Stress-Strength Parameter Estimation under Small Sample Size: A Testing Hypothesis Approach.

Ahmed Mostafa Khalil,Mohammad Mehdi Saber,M M Abd El-Raouf,Hassan Alsuhabi

doi:10.1155/2021/8705547

Abstract

In this paper, uniformly most powerful unbiased test for testing the stress-strength model has been presented for the first time. The end of the paper is recommending a method which is appropriate for no large data where a normal asymptotic distribution is not applicable. The previous methods for inference on stress-strength models use almost all the asymptotic properties of maximum likelihood estimators. The distribution of components is considered exponential and generalized logistic. A corresponding unbiased confidence interval is constructed, too. We compare presented methodology with previous methods and show the method of this paper is logically better than other methods. Interesting result is that our recommended method not only uses from small sample size but also has better result than other ones.

Highlights

In reliability literature, the quantity R P(X > Y) is often referred to the stress-strength model
We find Uniformly Most Powerful Unbiased Test (UMPUT) and its corresponding C.I for R in the case where components have exponential distribution. en, by using of relationship between exponential distribution and generalized logistic (GL) distribution, our findings are applied and modified to the case of GL distributed components
Lemma 1 and eorem 3 are held for case of GL distributed components. e most important matter which has value for repeat is this point that UMPUTs based on equations (23)–(27) are more powerful than the asymptotic tests by using of statistic Z (R􏽢 − r/σ􏽢GL). □

Summary

Introduction

The quantity R P(X > Y) is often referred to the stress-strength model. Regarding [1] an instance of real practice of the stress-strength model is in a clinical study, where Y and X are assumed as the outcomes of a treatment and a control group, respectively. In stress-strength literature, when distribution of components is GL, Asgharzadeh et al [11] and Rasekhi et al [12] have investigated in statistical inference of R and its multicomponent version, respectively. E mentioned methodology of this study has been applied for the first time in stressstrength literature For this goal, we find UMPUT and its corresponding C.I for R in the case where components have exponential distribution. GL distribution has been used in many other previous papers on stress-strength models, which is mentioned above.

UMPUT for R in Exponential Distribution

Testing R in GL Distribution with Known and Common Scale Parameter

Comparison between UMPUT and Asymptotic Test

Conclusion and Future Works