In this paper, the estimation of multi-component system reliability of Exponential-shanker Stress-Strength model with more than two stresses is studied. The estimation of models Rp = p [max (X1, …, Xr)<max (Z1, …., Zk)] and Rs = P [max (X1, …, Xr)<min (Z1…. Zk)] is studied when (Z1, Z2, …., Zk) are strengths subjected to one of the stresses X1,…, Xr assuming that Z1…. Zk follow independent shanker distribution and X1, …, Xr follow independent exponential distribution. The expression for system reliability of series and parallel systems for an exponential-shanker stress-strength model is derived. MLEs for the parameters and reliability functions with their asymptotic distributions are derived. Shrinkage methods (two types)estimators are derived. Also the performance of MLEs and Shrinkage estimators(two types) of reliability functions are studied by estimating MSEs through simulations.

1.
N.S.
Abbas
 and
F.H.
Sail
,
On Shrinkage Estimation of Based on Exponentiated Weibull distribution
(
International Journal of Science and Research
,
2017
), pp.
167
–
173
.
Google Scholar
 
2.
E. A.
Abdulateef
 and
A.N.
Salman
,
On Shrinkage Estimation for R (s,k) in Case of Exponentiated pareto Distribution
(
Ibn Al-Haitham Journal for Pure and Applied Science
,
2019
), pp.
147
–
156
.
https://doi.org/10.30526/32.1.1825
Google Scholar
 
3.
G. K.
Bhattacharyya
 and
R. A.
Johnson
,
Estimation of Reliability in a multicomponent stress-strength model
(
Journal of the American Statistical Association
,
1974
), pp.
966
–
970
.
https://doi.org/10.1080/01621459.1974.10480238
Google Scholar
 
4.
C.
Cheng
,
Reliability of Parallel Stress-Strength Model
(
Journal of Mathematical Research with Applications
,
2018
), pp.
427
–
440
.
Google Scholar
 
5.
A. A.
Hussein
,
M. K.
Yaseen
 and
A. N.
Salman
,
Applying Shrinkage Estimation Technique of Case of Generalized Exponential Distribution
(
Ibn Al-Haitham Journal For Pure and Applied Science
,
2020
), pp.
158
–
166
.
https://doi.org/10.30526/33.3.2480
Google Scholar
 
6.
N.
Karadayi
,
B.
Saracoglu
 and
A.
Pekgor
,
Stress-Strength Reliability its Estimation for a Which is Exposed tw Independent Stresses
(
Slcuk J. Appl. Math.
SpecialIssue.,
2011
), pp.
13135
.
Google Scholar
 
7.
N. S.
Karam
,
One Two and Multi-Component Gompertz Stress-strength Reliability Estimation
(
Mathematical Theoryand Modeling)
, No.
3
, ISSN:(22245804)(
2016
).
Google Scholar
 
8.
G. S.
Rao
,
Estimation of Reliability in Multicomponent Stress-strength Based on Generalized Exponential Distribution
(
Revista Colombiana de Estadística
,
2012
), pp.
6776
.
Google Scholar
 
9.
D.
Sezer
 and
I.
Kinaci
,
Estimation of Stress-Strength Parameter of a Parallel System for Exponential Distribution Based on Masked Data
(
Journal of Selçuk University Natural and Applied Science
,
2013
), pp.
60
–
68
.
Google Scholar
 
10.
R.
Shanker
,
Shanker Distribution and its Applications
(
International Journal of statistics and Applications
,
2015
), pp.
338
–
348
.
Google Scholar
 
11.
N.
Thomopoulos
,
statistical Distributions Applications and parameter estimates
,
USA
,
springer International publishing
(
2017
)
Google Scholar
 
12.
L.
Wang
,
S.
Dey
,
Y. M.
Tripathi
, and
S. J.
Wu
,
Reliability inference for a multicomponent stress-strength model based on Kumaraswamy distribution
(
Journal of Computational and Applied Mathematics
,
2020
),
376
,
112823
.
https://doi.org/10.1016/j.cam.2020.112823
Google Scholar
Crossref
Search ADS
 
13.
J. R.
Thompson
,
Some Shrinkage Techniques for Estimation the Mean
(
J. Amer. Statist Assoc
,
1968
), PP.
113
–
122
.
Google Scholar
 
14.
Rao
,
Estimation of Reliability in multicomponent stress-strength Based on Inverse exponential distribution
(
international journal of Statistics and Economics
,
2013
), pp.
28
–
37
.
Google Scholar
 
15.
J.J
Kim
 and
E.M.
Kank
,
Estimation of Reliability in multicomponent stress-strength model in Weibull Case
(
journal of the KSQC
,
1981
), pp.
3
–
11
Google Scholar
 
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