A diagnostic approach to Weibull‐Weibull stress‐strength model and its generalization

Purpose – The objective of the paper is to consider the problem of the strength of a manufactured item against stress, when the component follows Weibull failure law. Different cases of stress and strength with varying parameters are discussed for the Weibull‐Weibull stress‐strength model considered in this paper. The application of the proposed technique will help in understanding the design methodology of the system and addressing the risks involved in perceived quality and reliability levels by eliminating or at least reducing the risk impact at the design phase.Design/methodology/approach – Generalised Weibull‐Weibull stress‐strength models have been analysed for different cases of shape parameters for stress and strength to estimate the reliability of the system. The model is generalized using semi‐regenerative stochastic processes with the help of a state space approach to include a repair facility.Findings – Different cases of stress and strength with varying parameters have been discussed for the ...

[1]  Charles E Ebeling,et al.  An Introduction to Reliability and Maintainability Engineering , 1996 .

[2]  C. Berridge.  An Introduction to Reliability and Maintainability. , 1984 .

[3]  E. Çinlar.  Exceptional Paper---Markov Renewal Theory: A Survey , 1975 .

[4]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[5]  John H. K. Kao.  A Graphical Estimation of Mixed Weibull Parameters in Life-Testing of Electron Tubes , 1959 .

[6]  Shyam L. Kalla,et al.  A generalized gamma distribution and its application in reliabilty , 1996 .

[7]  Bradley M. Bell,et al.  Generalized gamma parameter estimation and moment evaluation , 1988 .

[8]  Norman L. Johnson,et al.  Cumulative Sum Control Charts and the Weibull Distribution , 1966 .

[9]  E. S. Pearson.  Biometrika tables for statisticians , 1967 .

[10]  Debasis Kundu,et al.  Estimation of P[Y, 2006, IEEE Transactions on Reliability.

[11]  Marvin Zelen,et al.  Mathematical Theory of Reliability , 1965 .

[12]  J. G. Jones.  On the numerical solution of convolution integral equations and systems of such equations , 1961 .

[13]  Toshio Nishida,et al.  Some applications of semi-regenerative processes to two-unit warm standby system , 1984 .

[14]  K. Pearson,et al.  Tables of the Incomplete Gamma-Function , 2013, Nature.

[15]  S. Kotz,et al.  The stress-strength model and its generalizations : theory and applications , 2003 .

[16]  Erhan Cinlar,et al.  Markov Renewal Theory: A Survey , 1973 .