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Burn‐in Time and Estimation of Change‐Point with Weibull‐Exponential Mixture Distribution *
Author(s) -
Chou Kuocheng,
Tang Kwei
Publication year - 1992
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1992.tb00429.x
Subject(s) - weibull distribution , warranty , burn in , exponential distribution , product (mathematics) , statistics , exponential function , point estimation , estimation , sample (material) , econometrics , distribution (mathematics) , failure rate , sensitivity (control systems) , shape parameter , mathematics , reliability engineering , economics , engineering , mathematical analysis , chemistry , geometry , management , chromatography , electronic engineering , political science , law
Many industrial products have three phases in their product lives: infant‐mortality, normal, and wear‐out phases. In the infant‐mortality phase, the failure rate is high, but decreasing; in the normal phase, the failure rate remains constant; and in the wear‐out phase, the failure rate is increasing. A burn‐in procedure may be used to reduce early failures before shipping a product to consumers. A cost model is formulated to find the optimal burn‐in time, which minimizes the expected sum of manufacturing cost, burn‐in cost, and warranty cost incurred by failed items found during the warranty period. A mixture of Weibull hyperexponential distribution with shape parameter less than one and exponential distribution is used to describe the infant‐mortality and the normal phases of the product life. The product under consideration can be either repairable or non‐repairable. When the change‐point of the product life distribution is unknown, it is estimated by using the maximum‐likelihood estimation method. The effects of sample size on estimation error and the performance of the model are studied, and a sensitivity analysis is performed to study the effects of several parameters of the W‐E distribution and costs on the optimal burn‐in time.