A diagnostic approach to Weibull‐Weibull stress‐strength model and its generalization
Authors: Samar Ali S. , Kannan S. 
Published: April 2011

PurposeThe 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/approachGeneralised 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.FindingsDifferent cases of stress and strength with varying parameters have been discussed for the Weibull‐Weibull stress‐strength models considered in this paper. The results show how the stress‐strength reliability model is affected by changes in the parameters of stress and strength. The application of the proposed technique will help in understanding the design methodology of the system, and also lead to the problem of addressing the risks involved in perceived quality and reliability levels by eliminating or at least reducing the risk impact in the design phase.Research limitations/implicationsThe present study is limited to a few special cases of Weibull‐Weibull stress‐strength models. The authors propose to continue to study the behaviour of general Weibull strength against exponential stress in particular and to identify the shape parameter that maximises the strength reliability.Practical implicationsThe application of the proposed technique will help in understanding the design methodology of the system, and also lead to the problem of addressing the risks involved in perceived quality and reliability levels by eliminating or at least reducing the risk impact at the design phase. The model has been extended and generalized to include a repair facility under the assumption that all the random variables involved in the analysis are arbitrarily distributed (i.e. general).Originality/valueIn the Weibull‐Weibull stress‐strength model of reliability, different cases have been considered. In the first case, both parameters of stress‐strength have the same values and are independent of the distribution. In the second case, if the shape parameter of the strength is twice that of the stress, the probability will have a normal distribution with different parameter values. In the third case, if the shape parameter of the stress is twice that of the strength, then probability distribution is a parabolic cylindrical function. The study shows how to proceed in all cases. The model is generalized to include a repair facility, with all the random variables involved in the analysis being arbitrarily distributed using semi‐regenerative stochastic processes.