## 4 Numerical Example
### Subsystem Division Based on Failure Decoupling of CNC Machine Tool
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of the CNC** & **Module Failure** & **Number of the CNC** & **Module Failure** \\
**Machine Tool** & & **Machine Tool** & **The link of the machine tool** \\ \hline \multirow{4}{*}{1} & Overmuch wear of the belt & & There is a taper in the head of the machine tool \\  & Runaway speed & & Water is unable to flow into the cooling pump \\  & Much noise of the hydraulic motor & 9 & The lathe dose not run after programming \\  & Noise of the main axis is abnormal & & The rotation of the main shaft is unstable \\  & The tool holder cannot rotate & & Bad lubrication \\ \hline \multirow{4}{*}{2} & Water leakage & & Loss of coordinate data after power failure \\  & Loose of the protective cover & & No input signal \\  & Hydraulic chuck does not work & 10 & The knife holder cannot change the knife \\  & The crumbs cannot be ruled out & & Bad cooling of the air-conditioning \\  & The monitor screen is not bright & & A short journey of the claw \\ \hline \multirow{4}{*}{3} & Cooling water pump tripping & & Z-axis stop suddenly \\  & Oil filling pipe burst & & No Lubricating oil on the guide way \\  & The main spindle does not work & 11 & Low accuracy of the hydraulic chuck \\  & No electricity can flow into the & & X-axis stop suddenly \\  & machine tool & & The torl holder is not located accurately \\  & The tool holder is not located accurately & & The artifact has a convex plane \\ \hline \multirow{4}{*}{4} & The lathe has no input signal & & There is motor noise when the X-axis moves \\  & The tool vibrates when the workpiece & & The bed saddle does not move with the input of \\  & is processed & & location instruction \\  & The noise of the main motor is abnormal & & The fuse is burned out frequently \\  & The air conditioner does not work & & X-axis Slide down after power off \\  & The oil pipe ruptures & & The servo alarm sounds the alarm \\ \hline \multirow{4}{*}{5} & Automatic power off of the CNC & & The oil pipe ruptures \\  & machine tools & & Black lines appear on the monitor \\  & The tool will rotate automatically with & & \\  & the electricity & & The hydraulic chuck pressure cannot be raised \\  & The knife dish shakes & & The rotation of the main shaft is unstable \\  & The CNC machine tools do not move & & The processed threads are not qualified \\  & with the hand-cranking & & The Stretch Speed of the stage is too slow \\ \hline \multirow{4}{*}{6} & The hydraulic chuck does not work & & The machined artifacts have a taper \\  & Water leakage of the machine tools & & The threading are not standard \\  & The main transformer was burnt & 14 & Crumbs cannot be ruled out quickly \\  & The voltage of the system drops sharply & & The oil pipe ruptures \\  & after changing the knife & & There is no brake when the main shaft \\  & The speed display is not accurate & & stops turning \\ \hline \multirow{4}{*}{7} & Protective glass crushing & & The program does not run after the change of \\  & The knife cannot stop turning & & the knife \\ \cline{1-1}  & The finished arc is not qualified & & A blank screen of the computer’s display settings \\ \cline{1-1}  & The hydraulic system cannot start & & The size of the sample workpiece is inconsistent \\ \cline{1-1}  & A blank screen of the computer’s & & The turning operation of Z-axis is not standard \\ \cline{1-1}  & display settings & & The blade cannot be accurately positioned \\ \hline \multirow{4}{*}{8} & X-axis can not move to the zero point & & No electric current can flow into the CNC \\  & Overmuch wear of the belt & & machine tools \\ \cline{1-1}  & Cutting vibration & & The workpiece processed have crow’s feet \\ \cline{1-1}  & The main shaft does not run after the & & The revolving speed of the X-axis is unstable \\ \cline{1-1}  & system is motivated & & Cutting vibration \\ \cline{1-1}  & The workpiece processed have crow’s feet & & Knives cannot be replaced at will \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data about module failures for 16 computer numerically controlled (CNC) machine tools.