Assessment of service quality for complex technical devices based on the Jaynes’ information principle

The Jaynes’ information principle (formalism) advanced for the solution of problems of statistical thermodynamics is applied to the solution of a task of assessing the fairness of a contractor who carries out restoration work on a technical system by the method of replacing elements. The task is the following. The customer possesses a fleet of similar technical devices (for example, cars) certain elements of which are subject to planned replacement. According to the contract, such replacements are carried out by a contractor. Spare elements of three types can be used: new original, new non-original and restored elements. The contract specifies what percentage of spare elements of each type may be used. It is difficult for the customer to check what type of element has been applied. However, for an element of each type it is possible to calculate the average time before the next replacement will be required. The actual average time between requirements for replacement is fixed by the customer. Based on these data and with the help of Jaynes’ information principle, it is possible to find the most objective probabilities of using elements of the various types. Having compared these probabilities with restrictions specified in the contract, the customer draws a conclusion about the fairness of the contractor and, if necessary, takes appropriate action. According to Jaynes’ principle, the most objective are probabilities for which entropy according to Shannon reaches a maximum under the set of restrictions. Respectively, the problem of finding their probabilities is simplified to a problem of finding the maximum nonlinear function under the set of restrictions. In this article, the task is formulated mathematically and solved for a case of three variables using the Lagrange method. Calculations for a real situation from the author’s practice are given.