Step-stress accelerated degradation test planning based on Wiener process with correlation

Figures & data

Table 1. MLEs and AIC of two different Wiener process models for the LEDs' data.

	a	b			β		AIC
		1.3035	12,819.21	–	1.4916	1594.93
		2.3262	–		1.4445	1502.81

Table 2. Optimal two-level SSADT plans under different .

						Total cost
1000	4	10	19	15	699.49	992.8
1500	6	11	25	19	435.58	1495.6
2000	8	11	31	24	324.72	2000.0
2500	10	13	32	25	261.53	2491.6
3000	12	13	36	29	219.20	2996.0

Table 3. Optimal three-level SSADT plans under different .

							Total cost
1000	4	10	21	1	12	648.63	992.8
1500	6	12	26	1	14	417.92	1494
2000	8	11	34	1	14	310.55	2000
2500	10	16	30	1	18	246.76	2496.4
3000	11	16	37	1	22	205.86	2999

Table 4. Optimal plans under various combination of .

4%	2%	8%	2%	6	11	26	18	510.42	4674.32
4%	0	0	0	6	11	26	18	653.51	5565.53
4%				6	12	24	17	842.74	6675.59
0	2%	0		6	11	24	20	568.85	4467.13
0	0		2%	6	11	25	19	331.53	3236.26
0		8%	0	6	11	24	20	442.69	3749.21
	2%		0	6	8	29	27	282.59	2555.69
	0	8%		6	11	22	22	372.93	2942.87
		0	2%	6	8	30	26	224.02	2170.88
0	0	0	0	6	11	25	19	435.58	3775.96

Table 5. Optimal plans under various combination of and with .

		6	11	25	19	435.58
		4	1	16	225	1302.41
		5	1	8	183	2976.79
		14	1	3	21	5649.51
		6	11	23	21	450.32
		4	1	13	228	1618.30
		7	1	5	120	4464.34
		6	8	24	32	482.67
		5	1	9	182	2530.13
		5	6	27	52	692.90

Figure 1. Plots of the trends revealed by Tabel 5.

Table 6. A stability analysis for the optimal SSADT plan with .

	12.9266	1.3080	123.04	1.4915	3804.08
	(0.5194)^b	(0.1208)	(37.19)	(0.0697)	(300.66)	224.28
	12.9571	1.3073	120.40	1.4958	3793.05
	(0.5237)	(0.1187)	(38.20)	(0.0702)	(295.78)	220.58
	12.9367	1.3065	118.57	1.4916	3795.13
	(0.4810)	(0.1125)	(33.34)	(0.0637)	(263.50)	219.20
	12.9507	1.3103	118.67	1.4951	3793.89
	(0.4617)	(0.1079)	(32.24)	(0.0605)	(259.48)	222.90
	12.9534	1.3089	120.20	1.4953	3800.73
	(0.4668)	(0.1112)	(36.43)	(0.0601)	(259.36)	223.39
True value	12.9156	1.3097	112.98	1.4906	3775.96

^aTS denotes the theoretical standard deviation of .

^bThe value in parentheses is the corresponding RMSE of the estimated parameter.