Application of Solutions of Uncorrected Tasksʼ Theory for Managing of Production Processesʼ Robustness

The industrial revolution of “Industry 4.0” is currently underway at an active pace. Individualization of provided products and services, transition to single production, the issues of acceptability of production processes at the stage of development and design have became urgent. The aim of this work was to develop a strategy for a fundamental solution to the task of guaranteed acceptability of production processes as an integral quality characteristic.

We have proposed a systematic approach to strategy development. The basis of the approach was the theory of incorrect tasks solving. We adapted signs of correctness of mathematical tasks by J. Adamar to the tasks of ensuring acceptability of production processes (technological and measurement). They were used in the part of identification of properties of display of incorrectness and ways of incorrectnessʼ management.

We have proposed to consider the property of robustness as a generalized index of acceptability for production processes (technological and measurement). We substantiate the equivalence of the concepts of incorrectness of tasks according to J. Adamar and losses of robustness of production processes. We conclude that the developed approaches and techniques of the theory of incorrect tasks can be put in a basis of the system approach to an estimation and management of losses of robustness of production processes. We have  proposed  a  classification  of  situations  of  robustness  losses  in  production  processes in accordance with the classification of the signs of incorrect tasks by J. Adamar.

We have developed a two-step algorithm for ensuring the robustness of production processes at the stage of their development. It included identification of the sources of robustness losses and management of input factors that cause significant variation in process output. This has given a practical implementation of a strategy to guarantee the acceptability of production processes. We have systematized the sources of potential losses in  the  robustness  of  production  processes  and  proposed  a  two-stage  mechanism for managing them. We have justified rational methods of ensuring the robustness of production processes for each stage based on, the practice of uncorrected tasks solving. We have proposed a method for ensuring high efficiency  of  robustness  loss  management  in  certain  situations.  The  principles of G. Taguchiʼs robust redesigning of production processes formed the basis of our method.

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