Optimal Constant-Stress Accelerated Life Test Plans for One-Shot Devices with Components Having Exponential Lifetimes under Gamma Frailty Models
Abstract
:1. Introduction
2. Model Description
3. Optimal CSALT Plans
3.1. Asymptotic Variance
3.2. Procedure of Obtaining the Optimal CSALT Plan
4. Simulation Study
5. Eye Data from Diabetic Retinopathy Study
6. Concluding Remarks
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
ALT | accelerated life test |
CSALT | constant-stress ALT |
MLEs | maximum likelihood estimates |
probability density function | |
MSE | mean square error |
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Setting | Optimal CSALT | Total Cost | ||||||
---|---|---|---|---|---|---|---|---|
V | MSE | |||||||
0.3 | 500K | 60 | (1,0,1) | (60, 0, 24) | (325, 0, 119) | 499.2K | 0.015 | 0.017 |
0.2 | 500K | 60 | (1,0,1) | (60, 0, 24) | (329, 0, 115) | 499.2K | 0.011 | 0.011 |
0.1 | 500K | 60 | (1,0,1) | (60, 0, 24) | (332, 0, 112) | 499.2K | 0.008 | 0.008 |
0.01 | 500K | 60 | (1,0,1) | (60, 0, 24) | (335, 0, 109) | 499.2K | 0.006 | 0.006 |
0.3 | 500K | 30 | (1,0,1) | (30, 0, 30) | (277, 0, 169) | 499.6K | 0.023 | 0.025 |
0.2 | 500K | 30 | (1,0,1) | (30, 0, 30) | (297, 0, 149) | 499.6K | 0.017 | 0.017 |
0.1 | 500K | 30 | (1,0,1) | (30, 0, 30) | (313, 0, 133) | 499.6K | 0.013 | 0.013 |
0.01 | 500K | 30 | (1,0,1) | (30, 0, 30) | (325, 0, 121) | 499.6K | 0.010 | 0.010 |
0.3 | 200K | 60 | (1,0,1) | (60, 0, 24) | (125, 0, 47) | 200K | 0.039 | 0.039 |
0.2 | 200K | 60 | (1,0,1) | (60, 0, 24) | (127, 0, 45) | 200K | 0.028 | 0.029 |
0.1 | 200K | 60 | (1,0,1) | (60, 0, 20) | (128, 0, 44) | 199.2K | 0.021 | 0.022 |
0.01 | 200K | 60 | (1,0,1) | (60, 0, 24) | (129, 0, 43) | 200K | 0.016 | 0.015 |
0.3 | 200K | 30 | (1,0,1) | (30, 0, 30) | (107, 0, 66) | 199.3K | 0.060 | 0.060 |
0.2 | 200K | 30 | (1,0,1) | (30, 0, 30) | (115, 0, 58) | 199.3K | 0.045 | 0.047 |
0.1 | 200K | 30 | (1,0,1) | (30, 0, 30) | (121, 0, 52) | 199.3K | 0.034 | 0.034 |
0.01 | 200K | 30 | (1,0,1) | (30, 0, 30) | (126, 0, 47) | 199.3K | 0.027 | 0.024 |
0.3 | 100K | 60 | (1,0,1) | (60, 0, 24) | (59, 0, 22) | 99.9K | 0.083 | 0.078 |
0.2 | 100K | 60 | (1,0,1) | (60, 0, 24) | (60, 0, 21) | 99.9K | 0.059 | 0.066 |
0.1 | 100K | 60 | (1,0,1) | (60, 0, 20) | (60, 0, 21) | 99.1K | 0.044 | 0.052 |
0.01 | 100K | 60 | (1,0,1) | (60, 0, 24) | (61, 0, 20) | 99.9K | 0.033 | 0.037 |
0.3 | 100K | 30 | (1,0,1) | (30, 0, 24) | (52, 0, 31) | 99.1K | 0.127 | 0.113 |
0.2 | 100K | 30 | (1,0,1) | (30, 0, 30) | (54, 0, 28) | 99.2K | 0.094 | 0.089 |
0.1 | 100K | 30 | (1,0,1) | (30, 0, 30) | (57, 0, 25) | 99.2K | 0.072 | 0.074 |
0.01 | 100K | 30 | (1,0,1) | (30, 0, 30) | (59, 0, 23) | 99.2K | 0.057 | 0.055 |
Setting | Optimal CSALT | Revenue | |||||||
---|---|---|---|---|---|---|---|---|---|
0.3 | 500K | 60 | (1,0,1) | (60, 0, 24) | (325, 0, 119) | 29,995 | 30,114 | 1216 | 1279 |
0.2 | 500K | 60 | (1,0,1) | (60, 0, 24) | (329, 0, 115) | 30,873 | 30,937 | 1197 | 1173 |
0.1 | 500K | 60 | (1,0,1) | (60, 0, 24) | (332, 0, 112) | 31,544 | 31,504 | 1172 | 1112 |
