Abstract
The study aims at modelling and assessment of survival probability of a component experiencing two kinds of shocks namely, damage shock and fatal shock. Shocks are occurring randomly in time as events of a Poisson Process. The two cases of fixed/random threshold of components are studied. Survival probabilities of proposed models are derived. Maximum likelihood estimators (MLEs) of survival probabilities are obtained using the data from life testing experiments. Fisher information and asymptotic distribution of MLEs of parameters are obtained when a constant threshold is considered. Computation and comparison of estimators of two cases (constant threshold and random threshold) are made through simulation studies. The study recommends the consideration of threshold as a random variable.
Highlights
The study aims at modelling and assessment of survival probability of a component experiencing two kinds of shocks namely, damage shock and fatal shock
Maximum likelihood estimators (MLEs) of survival probabilities are obtained using the data from life testing experiments
Study of reliability can be broadly classified into two major aspects i.e. reliability modelling and reliability assessments
Summary
Study of reliability can be broadly classified into two major aspects i.e. reliability modelling and reliability assessments. Abdel-Hameed and Proschan (1975) and Klefsjo (1981) considered general case in which shocks occur according to a nonstationary pure birth process [4] [5]. Munoli and Bhat (2011) derived the reliability function of non-accumulating damage shock model with successive shocks causing greater damage. They obtained Maximum Likelihood and Bayes estimators of reliability functions using the data from a type II censored sample without replacement life testing experiment [13]. The present study endeavours to model and assess survival probability of a component experiencing two kinds of shocks namely, damage shock and fatal shock. Results and findings are discussed in the same Section
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