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 °C. The Weibull cumulative failure distribution was found to be of the form Fs(t) = 1 - exp[-(t/42,900)^1.27], where t is the time in

Question

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 °C. The Weibull cumulative failure distribution was found to be of the form [latex]F_s(t)=1-exp[-(t/42,900)^{1.27}][/latex] , 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 ΔT(u) = 85 °C. If it is assumed that MTTF(u)(85 °C)/MTTF(s)(125 °C) = 1.7.
1. What is the acceleration factor?
2. Predict the failure rate under use conditions.
3. Derive an expression for [latex]F_u (t)[/latex].

Accepted Answer

1. Substituting in Eqn (9.38),

[latex]AF=\frac{N(u)}{N(s)}=\left[\frac{f(u)}{f(s)} ight]^{1/3}\left(\frac{\Delta T(s)}{\Delta T(u)} ight) ^2\left(\frac{MTTF(u)}{MTTF(s)} ight) [/latex]

noting that 1 cycle/45 min = 32 cycles/day, [latex]AF = (1/32) ^{1/3} (165/85)^{ 2} (1.7) = 2.02[/latex].
2. From Eqn 4.42

[latex]Weibull \ \ \ \ \lambda_u=(1/AF)^\beta imes \lambda_s(t)[/latex]

and the definition of Weibull failure rate (Eqn 4.15),

[latex]\lambda(t)=\frac{\beta t^{\beta-1}}{\alpha^\beta}[/latex]
[latex]\lambda_u(t)=(1/2.02)^{1.27} imes(1.27/42,900)(t/42,900)^{0.27} \ or \ 0.0,000,121(t/42,900)^{0.27} [/latex].
3. From Eqn 4.39,

[latex]F_u(t)=(1/AF) imes\left\{AF imes F_s(t/AF) ight\} =F_s(t/AF)[/latex]
[latex]F_u(t)=F_s(t/AF)[/latex].Therefore,[latex]F_u(t)=1-exp[-(t/2.02 imes 42,900)^{1.27}]=1-exp[-(t/86,700)^{1.27}][/latex].

Question 9.4: Accelerated temperature cycling of solder joints on a 256 pi...

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