Stochastic comparisons and ageing properties of residual lifetime mixture models

In this article, we enhance the study of stochastic comparisons and ageing properties of residual lifetime mixture models. To this aim, first we perform stochastic comparisons of two different mixture models under likelihood ratio, hazard rate, mean residual life and variance residual life orders having different baseline distributions as well as two different mixing distributions. Then, we develop some sufficient conditions which lead to the stochastic comparisons of these mixture models based on reversed hazard rate, mean inactivity time and variance inactivity time orders. Furthermore, we show that increasing likelihood ratio, increasing failure rate, decreasing mean residual life, increasing variance residual life and decreasing variance residual life classes are preserved under the formation of the model. Few applications in reliability engineering are also investigated.