# Safety Maintains Lean Sustainability and Increases Performance through Fault Control
## 4 Failure Mode and Effect Forecasting (FMEF) Formulation  
Sustainable Lean is equivalent to system reliability \(R(t)\) against fault occurrence, availability, and maintainability, which are important factors to guarantee the safety level. Sustainable Lean is affected by faults and malfunctions occur in the workplace. Therefore, the prediction and diagnosis of the faults are the core of this paper. Faults related to deviation behavior according to their form whether systematic or random, time behavior appears from draft to permanent path through noise and extent appears in local or global VSM. The Lean sustainability of many identical activities is defined by Equation (1). \[\textit{Fault Occurrence}=\ 1-R(t)=\omega=1-\frac{fault\ \textit{free activities}}{\textit{number of all activities at a certain \ function}} \tag{1}\]  
The fault occurrence rate defined as the instantaneous rate of malfunction or unplanned downtime at emergency case is defined by the Equation (2):  
\[\frac{d_{n}}{d_{t}}=\lambda_{t}=\frac{1}{\#of\ \textit{function activities}}\Bigg{(}\frac{\#of\ \textit{faults}}{\textit{time interval}}\Bigg{)} \tag{2}\]  
The severity \(S_{v}\) level proportion to a maintenance level (the repairability consuming time), whether planned or not as illustrated in Figure 6 to repair specific fault, is defined by the Equation (3) as follows:  
\[S_{v}=E\{T_{R}\}=\underset{N\rightarrow\infty}{\lim}\frac{1}{N}\sum_{i=1}^{N} T_{Ri} \tag{3}\]  
where \(T_{Ri}\) is time to repair the malfunction. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Lean Six Sigma (LSS) Roadmap**} \\ \hline  & \multicolumn{2}{c}{Define and Measures} & Analysis & Improve & Control \\ \hline Identify & \multicolumn{1}{c}{Project charter} & VSM & \begin{tabular}{c} Spaghetti \\ diagram for \\ functions \\ \end{tabular}  & \begin{tabular}{c} Poka-Yoke \\ \end{tabular}  & \begin{tabular}{c} Proficiency \\ level \\ \end{tabular}  \\ \hline Analysis & \multirow{3}{*}{ \begin{tabular}{c} Function/process/activities \\ map \\ \end{tabular}  } & \multirow{3}{*}{Run charts} & Regression & \ \begin{tabular}{c} Risk analysis \\ analysis \\ \end{tabular}  & \begin{tabular}{c} Dashboard \\ Prioritization \\ matrix \\ \end{tabular}  & Audit plans \\ \cline{2-6} \  
The concept of Ideality is introduced in the methodology of creative problem solving, which is very close to the value in value analysis. One variant is known as the \"Theory of Inventive Problem Solving\". While stipulating that a proposed framework has the main \"VA activity function\". The delivery of it is necessarily accompanied by loss functions (i.e., NNVA and NVA costs and time) that can be controlled via the proposed roadmap embeds with an effective framework. The better is the framework the fewer are the number of the loss functions (i.e., any undesired costs or downtimes) that addressed via ideality index_Py\({}_{i}\)_ as defined by the Equation (4). This value is considered a seed of using the Neural Networks of the optimization stage of fault tracking and forecasting based on specific scenarios (_i_). \[Py_{i}=\frac{\text{RPN}\times\sum_{i}(\text{VA})_{i}}{\sum_{i}(\text{NNVA})_{ i}+(\text{NVA})_{i}}=\frac{\sum_{i}(\text{VA}_{\text{Costs},\;time})_{i}}{\sum_{i}( \text{NNVA}_{\text{Costs},\;time})_{i}}=\frac{\text{RPN}\times\sum_{i}(\text{ VA}_{\text{Costs},\;time})_{i}}{\sum_{i}(\text{CoPP})_{i}} \tag{4}\]  
The question should be: how to execute the VA in a way that is not minimalist (NNVA). An Ideality defined by Equation (5) indicates the effectiveness of the proposed framework is calculated using the ratio of the number of valid causes to the total number of potential causes and averaged over the tackling scenarios for data collected in Tables 9 and 10. \[\textit{Ideality}(\text{HBL}_{VA})_{i}=\frac{1}{N}\sum_{i=1}^{i}\frac{Py_{i}}{ C_{i}\times n_{i}}\times w_{i} \tag{5}\]  
where  
\(N\) = number of correction scenarios investigated to reduce losses and faults opportunities in certain activity.