In this paper, we discuss the statistical inference of the lifetime distribution of components in a $n$-component coherent system when the system structure is known and the component lifetime follows the proportional hazard rate model. Different estimation methods, the maximum likelihood estimator, approximation of the maximum likelihood estimator, and Bayes estimator for the component lifetime parameter are discussed. Because the integrals of the Bayes estimates do not possess closed forms, the Metropolis-Hastings method and Lindley's approximate method are applied to approximate these integrals. Confidence intervals based on the asymptotic distribution of the MLE, likelihood ratio test, pivotal method, and highest posterior density credible are computed. Two numerical examples are used to illustrate the methodologies developed in this paper and a Monte Carlo simulation study is used to compare the performance of these estimation methods and recommendations are made based on these results.
Zaman, R., & Fallah, A. (2022). Statistical inference of component lifetimes in a coherent system under proportional hazard rate model with known signature. Journal of Statistical Modelling: Theory and Applications, 3(1), 147-167. doi: 10.22034/jsmta.2023.19734.1088
MLA
Roshanak Zaman; Adeleh Fallah. "Statistical inference of component lifetimes in a coherent system under proportional hazard rate model with known signature", Journal of Statistical Modelling: Theory and Applications, 3, 1, 2022, 147-167. doi: 10.22034/jsmta.2023.19734.1088
HARVARD
Zaman, R., Fallah, A. (2022). 'Statistical inference of component lifetimes in a coherent system under proportional hazard rate model with known signature', Journal of Statistical Modelling: Theory and Applications, 3(1), pp. 147-167. doi: 10.22034/jsmta.2023.19734.1088
VANCOUVER
Zaman, R., Fallah, A. Statistical inference of component lifetimes in a coherent system under proportional hazard rate model with known signature. Journal of Statistical Modelling: Theory and Applications, 2022; 3(1): 147-167. doi: 10.22034/jsmta.2023.19734.1088
)