## 1 Introduction  
A large proportion of market-available dishwashers are designed with a water softening device, and not without good reasons. The high calcium and magnesium ion content in process water can lead to the damage of internal hydraulic components by the formation of limescale [1]. It can lead to a drop in the energy efficiency of the dishwashing process via limescale insulation on heating surfaces [2]. Additionally, limescale creation inside a dishwasher can pose a hygiene risk, should the roughness of the surfaces be increased by these deposits [3; 4; 5]. The cleaning efficiency will drop if hard water is used for dishwashing, as dirt removal has been observed to deteriorate in the presence of Ca\({}^{2+}\) ions [6]. Whereas it could be indicated that small amounts of Ca\({}^{2+}\) ions can positively affect the cleaning efficiency by easing the formation of micelles by detergent's anionic surfactants which are critical to the chemical process of soil removal [7], the anionic particles of the surfactant carry a negative charge on the hydrophilic side and can be deactivated by the presence of Ca\({}^{2+}\) ions [8] Finally, in the presence of hard water ions, the foaming process of the detergents will also be affected [6].  
The benefits of effective softening in dishwashing, therefore, have a direct impact on its carbon footprint: according to the ASTM D3556 (Standard Guide for Deposition on Glassware During Mechanical Dishwasing ) dishwasher testing method, it was found that the use of softened water can allow for detergent savings of up to 70%, significant improvement with respect to dirt elimination at lower temperatures, and an overall drop in energy consumption by the dishwasher in the long term [9].  
There is a lot of research available on deionization methods, including ion-exchange resins [10; 11], zeolites, super-macroporous cryogels [12], and nanofiltration membrane method [13]. Recently, a lot of research has been carried out on capacitive deionization methods [14; 15; 16] using flow-through capacitors [17] or reverse osmosis. According to the data, membrane methods are the most popular for industrial applications [18]; however, the cost of these systems remains high in comparison to ion-exchange resins [19].  
As the use of ion-exchange resins is the industry standard for dishwashing systems, the market offers a variety of off-the-shelf strong acid cation-exchange resins for Ca\({}^{2+}\) and Mg\({}^{2+}\) ion elimination, regenerated by NaCl solution.  
The materials' operational capacity would usually be defined by the equivalent unit--'eq'--but this method has severe drawbacks in terms of the evaluation of operational efficiency [20].  
For the commercial success of a design in the household appliance industry, it is necessary to ensure the best cost-to-performance ratio of products, considering the behavioral differences between nominally comparable configurations. These differences create a need for a robust comparison method, taking into consideration both the chemical behavior of the material under the given conditions, as well as the cost-related aspect of the product application.  
The purpose of this paper was to present a new method for strong acid cation-exchange resin comparison, which allows raw material costs regarding production-level efficiency to be compared.  
The method is intended for use in further research on household appliance ion-exchange production cost optimization, in parallel with the authors' model-based systems engineering (MBSE) methodology [21; 22; 23], effectively used for evaluation, optimization, and improvements in robustness and efficiency.