Mathematical model of failure prediction by statistical method at testing of prototypes of heat-power equipment

Abstract

The object of research is the power equipment (steam boiler, steam turbine, turbine generator, etc.) of modern heat power systems. When creating, operating and repairing expensive power equipment, one faces a relevant problem of failure prediction. To solve this problem, a task is set to develop a mathematical model of planning the scope of tests of power equipment prototypes. During the testing of test samples, the entire testing period is generally divided into a number of stages, at each of which the scope of tests is recorded, expressed in hours or cycles, depending on whether the power equipment is continuously or cyclically operating. At each stage, the number of failures is recorded, as well. After the cause of the failure is identified, the main equipment of the TPP is elaborated. The elaboration is considered effective if it is followed by the same scope of tests, with no failures recorded. Two methods for planning the scope of tests have been presented. The first method is based on double sampling, the second one — on multiple sampling. When planning the scope of tests, mathematical models of failure prediction for both double and multiple sampling have been developed on the condition of no failures, or the occurrence of no more than one failure after elaboration in a subsequent sample. The presented method is simple in practical application. In order to assess the effectiveness of the elaboration, the fitting criteria in binomial and normal laws of failure distribution have been proposed. The conducted research allows to obtain mathematical models of failure prediction during testing of prototypes of power equipment of TPP, as well as mathematical models of the fitting criteria in binomial and normal distribution laws.