高质量低成本视角下的参数和容差整合设计

doi:10.16381/j.cnki.issn1003-207x.2021.1584

Abstract

Abstract:

Due to the limitation of the experimental data or the unknown random effects in the experiment， it may lead to large errors in the parameters estimation during modeling process， and a reliable quality design cannot be obtained.Therefore， the joint confidence region is constructed to quantify the uncertainty of input parameters （model parameters and parameters to be estimated in noise variables）.Secondly， according to the distribution information of noise variable and design variable tolerance， a new expected quality loss function based on the confidence region is proposed.Then from the perspective of robustness and economy， optimization object function is constructed based on the interval estimation theory， which includes the location and dispersion effects of quality loss and tolerance cost.Finally， the effectiveness of the proposed method is verified by experimental simulation and industrial example.The results show that the method simultaneously incorporates the two important uncertainty into the objective function. It not only has good robustness to the disturbance of uncertainty， but also can make a reasonable trade-off between quality loss and tolerance cost to achieve a lower total cost.

Key words: input parameter uncertainty, integrated design of parameters and tolerances, interval estimation, economic quality design

CLC Number:

F253.3

Yunxia Han,Yizhong Ma,Linhan Ouyang,Jing Xu,Guanxin Yao. Integrated Design of Parameters and Tolerances under High-quality and Low-cost Perspective[J]. Chinese Journal of Management Science, 2024, 32(8): 159-169.

Figures/Tables 10

方法	$E y ? 1$	$E y ? 2$	$V a r y ? 1$	$V a r y ? 2$
P_two ( x_c, t )	3.3173	947.9518	0.0003	5.0635
P_Para ( x_c, t )	2.8945	951.6692	0.0061	192.2338
P_Noise ( x_c, t )	0.8171	950.2291	1.8905	28.3754
P_No ( x_c, t )	5.2282	951.7802	0.1021	125.7883

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系统波动	模型	N=5		N=50
系统波动	模型	均值	标准差	均值	标准差
σ=0.5	TC_two	9.0285	3.1759	10.1087	2.8331
	TC_noise	15.4663	7.7830	12.8265	5.1158
	TC_paramete	10.6170	3.9090	11.7132	5.0364
	TC_no	23.3581	3.2231	11.4878	5.4659
σ=1	TC_two	10.4420	4.0232	13.6807	3.0535
	TC_noise	14.1366	10.3491	18.9236	5.5220
	TC_paramete	10.2309	5.6597	19.4365	4.6053
	TC_no	38.0562	9.2041	28.7739	7.1770
σ=2	TC_two	10.4264	3.5951	10.1101	3.2478
	TC_noise	20.6499	9.2949	34.7146	5.9799
	TC_paramete	13.9796	7.3827	10.8615	5.0597
	TC_no	39.3877	11.8323	34.7605	8.3423
σ=3	TC_two	10.3550	3.6350	11.2385	3.4782
	TC_noise	59.0512	11.4735	48.1652	9.8732
	TC_paramete	14.8975	6.9302	11.4515	5.9448
	TC_no	42.0063	15.4112	37.0847	14.0583
σ=4	TC_two	11.2815	3.9936	11.2246	3.7550
	TC_noise	67.9194	16.5505	42.5789	7.1289
	TC_paramete	18.1996	9.9551	12.1223	5.2274
	TC_no	87.2339	36.7507	62.8186	12.8056

模型	均值				标准差
模型	TC_two	TC_noise	TC_parameter	TC_no	TC_two	TC_noise	TC_parameter	TC_no
1	13.7278	19.7771	34.4455	42.2050	4.3806	10.7169	8.0675	12.4596
2	11.8494	21.0069	37.9097	67.3059	3.7088	12.9003	7.3785	12.2819
3	10.5158	17.0240	31.0758	53.5854	4.2750	10.2861	7.7080	11.0514
4	11.0538	19.7079	36.7221	45.5576	3.5072	10.3275	6.1530	8.8302
5	11.4662	17.2094	40.0845	50.1126	4.0890	7.0945	6.1768	10.4443
6	12.4984	20.4443	41.3782	35.6293	4.1108	9.3315	6.0060	10.8889
7	12.2015	17.7061	23.8917	68.1096	4.4474	7.7128	4.4565	8.1572
8	11.5529	19.7147	45.4982	50.4362	3.6449	9.3947	7.1898	13.1941
9	10.6276	43.1173	17.8292	55.9469	3.2123	8.0065	10.1419	11.0641
10	10.7826	20.0224	43.9458	49.9944	3.4757	10.2191	7.8870	9.6003
真实模型	7.9658				0.0574

序号	设计变量			噪声变量		质量特性
序号	x₁	x₂	x₃	z₁	z₂	y₁	y₂
1	-1	-1	1	-1	-1	4.75	1082
2	-1	-1	-1	1	-1	4.00	824
3	1	-1	-1	-1	-1	5.00	953
4	1	-1	1	1	-1	9.50	759
5	-1	-1	-1	-1	1	4.00	1163
6	-1	-1	1	1	1	5.00	839
7	1	-1	1	-1	1	3.00	1343
8	1	-1	-1	1	1	7.00	736
9	-1	1	-1	-1	-1	5.25	1027
10	-1	1	1	1	-1	5.00	836
11	1	1	1	-1	-1	3.00	1272
12	1	1	-1	1	-1	6.50	825
13	-1	1	1	-1	1	3.25	1363
14	-1	1	1	1	1	5.00	855
15	1	1	-1	-1	1	2.75	1284
16	1	1	1	1	1	5.00	851
17	0	0	0	-2	0	3.75	1283
18	0	0	0	2	0	11.00	651
19	-2	0	0	0	0	4.50	1217
20	2	0	0	2	0	4.00	982
21	0	0	0	2	-2	5.00	884
22	0	0	0	2	2	3.75	1147
23	0	-2	0	2	0	3.75	1081
24	0	2	0	2	0	4.75	1036
25	0	0	-2	2	0	4.00	1213
26	0	0	2	2	0	3.50	1103
27	0	0	0	0	0	3.50	1179
28	0	0	0	0	0	3.50	1183
29	0	0	0	0	0	4.00	1120
30	0	0	0	0	0	3.50	1180
31	0	0	0	0	0	3.00	1195

方法	( x_c, t )	I _D ( x_c, t )	I _L ( x_c, t )	C _M ( t )	TC( x_c, t )
P_two ( x_c, t )	[0 0.0039 0 0.6004 0.0079 0.0318]	7.5809e+04	4.4531e+04	67.0127	1.2041e+05
P_Para ( x_c, t )	[-1.2176 -1.1812 -0.6161 0.2098 0.0082 0.0521]	1.0960e+05	5.8960e+04	53.4222	1.6861e+05
P_Noise ( x_c, t )	[-0.9564 0.4955 -1.6797 0.4506 0.0056 0.0267]	1.1766e+05	6.2907e+04	75.2669	1.8064e+05
P_No ( x_c, t )	[-1.9995 -0.0410 -0.0217 0.9999 0.0150 0.0358]	1.2035e+05	6.4299e+04	55.8853	1.8470e+05

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Integrated Design of Parameters and Tolerances under High-quality and Low-cost Perspective

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x₁	x₂	z	y
-1	-1	-1	y₁
1	-1	-1	y₂
-1	1	-1	y₃
1	1	-1	y₄
-1	-1	1	y₅
1	-1	1	y₆
-1	1	1	y₇
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