ON THE PROXIMITY OF WEIGHTED AND EXPONENTIAL DISTRIBUTIONS

In this paper stochastic relations and closure results for weighted and transformed distributions including the proportional hazards model are presented. Exponential approximations to the class of increasing failure rate (IFR) and decreasing failure rate (DFR) weighted distributions including transformed distributions with monotone weight functions are obtained. These include approximations via the proportional hazards and length-biased exponential distributions. Also, bounds and moment-type inequalities for weighted life distributions including proportional hazards models and some applications are presented.

Total Time on Test Transforms of Order n and Their Implications in Reliability Analysis

In this paper we study the properties of total time on test transforms of order n and examine their applications in reliability analysis. It is shown that the successive transforms produce either distributions with increasing or bathtub-shaped failure rates or distributions with decreasing or upside bathtub-shaped failure rates. The ageing properties of the baseline distribution is compared with those of transformed distributions, and a partial order based on nth-order transforms and their implications are discussed.

Total Time on Test Transforms of Order n and Their Implications in Reliability Analysis

In this paper we study the properties of total time on test transforms of order n and examine their applications in reliability analysis. It is shown that the successive transforms produce either distributions with increasing or bathtub-shaped failure rates or distributions with decreasing or upside bathtub-shaped failure rates. The ageing properties of the baseline distribution is compared with those of transformed distributions, and a partial order based on nth-order transforms and their implications are discussed.