It's possible you're thinking of:
* The Mills Brothers, a popular vocal group who were active during the 1930s. They may have been featured in some films or television programs of the era, but a specific production titled "Mills Blue Rhythm Band - 1933" doesn't exist.
* A different film or television production altogether. Could you provide more details about the production you are asking about?
Please clarify your request so I can help you find the information you are looking for.