Statistical inference of reliability for a K-out-of-N: G system with switching failure under Poisson shocks

Figures & data

Table 1. Case 1: MTTF with different parameters ${\lambda }_a$ and ${\lambda }_b$.

$n$	${\lambda }_a$	${\lambda }_b=0.02$	${\lambda }_b=0.04$	${\lambda }_b=0.06$	${\lambda }_b=0.08$	${\lambda }_b=0.10$
	0.02	66.3193	48.2686	38.2834	31.4065	27.0813
	0.04	40.5532	33.4304	27.9653	24.3838	21.3521
20	0.06	29.3949	25.6585	22.3474	19.8548	17.7616
	0.08	23.3466	20.5124	18.4310	16.4604	15.3443
	0.10	19.2287	17.3226	15.5825	14.5111	13.4224
	0.02	66.4891	49.1402	38.8552	31.9187	27.2536
	0.04	41.2020	33.7399	28.2266	24.6389	21.6927
40	0.06	29.8685	25.6951	22.5258	19.9999	18.0393
	0.08	23.4344	20.8934	18.5713	16.9197	15.4005
	0.10	19.2233	17.3667	15.8467	14.5965	13.5127
	0.02	66.7041	49.5959	38.8698	32.0381	27.3628
	0.04	41.5149	33.8023	28.5466	24.6800	21.7475
60	0.06	30.0807	25.7095	22.4824	19.9928	18.0856
	0.08	23.2127	20.7820	18.6734	16.9283	15.4993
	0.10	19.2724	17.3828	15.8293	14.6386	13.6491
	0.02	67.4707	49.2862	38.8542	32.1585	27.2466
	0.04	41.4846	33.8371	28.6121	24.8947	21.8146
80	0.06	29.9387	25.7964	22.5858	20.1215	18.1356
	0.08	23.3843	20.8197	18.6243	16.9655	15.5668
	0.10	19.3325	17.4879	15.9302	14.6666	13.5851
	0.02	67.6106	49.4471	38.9872	32.2813	27.4572
	0.04	41.4937	33.7832	28.6858	24.8080	21.8087
100	0.06	30.0497	25.8933	22.6619	20.1709	18.2224
	0.08	23.4872	20.8553	18.7317	16.9989	15.5638
	0.10	19.2998	17.4309	15.8992	14.6278	13.6277
	0.02	67.7838	49.6576	39.1625	32.3239	27.5165
	0.04	41.6785	34.0674	28.7946	24.9293	21.9758
True	0.06	30.0802	25.9123	22.7516	20.2740	18.2805
	0.08	23.5298	20.9037	18.8004	17.0789	15.6443
	0.10	19.3215	17.5164	16.0168	14.7517	13.6704

Table 2. Case 2: MTTF with different parameters ${\lambda }_a$ and ${\lambda }_b$.

$n$	${\lambda }_a$	${\lambda }_b=0.02$	${\lambda }_b=0.04$	${\lambda }_b=0.06$	${\lambda }_b=0.08$	${\lambda }_b=0.10$
	0.02	71.3434	53.5257	43.0248	36.1888	31.1768
	0.04	42.8080	35.6201	30.7101	26.8521	23.9329
20	0.06	30.5650	26.8527	23.6848	21.5014	19.4837
	0.08	23.6452	21.4061	19.5342	17.9598	16.6084
	0.10	19.6389	17.9654	16.4747	15.2320	14.3036
	0.02	72.1648	54.4767	43.9479	36.6323	31.4713
	0.04	43.1231	36.0099	31.0028	27.4702	24.3018
40	0.06	30.6741	27.1006	24.2454	21.8293	19.7547
	0.08	24.0802	21.5858	19.7146	18.0369	16.6627
	0.10	19.4457	18.0438	16.7400	15.4423	14.5115
	0.02	72.0168	54.8743	43.9760	36.9447	31.8516
	0.04	43.5128	36.2425	31.2593	27.3968	24.4605
60	0.06	31.0299	27.1933	24.2945	21.8526	19.9589
	0.08	24.0722	21.6064	19.7824	18.2767	16.9305
	0.10	19.7927	18.0215	16.7331	15.5846	14.5762
	0.02	72.6431	54.6920	44.0991	36.6622	31.7637
	0.04	43.1634	36.4578	31.3398	27.4294	24.6660
80	0.06	31.0303	27.2206	24.2918	21.9129	20.0724
	0.08	24.1279	21.6639	19.7943	18.2275	16.8500
	0.10	19.7152	18.1301	16.7525	15.6053	14.5848
	0.02	72.6174	54.8024	44.1801	36.9918	31.7781
	0.04	43.2944	36.3479	31.4296	27.5397	24.6135
100	0.06	30.9124	27.1658	24.2275	21.8587	20.0653
	0.08	24.0407	21.8375	19.8635	18.2533	16.8307
	0.10	19.6664	18.0385	16.7538	15.6131	14.6210
	0.02	72.7120	55.1405	44.3826	37.1256	31.9026
	0.04	43.4849	36.5550	31.5171	27.6923	24.6909
True	0.06	31.0083	27.3242	24.4155	22.0620	20.1195
	0.08	24.0934	21.8119	19.9209	18.3288	16.9704
	0.10	19.6997	18.1491	16.8221	15.6741	14.6714

Figure 1. Case 1: Coverage rate of the 95% confidence interval of the MTTF.

Figure 2. Case 2: Coverage rate of the 95$\mathrm{\%}$ confidence interval of the MTTF.

Table 3. Case 1: ML and SD.

n	20	30	50	100	300	500	700	1000
ML	21.1661	17.5473	13.6808	9.6781	5.6018	4.3411	3.6751	3.0714
SD	3.4699	2.1647	1.4283	0.6667	0.2193	0.1347	0.0970	0.0677

Table 4. Case 2: ML and SD.

n	20	30	50	100	300	500	700	1000
ML	23.3519	19.2591	15.0537	10.6336	6.1703	4.7861	4.0379	3.3802
SD	3.5426	2.4887	1.4983	0.7956	0.2484	0.1523	0.1102	0.0738

Figure 3. Case 1: Power function value of the test.

Figure 4. Case 2: Power function value of the test.

Figure 5. Case 1: Type I error rate of the test.

Figure 6. Case 2: Type I error rate of the test.