Tolerance interval for exponential distribution

Abstract

Tolerance interval is a kind of interval that assures the probability of at least a given proportion of population falls into the interval attains to a fixed level. It is widely needed in various industrial practices and business activities, such as product design, reliability analysis, and quality inspection. However, comparing to its widely needs, the research on it is still quite limited. In this paper, we propose a numerical method to compute the tolerance interval for exponential distribution. As the simulation study illustrates, our method performs consistently well as the sample size varies. In particular, its good performance for small sample endows itself broadly potential usefulness in practice.

Keywords

Tolerance interval / exponential distribution

References

[1] Ashkar F, Ouarda T B M J. Approximate confidence intervals for quantiles of gamma and generalized gamma distributions. Journal of Hydrologic Engineering, 1998, 3: 43-51

[2] Bain L J, Engelhardt M, Shiue W. Approximate tolerance limits and confidence limits on reliability for the gamma distribution. IEEE Transactions on Reliability, 1984, 33: 184-187

[3] Krishnamoorthy K, Mathew T, Mukherjee S. Normal based methods for a gamma distribution: prediction and tolerance intervals and stress-strength reliability. Technometrics, 2008, 50: 69-78

[4] Reiser B, Rocke M D. Inference for stress-strength problems under the gamma distribution. IAPQR Transactions, 1993, 18: 1-22

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg