If you provide additional information, we can provide better answers. Are these 17 characteristics taken at 36 different locations on a single part? Is the design of the study fully at your discretion, or is a customer dictating the method?
If it is at your discretion, I would focus only on those characteristics of the 17 that are the most important. Do not waste time on characteristics that do not result in rework/scrap/returns unless they are important.
If the locations are on the same part, and you have the statistical expertise, design an experiment that combines the multiple parts, multiple operators and repeated measurements with multiple locations. You can then analyze this using ANOVA. You do not need to measure all locations. I would recommend 3-5 different locations that represent the range of easiest through hardest to measure.