Effects of manufacturing defects on the device failure rate

Abstract This study investigates the effect of manufacturing defects on the failure rate for a population of repairable devices and for a population of non-repairable devices. A reliability function is obtained for a random number of manufacturing defects in a device following a general distribution. We observe that for any population, the failure rate decreases if the device-to-device variability of the number of defects is large enough. Considering a case further where the defect size initially follows a linear-power-law distribution and increases at a rate that is proportional to the defect size at any instant during field operation, we show that the defect growth and defect clustering plays an important role in inducing the decreasing property in the failure rate function.

[1]  Myung Hwan Na,et al.  Optimal burn-in with random minimal repair cost , 2010 .

[2]  D. N. P. Murthy,et al.  Parametric study of sectional models involving two Weibull distributions , 1997 .

[3]  Kyungmee O. Kim,et al.  Optimal burn-in for maximizing reliability of repairable non-series systems , 2009, Eur. J. Oper. Res..

[4]  K. R. Forbes,et al.  Using time-dependent reliability fallout as a function of yield to optimize burn-in time for a 130 nm SRAM device , 2003, IEEE International Integrated Reliability Workshop Final Report, 2003.

[5]  Kyungmee O. Kim,et al.  A relation model of gate oxide yield and reliability , 2004, Microelectron. Reliab..

[6]  Barry P. Linder,et al.  Statistics of progressive breakdown in ultra-thin Oxides , 2004 .

[7]  M. Meerschaert,et al.  Parameter Estimation for the Truncated Pareto Distribution , 2006 .

[8]  Murat Tiryakioğlu,et al.  On the relationship between statistical distributions of defect size and fatigue life in 7050-T7451 thick plate and A356-T6 castings , 2009 .

[9]  Boris Vladimirovič Gnedenko,et al.  Mathematical methods in the reliability theory , 1969 .

[10]  Henry W. Block,et al.  Initial and final behaviour of failure rate functions for mixtures and systems , 2003, Journal of Applied Probability.

[11]  Adit D. Singh,et al.  Extending integrated-circuit yield-models to estimate early-life reliability , 2003, IEEE Trans. Reliab..

[12]  Dong Shang Chang.  Optimal burn-in decision for products with an unimodal failure rate function , 2000, Eur. J. Oper. Res..

[13]  Gauss M. Cordeiro,et al.  Computational Statistics and Data Analysis a Generalized Modified Weibull Distribution for Lifetime Modeling , 2022 .

[14]  T. B. Petersen.  The laws of defect-size distribution in the failure of materials , 2001 .

[15]  Zhenmin Chen.  A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function , 2000 .

[16]  P. Zarkesh-Ha,et al.  Random Yield Prediction Based on a Stochastic Layout Sensitivity Model , 2009, IEEE Transactions on Semiconductor Manufacturing.

[17]  Trevor C. Lindley,et al.  Statistical modeling of microstructure and defect population effects on the fatigue performance of cast A356-T6 automotive components , 2006 .

[18]  Ingram Olkin,et al.  Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families , 2007 .

[19]  Manoj Sachdev,et al.  Defect-Oriented Testing for Nano-Metric CMOS VLSI Circuits , 2007 .

[20]  Shey-Huei Sheu,et al.  Optimal burn-in time to minimize the cost for general repairable products sold under warranty , 2005, Eur. J. Oper. Res..

[21]  Kyungmee O. Kim.  Burn-in considering yield loss and reliability gain for integrated circuits , 2011, Eur. J. Oper. Res..

[22]  S. Loukas,et al.  A lifetime distribution with decreasing failure rate , 1998 .

[23]  Ronald E. Glaser,et al.  Bathtub and Related Failure Rate Characterizations , 1980 .

[24]  Kyungmee O. Kim,et al.  Reliability functions estimated from commonly used yield models , 2008, Microelectron. Reliab..

[25]  John C. Houghton,et al.  Use of the truncated shifted Pareto distribution in assessing size distribution of oil and gas fields , 1988 .