Abstract
The study endeavors to provide statistical inference for a (1 + 1) cascade system for exponential distribution under joint effect of stress-strength attenuation factors. Estimators of reliability function are obtained using Maximum Likelihood Estimator (MLE) and Uniformly Minimum Variance Unbiased Estimator (UMVUE) of the parameters. Asymptotic distribution of the parameters is also obtained. Comparison between estimators is made using data obtained through simulation experiment.
Highlights
As the complexity of a system increases, its reliability decreases unless compensatory measures are taken
The brunt of attack, in the first instance is borne by the active component
To determine reliability function for the model under study, let us consider the strength of the two components to be X1 and X 2 respectively, where X1, X 2 are independently and identically distributed (i.i.d) exponential random variables with parameter “ λ ”
Summary
As the complexity of a system increases, its reliability decreases unless compensatory measures are taken. Raghavachar, Rao and Ramacharyulu (1983) presented a closed form solution of stress attenuated reliability function for n-cascade system when both stress and strength follow identical distributions [2]. Maheshwari, Rekha, Rao and Raghavachar (1993) studied stress attenuated reliability for n-cascade system whose stress and strength follow normal and exponential distributions respectively [3]. Rekha and Shyam Sunder (1997) have highlighted a similar cascade system where stress and strength follow gamma and exponential distributions respectively They showed that for higher parametric values and lower attenuation factors a high degree of reliability could be attained [4]. Rekha and ChechuRaju (1999) endeavored to present a closed form solution of stress attenuated reliability function for n-cascade system with exponential stress and standby strengths following Rayleigh and exponential distributions [5]. Reliability assessment (estimation of reliability function) is carried using the standard methods [7]-[10]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
