Evaluation of reliability of complex systems by means of a discretizing approach

Abstract

This paper examines the suitability of the discretizing approach of Roy and Dasgupta, based on the discrete concentration method of Roy, for determination of reliability of complex systems under Weibull set‐up. A system is said to be complex if its distribution is intractable and analytical evaluation of probability is not available. Numerical analyses on a hollow cylinder, solid shaft, hollow rectangular tube, and the power dissipated by a resistor have been worked out to examine the closeness between the discretized reliability estimators and the simulated values based on Monte Carlo method. Also, it may be observed that the proposed approach has superior performance in comparison to the discretizing approach of English et al., based on the moment equalization method of Taguchi. The mean absolute deviation under the discrete concentration approach is much less than the same under the moment equalization approach for the Weibull set‐up.

Approximation of continuous random variables for the evaluation of the reliability parameter of complex stress–strength models

“…English et al (1996) extended this method up to 6 points and applied it in the solution of four engineering problems. Roy and Dasgupta (2001), Roy and Dasgupta (2002), Barbiero (2012) employed their own discretization techniques, which will be described in the next section, to evaluate the reliability parameter of the complex stress-strength models investigated in English et al (1996).…”

“…For symmetrical unimodal distributions the optimal value is 0.5. Roy and Dasgupta (2002) and Roy (2004) extended the discretization approach in Roy and Dasgupta (2001) to two asymmetrical distributions defined on R + , the Weibull and Rayleigh distributions respectively, after defining the parameter values leading to a "standard" version of the distribution.…”

Evaluation Methods in Systems Research

“…Finally, they may be treated as the evidences of country development level in general. Complex systems appear, operate and develop within long periods of time and with natural processes of "aging", despite regular improvements, more strict and accurate control over their behaviour is required [3,4]. This is why the development of methods for evaluation and forecasting the state, operation quality and interaction between structural elements of complex systems, presented in this work, takes especially important place.…”

Parameter Estimation for Type III Discrete Weibull Distribution: A Comparative Study

“…The third, which is referred to as type III and this paper considers, was introduced in Padgett and Spurrier [6]: their approach does not start from the continuous Weibull distribution but tries to generalize the notions of hazard rate and mean residual life to the discrete case [7]. From a different perspective and with a different objective, Roy and Dasgupta [8] proposed a discretization method for continuous random variables for 2 Journal of Probability and Statistics computing reliability in complex stress-strength models, with a specific application to the Weibull r.v. ; however, the support of the discrete r.v.…”