## 3 Case Study of Boiler System Used in Textile Process Industries
Table 11 shows the multiplication matrix of \(N_{ij}\) and \(w_{j}\). * **Step 11:** Calculate the criticality index for all components, and finally, ranks are given. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline
**Component** & **Failure Mode** & **Failure Cause** & **Failure Effect** & **SV** & **O** & **D** & **M** & **S** & **L** \\ \hline \multirow{4}{*}{Rust of tank} & The strainer failure & The strainer is clogged & Pump fails & 0.8432 & 0.6967 & 0.9862 & 1.0007 & 0.7326 & 0.859 \\ \cline{2-9}  & The strainer failure & The strainer is clogged & Pump fails & 0.8432 & 0.6967 & 0.9862 & 1.0007 & 0.7326 & 0.859 \\ \cline{2-9}  & Rust of tank & A lot of sediment in the water & Failure of mechanical seal & & & & & & \\  & the water & and cause a leak & & & & & & & \\ \hline \multirow{4}{*}{condensate is too hot for the pump} & condensate is too hot for & & Failure of the & & & & & & \\  & the pump & steam traps fail & pump’s impeller & 0.9122 & 0.6777 & 1.0018 & 0.9993 & 0.6648 & 0.9224 \\ \cline{2-9}  & mechanical seal failure & Pump leakage & Pump failure & 0.8323 & 0.7919 & 0.8231 & 0.7422 & 0.6310 & 0.8216 \\ \cline{2-9}  & Electrical failure of the pump & The voltage supplied to the pump is not correct. & Failure of circuit breaker and winding burns & 0.776 & 0.7457 & 0.9337 & 0.7414 & 0.6864 & 1.0008 \\ \cline{2-9}  & Impeller Failure & Impeller is clogged & Mechanical failure of the pump & & & & & & \\ \hline \multirow{4}{*}{Feed Water} & \multirow{4}{*}{Shaft failure} & Overload work, & & & & & & & \\  & misalignment, corrosion & & & & & & & & \\  & provide flow & & & & & & & & \\ \hline \multirow{4}{*}{Pump} & Lubrication failure & Insfficient flow & 0.8292 & 0.8224 & 0.7782 & 0.6915 & 0.8159 & 0.8547 \\ \cline{2-9}  & Improper mountings & Pump vibrates or is noisy. & 0.8308 & 0.7471 & 0.8178 & 0.7673 & 0.8657 & 0.8833 \\ \cline{2-9}  & Abnormal load on & Pump failure & 0.6683 & 0.8033 & 0.7615 & 0.7327 & 0.9098 & 0.7811 \\ \cline{2-9}  & Contamination present & Pump failure & 1.0022 & 0.7383 & 0.8303 & 0.7147 & 0.8266 & 0.8959 \\ \hline Pump housing voltage & Cavitation, corrosion & & & & & & & & \\ \cline{2-9}  & damaged/Volute erosion & and vibration & Leak in the pump body & 0.8041 & 0.8899 & 0.9628 & 0.7252 & 0.7436 & 0.8038 \\ \hline \multirow{4}{*}{Pump low efficiency} & Electric motor failed & Low flow warming & 0.850 & 0.8997 & 0.9055 & 0.7476 & 0.8426 & 0.7204 \\ \cline{2-9}  & Low discharge pressure & 0.9421 & 0.9242 & 0.8552 & 0.8283 & 0.7759 & 0.9231 \\ \hline Reduction in pump pressure & Pump cavitation & Pump noise and vibration & 0.7446 & 0.9017 & 0.8243 & 0.7198 & 0.6560 & 0.9690 \\ \hline \end{tabular}
\end{table} 
Table 10: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  
The criticality index values for all the failure modes are estimated using Equation (7). Finally, the criticality index of the components can be estimated by summing the criticality index values of all the failure modes of the component. A similar analysis was carried out for all 124 failure modes of the25 selected boiler system components. Finally, the criticality ranks of the components are given based on their criticality index values, and the results of all 25 selected components of the boiler system are shown in Table 12. There are several root causes for some of the failure modes. However, prominent root causes are considered for the study. The criticality index values and their ranks for a few selected boiler sub-systems are also presented in Table 12.