A Distribution-Free Approach to Stochastic Efficiency Measurement with Inclusion of Expert Knowledge

Table 15

Ranking of efficient DMUs according to robustness based on their standard deviations. The DMUs in bold denote the empirically efficient DMUs.

	Simulation 1			Simulation 2			Simulation 3			Simulation 4
	𝜃𝛼=0.75	Std. dev.		𝜃𝛼=0.75	Std. dev.		𝜃𝛼=0.675	Std. dev.		𝜃𝛼=0.725	Std. dev.
DMU9	1	0.34111	DMU15	1	0.45149	DMU13	1	0.16546	DMU13	1	0.15033
DMU2	1	0.36819	DMU3	1	0.46499	DMU7	1	0.32591	DMU3	1	0.30285
DMU1	1	0.53889	DMU12	1	0.5823	DMU1	1	0.47956	DMU2	1	0.39775
DMU14	1	0.93225	DMU8	1	0.62735	DMU2	1	0.55027	DMU7	1	0.45771
DMU15	1	1.63455	DMU1	1	0.66871	DMU15	1	1.23418	DMU1	1	0.56972
DMU4	0.98	0.43388	DMU7	0.947	0.3218	DMU14	1	17.971	DMU11	1	0.68462
DMU11	0.906	0.57657	DMU13	0.944	0.13124	DMU5	0.985	0.31947	DMU15	1	1.24437
DMU6	0.896	0.28298	DMU14	0.943	0.4051	DMU11	0.921	0.2745	DMU14	1	2.0849
DMU3	0.883	0.28164	DMU11	0.906	0.17515	DMU9	0.905	0.97149	DMU12	0.969	0.17444
DMU7	0.874	0.32605	DMU10	0.89	0.34217	DMU4	0.877	0.25512	DMU4	0.899	0.32244
DMU13	0.867	0.13958	DMU2	0.874	0.85998	DMU8	0.87	0.20386	DMU10	0.818	0.16313
DMU10	0.779	0.16935	DMU9	0.843	0.17572	DMU3	0.833	0.21305	DMU9	0.774	0.28765
DMU12	0.742	0.11335	DMU6	0.837	0.29614	DMU12	0.803	0.15726	DMU8	0.754	0.28786
DMU8	0.712	0.25534	DMU5	0.812	0.2938	DMU10	0.774	0.1347	DMU5	0.747	0.3701
DMU5	0.664	0.2745	DMU4	0.594	0.25039	DMU6	0.765	0.24013	DMU6	0.6	0.27103