Journal of the Iranian Statistical Society
پژوهشنامه انجمن آمار ایران
JIRSS
Basic Sciences
http://jirss.irstat.ir
1
admin
1726-4057
2538-189X
8
10.29252/jirss
14
1726-4057
13
en
jalali
1399
3
1
gregorian
2020
6
1
19
1
online
1
fulltext
en
Sequential-Based Approach for Estimating the Stress-Strength Reliability Parameter for Exponential Distribution
62Lxx: Sequential methods
62Lxx: Sequential methods
Original Paper
Original Paper
<p style="text-align: justify;">In this paper, two-stage and purely sequential estimation procedures are considered to construct fixed-width confidence intervals for the reliability parameter under the stress-strength model when the stress and strength are independent exponential random variables with different scale parameters. The exact distribution of the stopping rule under the purely sequential procedure is approximated using the law of large numbers and Monte Carlo integration. For the two-stage sequential procedure, explicit formulas for the distribution of the total sample size, the expected value and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress-strength model are provided. Moreover, it is shown that both proposed sequential procedures are finite, and in exceptional cases, the exact distribution of stopping times is degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally using real data, the procedures are clearly illustrated.</p>
Law of Large Numbers, Purely Sequential Sampling, Stopping Rule, Two-stage Sequential Sampling.
85
120
http://jirss.irstat.ir/browse.php?a_code=A-11-407-3&slc_lang=en&sid=1
Ashkan
Khalifeh
khalifeh68@yahoo.com
`10031947532846003371`

10031947532846003371
No
Department of Statistics, Yazd University, Yazd, Iran.
Eisa
Mahmoudi
emahmoudi@yazd.ac.ir
`10031947532846003372`

10031947532846003372
Yes
Department of Statistics, Yazd University, Yazd, Iran.
Ali
Dolati
adolati@yazd.ac.ir
`10031947532846003373`

10031947532846003373
No
Department of Statistics, Yazd University, Yazd, Iran.