In this paper, the ranking performance of six most popular and easily comprehensive multi-criteria decision-making (MCDM) methods, i.e. weighted sum method (WSM), weighted product method (WPM), weighted aggregated sum product assessment (WASPAS) method, multi-objective optimization on the basis of ratio analysis and reference point approach (MOORA) method, and multiplicative form of MOORA method (MULTIMOORA) is investigated using two real time industrial robot selection problems. Both single dimensional and high dimensional weight sensitivity analyses are performed to study the effects of weight variations of the most important as well as the most critical criterion on the ranking stability of all the six considered MCDM methods. The identified local weight stability interval indicates the range of weights within which the rank of the best alternative remains unaltered, whereas, the global weight stability interval determines the range of weights within which the overall rank order of all the alternatives remains unaffected. It is observed that for both the problems, multiplicative form of MOORA is the most robust method being least affected by the changing weights of the most important and the most critical criteria.