0.01 | 500K | 60 | (1,0,1) | (60, 0, 24) | (335, 0, 109) | 32,493 | 32,462 | 1146 | 1176 |
0.3 | 500K | 30 | (1,0,1) | (30, 0, 30) | (277, 0, 169) | 28,817 | 28,854 | 1287 | 1297 |
0.2 | 500K | 30 | (1,0,1) | (30, 0, 30) | (297, 0, 149) | 29,815 | 29,777 | 1284 | 1271 |
0.1 | 500K | 30 | (1,0,1) | (30, 0, 30) | (313, 0, 133) | 30,863 | 30,801 | 1277 | 1265 |
0.01 | 500K | 30 | (1,0,1) | (30, 0, 30) | (325, 0, 121) | 31,848 | 31,846 | 1266 | 1251 |
0.3 | 200K | 60 | (1,0,1) | (60, 0, 24) | (125, 0, 47) | 11,618 | 11,641 | 757 | 728 |
0.2 | 200K | 60 | (1,0,1) | (60, 0, 24) | (127, 0, 45) | 11,958 | 11,918 | 745 | 755 |
0.1 | 200K | 60 | (1,0,1) | (60, 0, 20) | (128, 0, 44) | 12,601 | 12,560 | 734 | 715 |
0.01 | 200K | 60 | (1,0,1) | (60, 0, 24) | (129, 0, 43) | 12,583 | 12,565 | 713 | 714 |
0.3 | 200K | 30 | (1,0,1) | (30, 0, 30) | (107, 0, 66) | 11,173 | 11,176 | 801 | 834 |
0.2 | 200K | 30 | (1,0,1) | (30, 0, 30) | (115, 0, 58) | 11,563 | 11,586 | 799 | 799 |
0.1 | 200K | 30 | (1,0,1) | (30, 0, 30) | (121, 0, 52) | 11,965 | 11,986 | 795 | 807 |
0.01 | 200K | 30 | (1,0,1) | (30, 0, 30) | (126, 0, 47) | 12,352 | 12,393 | 789 | 809 |
0.3 | 100K | 60 | (1,0,1) | (60, 0, 24) | (59, 0, 22) | 5472 | 5471 | 519 | 539 |
0.2 | 100K | 60 | (1,0,1) | (60, 0, 24) | (60, 0, 21) | 5632 | 5629 | 511 | 510 |
0.1 | 100K | 60 | (1,0,1) | (60, 0, 20) | (60, 0, 21) | 5935 | 5936 | 504 | 514 |
0.01 | 100K | 60 | (1,0,1) | (60, 0, 24) | (61, 0, 20) | 5927 | 5915 | 490 | 507 |
0.3 | 100K | 30 | (1,0,1) | (30, 0, 24) | (52, 0, 31) | 5615 | 5573 | 560 | 572 |
0.2 | 100K | 30 | (1,0,1) | (30, 0, 30) | (54, 0, 28) | 5474 | 5500 | 550 | 551 |
0.1 | 100K | 30 | (1,0,1) | (30, 0, 30) | (57, 0, 25) | 5665 | 5657 | 547 | 534 |
0.01 | 100K | 30 | (1,0,1) | (30, 0, 30) | (59, 0, 23) | 5840 | 5870 | 542 | 559 |
Juvenile | Adult | |||
---|---|---|---|---|
Mean age | 10.21 | 35.30 | ||
Treated eye | Untreated eye | Treated eye | Untreated eye | |
Mean time to blindness | 36.48 | 33.33 | 42.16 | 30.85 |
Patient | (months) | K |
---|---|---|
Juvenile | 60 | 80 |
Adult | 60 | 120 |
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Ling, M.-H. Optimal Constant-Stress Accelerated Life Test Plans for One-Shot Devices with Components Having Exponential Lifetimes under Gamma Frailty Models. Mathematics 2022, 10, 840. https://doi.org/10.3390/math10050840
Ling M-H. Optimal Constant-Stress Accelerated Life Test Plans for One-Shot Devices with Components Having Exponential Lifetimes under Gamma Frailty Models. Mathematics. 2022; 10(5):840. https://doi.org/10.3390/math10050840
Chicago/Turabian StyleLing, Man-Ho. 2022. "Optimal Constant-Stress Accelerated Life Test Plans for One-Shot Devices with Components Having Exponential Lifetimes under Gamma Frailty Models" Mathematics 10, no. 5: 840. https://doi.org/10.3390/math10050840
APA StyleLing, M.-H. (2022). Optimal Constant-Stress Accelerated Life Test Plans for One-Shot Devices with Components Having Exponential Lifetimes under Gamma Frailty Models. Mathematics, 10(5), 840. https://doi.org/10.3390/math10050840