Multiple inverse problem

The problem of providing the required level of quality of products and/or technological processes often becomes difficult due to the fact that there is no general theory for determining optimal sets of values of primary factors, i.e. output parameters of parts and units comprising an object as well as ensuring the equivalence of object parameters to the quality requirements. This is the main reason why the development of complex systems and objects of vital importance takes several years. To create this theory, one has to overcome a number of difficulties and solve the following tasks: creation of reliable and stable mathematical models that indicate the influence of primary factors on output parameters; determination of accurate solutions when mathematical models are poorly stipulated; and creation of a method of assigning nominal values and tolerances for primary factors with regard to economical, technological and other criteria. All of the above-listed tasks are equally important. The present work is an attempt to describe a solution for this problem. The mathematically formalized aspect of the problem of providing the required level of quality has been called the "multiple inverse problem".