Question 9.4: Accelerated temperature cycling of solder joints on a 256 pi...
Accelerated temperature cycling of solder joints on a 256 pin quad flat package (QFP) was carried out at a frequency of 1 cycle/45 min over the range -40 to 125^{\circ }C . The Weibull cumulative failure distribution was found to be of the form F_{s}\left(t\right)=1-\exp\left[-\left( t/42,900\right)^{1,27}\right] , where t is the time in minutes. This chip will be used in a computer, where it undergoes 1 thermal cycle per day and is exposed to \Delta T\left( u \right)=85^{\circ}C . If it is assumed that MTTF\left( u \right)\left( 85^{\circ }C \right)/MTTF\left( s \right)\left( 125^{\circ }C \right)=1.7 ,
a. What is the acceleration factor?
b. Predict the failure rate under use conditions.
c. Derive an expression for F_{u}\left( t \right).
a. Substituting in Eq. 9-36, noting that 1 cycle/45 min = 32 cycles/day,
AF=\frac{N\left(u\right)}{N\left(s\right)}=\left[\frac{f\left( u \right)}{f\left( s \right)} \right]^{1/3}\left( \frac{\Delta T\left( s \right)}{\Delta T\left( u \right)} \right)^{2}\left( \frac{MTTF\left(u\right)}{MTTF\left(s\right)} \right). (9-36)
AF=\left( 1/32 \right)^{1/3}\left( 165/85 \right)^{2}\left( 1.7 \right)=2.02b. From Eq. 4-42 and the definition of WeibuU failure rate (Eq. 4-15),
\lambda_{u}\left( t \right)=\left( 1/AF \right)^{\beta}×\lambda_{s}\left( t \right) (4-42)
\lambda\left( t \right)=\frac{\beta t^{\beta-1}}{\alpha^{\beta}}. (4-15)
\lambda_{u}\left( t \right)=\left( 1/2.02 \right)^{1.27}×\left( 1.27/42900 \right)\left( t/42900 \right)^{0.27} or 0.0000121\left( t/42900 \right)^{0.27}.c. From Eq. 4-39, F_{u}\left( t \right)=F_{s}\left( t/AF \right). Therefore,
F_{u}\left( t \right)=\left( 1/AF \right)×\left\{ AF×F_{s}\left( t/AF \right) \right\}=F_{s}\left( t/AF \right) (4-39)
F_{u}\left( t \right)=1-exp \left[ -\left( t/2.02×42,900 \right)^{1.27} \right]=1-exp\left[ -\left( t/86700 \right)^{1.27} \right].