If you want you constructor function to be a singleton, you are going to have to make a few tweaks to your code:

var Mui = (function (window, document, undefined) {

    var Mui = function () {
        //the cached instance
        var instance;
        
        //rewrite the constructor
        Mui = function() {
            return instance;
        };
        
        //carry over the prototype properties
        Mui.prototype = this;
        
        //the instance
        instance = new Mui();
    
        //reset the constructor pointer
        instance.constructor = Mui;
    
        //all the functionality
        instance.version = {
            Major  : '0',
            Minor  : '1',
            Bugfix : '0'
        };
    };

    Mui.prototype.sayHi = function () {
        alert('hi');
    };

    return Mui;

}(window, this.document));

var mui_1 = new Mui();
var mui_2 = new Mui();
mui_1 === mui_2; //true

If you want you constructor function to be a singleton, you are going to have to make a few tweaks to your code:

var Mui = function () {
    //the cached instance
    var instance;

    //rewrite the constructor
    Mui = function Mui() {
        return instance;
    };

    //carry over the prototype properties
    Mui.prototype = this;

    //the instance
    instance = new Mui();

    //reset the constructor pointer
    instance.constructor = Mui;

    //all the functionality
    instance.version = {
        Major  : '0',
        Minor  : '1',
        Bugfix : '0'
    };
    return instance;
};

Mui.prototype.sayHi = function() {
    alert('Hi');
};

var mui_1 = new Mui();
var mui_2 = new Mui();
alert(mui_1 === mui_2); //true​

You can see this working here: http://jsfiddle.net/34vCH/3/

If you want you constructor function to be a singleton, you are going to have to make a few tweaks to your code:

var Mui = (function (window, document, undefined) {

    var Mui = function () {
        //the cached instance
        var instance;
        
        //rewrite the constructor
        Mai = function() {
            return instance;
        };
        
        //carry over the prototype properties
        Mai.prototype = this;
        
        //the instance
        instance = new Mai();
    
        //reset the constructor pointer
        instance.constructor = Mai;
    
        //all the functionality
        instance.version = {
            Major  : '0',
            Minor  : '1',
            Bugfix : '0'
        };
    };

    Mui.prototype.sayHi = function () {
        alert('hi');
    };

    return Mui;

}(window, this.document));

var mai_1 = new Mai();
var mai_2 = new Mai();
mai_1 === mai_2; //true

If you want you constructor function to be a singleton, you are going to have to make a few tweaks to your code:

var Mui = (function (window, document, undefined) {

    var Mui = function () {
        //the cached instance
        var instance;
        
        //rewrite the constructor
        Mui = function() {
            return instance;
        };
        
        //carry over the prototype properties
        Mui.prototype = this;
        
        //the instance
        instance = new Mui();
    
        //reset the constructor pointer
        instance.constructor = Mui;
    
        //all the functionality
        instance.version = {
            Major  : '0',
            Minor  : '1',
            Bugfix : '0'
        };
    };

    Mui.prototype.sayHi = function () {
        alert('hi');
    };

    return Mui;

}(window, this.document));

var mui_1 = new Mui();
var mui_2 = new Mui();
mui_1 === mui_2; //true