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# MATHEMATICAL MODEL OF ACCELERATED LIFE TESTING USING GEOMETRIC PROCESS FOR MARSHALLOLKIN EXTENDED EXPONENTIAL DISTRIBUTION

 Sadia Anwar1, Mustafa Kamal1, Arif-Ul-Islam2 Research Scholar, Dept of Statistics & Operations Research, Aligarh Muslim University, Aligarh, U.P, India Professor, Dept of Statistics & Operations Research, Aligarh Muslim University, Aligarh, U.P, India Related article at Pubmed, Scholar Google

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## Abstract

In accelerated life testing researcher generally use a life stress relationship between life characteristic and stress to estimate the parameters of failure time distributions at use condition which is just a re-parameterization of original parameters but from statistical point of view it is easy and reasonable to deal with original parameters of the distribution directly instead of developing inference for the parameters of the life stress relationship. By assuming that the lifetimes at increasing stress levels forms a geometric process one can easily handle the original parameters of life distribution directly in accelerated life testing. In this paper a mathematical model for the analysis of constant stress accelerated life testing by using geometric process for Marshall-Olkin Extended Exponential distribution is developed. The estimates of parameters are obtained by using the maximum likelihood method for complete data. In order to get the asymptotic variance of the ML estimator, the Fisher information matrix is constructed. The asymptotic interval estimates of the parameters are then obtained by using this asymptotic variance. In the last a simulation study is performed to illustrate the statistical properties of the parameters and the confidence intervals

### Keywords

Maximum Likelihood Estimation; Reliability Function; Fisher information Matrix; Confidence Intervals; Simulation Study.

### VI. SIMULATION STUDY

In order to obtain MLEs of ,and to study the properties of these estimates through Mean squared errors (MSEs), relative absolute biases (RABs) and confidence limits for 95% and 99% asymptotic confidence interval, a simulation study is performed. For this purpose, first different random samples with sizes n 100,200,...,500are generated from MOEE distribution. The combinations (,) of values of the parameters are chosen to be (1.0,1.5,2.0) and (1.25,0.5,2.5) . The number of stress levels s is assumed to be 4 and 6 throughout the study. For different sample sizes and stress level, MLEs, MSEs, RABs and the lower and upper CI limits of 95% and 99% confidence interval of parameters based on 500 simulations are obtained by our proposed model and summarized in Table 1, 2, 3, and 4.

### VII. DISCUSSION AND CONCLUSION

This paper deals with use of GP model in the analysis of CSALT plan for MOEE distribution with complete data. The MLEs, MSEs and RABs of the model parameters were obtained. Based on the asymptotic normality, the lower and upper CI limits of 95% and 99% confidence interval of the model parameters were also obtained. From the results in Table 1, 2, 3 and 4, it is easy to find that estimates of and perform well. For fixed and we find that as sample size n increases, MSEs, RABs and the confidence intervals get narrower. This is very usual because big samples increase the efficiency of the estimators. From these results, it may be concluded that the present model work well for complete data.

### ACKNOWLEDGMENT

This work has been funded by University Grant Commission under Maulana Azad National Fellowship.

### References

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