.value) || +(a.value === b.value) - 1;

});

// container for the resulting order

var result = mapped.map(function(el){

  return list[el.index];

});

alert(result);