A quasi exponential distribution

The exponential distribution provides a simple, elegant and closed form solution to many problems in lifetime testing and reliability studies. One reason for the wide popularity of the exponential distribution in reliability is that it is the limiting lifetime distribution of a series system of substantially similar components. Also the exponential distribution is important due to its memory loss property. However, the exponential distribution does not provide a significant fit for some real lifetime applications, where the failure rates are not constant. Epstein1 has detailed study on exponential distribution and its role in life testing. Sato et al.2 obtained a discrete exponential distribution and discussed its properties and applied the distribution to model defect count distribution in semi-conductor deposition equipment and defect count distribution per chips. Gupta & Kundu3 have introduced generalized exponential distribution and discussed its properties and applications. Most of the works done on exponential distribution, its extension, mixture and applications in different fields of knowledge are available in Ahsanullah &Hamedani.4 Although exponential distribution was the first one parameter lifetime distribution for modeling lifetime data from engineering and biomedical sciences, but due to one parameter it is not always a suitable lifetime distribution. Also the hazard rate function and the mean residual life function of exponential distribution are always constant.