A diagnostic system and method for a valve, especially a check valve of a positive displacement pump, including at least one solid-borne sound sensor is provided. The method includes the steps of completing shading operations for a pixel set including one or more pixels to generate per-sample shaded attributes according to a shader program executed by a processing pipeline. The additive used in the electrochemical device effectively controls the surface of a cathode active material, which otherwise causes side reactions with an electrolyte, due to the basic skeleton structure and polar side branches of the additive.