Mixture Probability with Rayleigh Model and Application in Reliability

Abstract

Single Rayleigh distribution (RD) is a unimodal two tailed probability distribution. It is useful for the data which spreads equally to the two sides of its modal value. Some properties of the Rayleigh distribution have been discussed in this paper. Mixture distributions arise in engineering, economics, sciences, biosciences, medical sciences and play vital role. While modeling a great variety of data, a mixture model has been defined (investigated) with mixture of two Rayleigh distributions (MTRD) with different parameters. The properties of this mixture model have been derived like mathematical expectation (Mean), variance and the distribution function. Graphical representations are also given. This paper focuses on the application of the mixture distribution in reliability engineering only. The probability representation of reliability expression is derived. There are two systems in which reliability has been derived; in one system, there are two components which are connected in parallel and in another system, when the components are connected in series. Graphs have been shown for each type of reliability. The mixing probability is based on the uniform probability density function.

Keywords: Rayleigh, distribution, probability, function

Cite this Article

Ehtesham Hussain, Masoodulhaq. Mixture Probability with Rayleigh Model and Application in Reliability. Research & Reviews: Journal of Statistics. 2018; 7(3): 17–27p.