A New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods

Table 1

Numerical results for the considered sampling schemes, as well as their efficiency with regard to SRS for even set size for cycles.

(n, m)	SRS			(n, m)	RSS			MRSS			Efficiency
		AB	MSE			AB	MSE		AB	MSE
R = 0.6, (α, β) = (3, 2)
(10,10)	0.58590	0.01410	0.00962	(2,2)	0.59378	0.0062	0.00721	0.58687	0.01313	0.00957	1.334	1.005	0.753
(20,20)	0.57552	0.02448	0.00419	(4,4)	0.59572	0.0043	0.00314	0.61566	0.01566	0.00257	1.334	1.630	1.222
(30,30)	0.58033	0.01967	0.00323	(6,6)	0.59456	0.00544	0.00166	0.60022	0.00022	0.00132	1.946	2.447	1.258
R = 0.714, (α, β) = (5, 2)
(10,10)	0.66237	0.05192	0.00828	(2,2)	0.71570	0.0014	0.00801	0.71802	0.00374	0.00327	1.034	2.532	2.450
(20,20)	0.67325	0.04103	0.00452	(4,4)	0.70793	0.0064	0.00246	0.70897	0.00531	0.00217	1.837	2.083	1.134
(30,30)	0.67316	0.04113	0.00348	(6,6)	0.71232	0.0020	0.00133	0.71331	0.00097	0.00096	2.617	3.625	1.385
R = 0.833, (α, β) = (5, 1)
(10,10)	0.77568	0.05765	0.00716	(2,2)	0.82910	0.0042	0.00366	0.83314	0.00020	0.00279	1.956	2.566	1.312
(20,20)	0.78243	0.05090	0.00437	(4,4)	0.83501	0.0017	0.00086	0.83006	0.00327	0.00114	5.081	3.833	0.754
(30,30)	0.78296	0.05037	0.00378	(6,6)	0.82980	0.0035	0.00055	0.82888	0.00445	0.00037	6.873	10.216	1.486
R = 0.9, (α, β) = (4, 0.4)
(10,10)	0.87219	0.03690	0.00317	(2,2)	0.89599	0.0131	0.00137	0.90395	0.00514	0.00087	2.314	3.644	1.575
(20,20)	0.86806	0.04103	0.00276	(4,4)	0.90907	0.00004	0.00034	0.90762	0.00147	0.00031	8.118	8.903	1.097
(30,30)	0.86770	0.04139	0.00230	(6,6)	0.90665	0.0024	0.00020	0.90703	0.00206	0.00014	11.500	16.429	1.429