## 2 Parametric Accelerated Life Testing for Mechanical Product
### Generalized Time to Failure Model and Sample Size Equation for Parametric ALT  
Mechanical systems have subsystems that transmit (generated) power from one component to another through various mechanisms in the system. If there is a design flaw in a component that has an insufficient strength (or stiffness) during repeated loading of the component, it can fail prematurely before achieving its expected lifetime. In reproducing the field failure by parametric ALT, a designer must understand the loading experienced in the field and failure process before being able to both redesign the product shape and change materials selection to achieve the desired reliability of the product. The system must survive the minimum repeated loads in its lifetime so that it can attain the objective reliability (or lifetime) (Figure 4). The primary goal for reliability testing is determining how early the probable failure mode might be obtained in the process. A failure model that connects the relevant coefficients must be derived. That is, the life-stress (LS) model, which includes stresses \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Field Data**} & \multicolumn{4}{c}{**Expected Reliability**} & \multicolumn{2}{c}{**Targeted Reliability**} \\ \cline{2-10}
**Modules** & **Failure Rate per Year,** & **BX Life,** & **Failure Rate per Year,** & **BX Life,** & **Failure Rate per Year,** & **BX Life,** \\  & \(\lambda\) **(\%/Year)** & \(L_{B}\) **(Year)** & & \(\lambda\) **(\%/Year)** & \(L_{B}\) **(Year)** & \(\lambda\) **(\%/Year)** & \(L_{B}\) **(Year)** \\ \hline A & 0.35 & 2.9 & Same & \(\times 1\) & 0.35 & 2.9 & 0.10 & 10 (BX = 1.0) \\ B & 0.24 & 4.2 & Newly & \(\times 5\) & 1.20 & 0.83 & 0.10 & 10 (BX = 1.0) \\ C & 0.30 & 3.3 & Same & \(\times 1\) & 0.30 & 3.33 & 0.10 & 10 (BX = 1.0) \\ D & 0.31 & 3.2 & Altered & \(\times 2\) & 0.62 & 1.61 & 0.10 & 10 (BX = 1.0) \\ E & 0.15 & 6.7 & Altered & \(\times 2\) & 0.30 & 3.33 & 0.10 & 10 (BX = 1.0) \\ Others & 0.50 & 10.0 & Same & \(\times 1\) & 0.50 & 10.0 & 0.50 & 10 (BX = 5.0) \\ Product & 1.9 & 2.9 & - & - & 3.27 & 0.83 & 1.00 & 10 (BX = 10) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Complete ALT scheme of mechanical system such as refrigerator. Figure 4: Fatigue failure on the product produced by repeated load and design defects. Figure 3: Parameter diagram of drawer system. and reaction parameters, may clarify numerous failures such as fatigue on the structure. Product failure appears from the emergence of microscopic material imperfections when repetitively subjected to a varying compression and tensile loading under the consumer usage. A life-stress model may be determined from such a viewpoint. Linear transport processes can be expressed as follow:  
\[J=LX \tag{10}\]  
where \(J\) is a flux vector that is associated with some transport property such as mass, momentum, energy, charge, etc. Similarly, \(X\) is defined as a (driving or thermodynamic) force that is associated with a disequilibrium in some physical property, such as gradients of concentration, fluid velocity, temperature, electrical potential, etc. \(L\) is a phenomenological transport coefficient, which makes a connection between fluxes and forces. Transport processes in essence are dissipative when happening in some physical system, which begin to form the system in equilibrium when any net transport comes to stop (Table 2). For example, when an electric magneto-motive force, \(\xi\), is applied, the impurities in materials, generated by electronic motion, easily migrate as the levels of junction energy are lessened. The processes for evaluating solid-state diffusion of impurities in a silicon can be summarized as follows: (1) electro-migration-induced voiding; (2) build-up of chloride ions; (3) trapping of electrons or holes.