APPLICATION OF THE MIXED NJEIBULL DISTRIBUTION IN DATA PROCESSING OBTAINED IN RELIABILITY AND DURABILITY TESTINGS OF MILITARY TECHNICAL SYSTEMS

Dragoljub M. Brkić

Abstract:

In this technical information, the theoretical background is exposed for the mixed Weibull distribution constituted by tWo two-parameter Weibull distributions With the parameters b1, c1 and b2, c2,, respectively, and the mixture parameter ε. This mixed distribution is very appropriate in data processing obtained in reliability and durability testing of complex technical systems composed of electronic and electromechanical components, Where times to/between failures of these two types of components have tWo-parameter Weibull distributions With different parameters, i.e. With different distributions (for example, the shape parameter c1=1 for electronic components and c2>1 for electromechanical components). In practice, the obtained values of times to/betWeen failures of a technical ssystem under testing are included in one single set of data, regardless to which types of components the observed time to/between failures refers. Therefore, for data processing of such a set of data it is most appropriate to apply the mixed Weibull distribution. In order to apply the mixed Weibull distribution it is necessary to determine the point estimates of this distribution parameters. Since the mathematical expression of the probability density function of this distribution is very complex and has many parameters (five parameters), the application of Well knoWn methods for determining of distribution parameters is inappropriate. So, the distribution parameters of this mixed distribution are determined by using the Monte Carlo method With the modified least sljuares method. This proposed combined method is very appropriate, but it reljuires computer application. The validity of the proposed method was computer-tested many times, and it is illustrated here by many examples solved by applying a computer program specially developed for this purpose.

Key Words: mixed distribution, Weibull distribution, distribution function, distribution model, system reliability, reliability testing, time to failure, electronic system, electromechanical system, military technical systems