A Bayesian Framework for Parameters Estimation in Complex System ADRIANA CALAPOD 1 , LUIGE VLĂDĂREANU 2 , RADU ADRIAN MUNTEANU 3 , DAN GEORGE TONŢ 4 , GABRIELA TONŢ 4 1 Agency of Environment Protection, Bihor County, Dacia nr.25/A , Oradea, 410464, ROMÂNIA http://www.apm-bihor.ro/ 2 Institute of Solid Mechanics of Romanian Academy C-tin Mille 15, Bucharest 1, 010141, ROMÂNIA, luigiv@arexim.ro, http://www.acad.ro 3 Department of Electrical Measurements, Faculty of Electrical Engineering, Technical University Cluj Napoca, Constantin Daicoviciu st. no 15, 400020 Cluj - Napoca, ROMÂNIA, radu.a.munteanu@mas.utcluj.ro 4 Department of Electrical Engineering, Measurements and Electric Power Use, Faculty of Electrical Engineering and Information Technology University of Oradea Universităţii st., no. 1, zip code 410087, Oradea, ROMÂNIA, gtont@uoradea.ro dtont@uoradea.ro, http://www.uoradea.ro Abstract: -. The real-life complex development situations express that the methods applied to new product development process content reliability risks which require assessment and quantification at the earliest stage, extracting relevant information from the process. Reliability targets have to be realistic and systematically defined, in a meaningful way for marketing, engineering, testing, and production. Potential problems proactively identified and solved during design phase and products launched at or near planned reliability targets eliminate extensive and prolonged improvement efforts after start on. Once in the market, products standard procedures require monitoring of early signs of issues, allowing corrective action to be quickly taken. Reliability validation before a product goes to market by the means of Bayesian statistical method because the model has shorter confidence intervals than the classical statistical inference models, allowing a more accurate decision-making process. The paper proposes the estimation of the shape parameters in a complex data structures approached with exponential gamma distribution as model of life time, reliability and failure rate functions. The numerical simulation performed in the case study validates the correctness of the proposed methodology. Key-Words: - failure, rate, Bayesian model, adequate function, distribution, simulation. 1 Introduction The systematic reduction of product development time and cost without risking or sacrificing reliability includes procedures and standards regarding the choice of types of components of product, research and selection of manufacturers, suppliers, purchasing specifications, analysis of faults, the reliability of their introduction into manufacturing and thereafter etc. Based on experience with similar components, specifying target reliability prediction is based on laboratory tests and a large amount of data obtained in operational regime. Variables influencing the failure rate of components are: 1. criteria for failure: critical values of certain accessible parameters of the component as is considered defective (failure may be total, catalectic or derived) 2. electrical constraints such as: current, power, noise, etc.. 3. thermal constraints which depend on the type of the studied components a. Passive components are characterized by ambient temperature and the capsule or layer temperature b. Active components are characterized by two types of temperature: a junction and normalized junction 4. constraints climate: humidity, pressure, dust, altitude 5. mechanical constraints: shock, vibration MATHEMATICAL METHODS AND APPLIED COMPUTING ISSN: 1790-2769 719 ISBN: 978-960-474-124-3