Abstract
This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.
Highlights
In standby systems one component work's and the other components are standby
Percentile Estimation Method (Pr) 0.2030 0.0055 0.2684 0.2009 0.0021 0.1685 0.2004 0.0015 0.1420 0.2026 0.0035 0.2153 0.2047 0.0024 0.1780 0.1961 0.0030 0.1972. These conclusions are according to the results of simulation: A
We conclude from table (1) the following: 1- Reliability of model decreases with the increasing values of σ
Summary
In standby systems one component work's and the other components are standby. Cascade is a special kind of strength and stress reliability model. Ozler and Gurler (2012) (1) considered reliability of the k-out-of-n: F systems and its conditional shape with exchangeable components in stress-strength setup. Umamaheswari and Swathi (2013) (4) studied generalized exponential distribution for cascade model. The Mathematical Formula Reliability: In this model strength-stress random variables of (comp[1] and comp[2] are basics and comp[3] is stand by) to be (Xi; i = 1,2,3) and (Yj; j = 1,2,3) respectively , where Xi and Yj are independently identically distributed Inverse Weibull random variables with common known shape parameter σ and unknown scale parameters ρi; i=1,2,3 , θj; j=1,2,3. Substitution (6),(7) and ,(8) in (5) the reliability function; R, will be as: R
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
