Mixture of Two LindleyProbability Models And Application In Reliability

Abstract

<span>Mixture probability models are developed in general<br /><span>from Uni variate Probability functions (say)<br /><span><em>g</em><span>1 <span>(<span><em>x</em><span>) <span><em>and g</em><span>2 <span>(<span><em>x</em><span>) <span>. The mixture of these two is defined by<br /><span><em>f</em><span>(<span><em>x</em><span>)  <span><em>p</em><span>.<span><em>g</em><span>1 <span>(<span><em>x</em><span>)  (1  <span><em>p</em><span>) <span><em>g</em><span>2 <span>(<span><em>x</em><span>) <span>where “p” is the mixing<br /><span>ratio. The function that we have in the present paper is the<br /><span>Mixture of two Lindley probability distributions, each of<br /><span>which is having a different parameter. Lindley models are<br /><span>also useful for data showing decaying trends. The properties<br /><span>of Lindley probability distribution that have been shown<br /><span>are Mathematical Expectation, Second Moment, and the<br /><span>Distribution Function. An application of the Mixture Model<br /><span>which has been derived in the present research , has been<br /><span>applied to the Reliability function , in a two component<br /><span>system , when the components are connected in series. The<br /><span>Reliability of the discussed system is compared with<br /><span>reliability values when the Lindley probabilities in the same<br /><span>system , are independent.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /><br class="Apple-interchange-newline" /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>