Minimum variance unbiased estimation of stress–strength reliability under bivariate normal and its comparisons

ABSTRACT

In many industrial and natural phenomena, we need the probability that a component is smaller than the other component. Under a stress–strength model, this is reliability of an item. Under independent setup, there are different approaches for the estimation of such reliability. Here, estimation is considered under the dependent case. Under bi-variate setup uniformly minimum variance unbiased estimator is obtained. Also comparison with available estimator based on Maximum Likelihood Estimate (MLE) is done through Mean Square Error (MSE) and bias. Also these are compared by computing L₁ distance between their distribution functions. From this idea and numerical computations, UMVUE appears to be good.

KEYWORDS:

• Basu’s theorem
• L₁ norm
• Reliability

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F10

Acknowledgments

We thank Dr. R. Das, Dept. of Statistics, Presidency University, Kolkata, for his inspiration and two referees, for their valuable suggestions for improvement. We also thank Editor in Chief for his advice.