Analysis of bivariate accelerated life test data for the bivariate exponential distribution. (English) Zbl 0628.62096
Consider the survival function \(\bar F(x,y)=\exp \{-\lambda_ 1x- \lambda_ 2y-\lambda_ o\max (x,y)\}\) which corresponds to the A. W. Marshall and I. Olkin [J. Am. Stat. Assoc. 62, 30-44 (1967; Zbl 0147.381)] bivariate exponential distribution. Suppose bivariate observations from this distribution are available under several stress levels \(V_ 1,...,V_ J\). It is assumed that the parameters \(\lambda_{1j}\), \(\lambda_{2j}\) and \(\lambda_{0j}\) of the bivariate exponential distribution under stress \(V_ j\) satisfy \(\lambda_{ij}=C_ iV_ j^ P\), \(i=0,1,2\); \(j=1,...,J.\)
The maximum likelihood estimators of \(C_ i\) and P are derived. Their asymptotic distribution is obtained. Also some method of moments type estimators of \(C_ i\) and P are suggested.
The maximum likelihood estimators of \(C_ i\) and P are derived. Their asymptotic distribution is obtained. Also some method of moments type estimators of \(C_ i\) and P are suggested.
Reviewer: M.Shaked
MSC:
| 62N05 | Reliability and life testing |
| 62F10 | Point estimation |
| 62E20 | Asymptotic distribution theory in statistics |
Keywords:
accelerated life testing; 2-component system; survival function; bivariate exponential distribution; maximum likelihood estimators; method of moments type estimatorsCitations:
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