diff --git a/docs/Availability Modelling.md b/docs/Availability Modelling.md index 0fa9dd2..7dee010 100644 --- a/docs/Availability Modelling.md +++ b/docs/Availability Modelling.md @@ -12,8 +12,7 @@ TBD | Performance Intensity | $j_p$ | The intensity of the performance, rough indicator of the impact of a performance on the reliability of certain components | | Performance Frequency | $p_f$ | The average amount of performances per month. It can be used along side **maintenance time between performance**, and **technician availability** to compute the interruption percentage. **SIMULATION ONLY** | | Technician Availability | $A_{tech}$ | The average amount of hours a technician/luthier is available to fix any issues an artist can’t fix with their instrument per month. **SIMULATION ONLY** | -| Technician Turnaround | $t_{tech}$ | The average amount of business days it takes for the technician/luthier to return the instrument to the artist/musician. **SIMULATION ONLY** - | +| Technician Turnaround | $t_{tech}$ | The average amount of business days it takes for the technician/luthier to return the instrument to the artist/musician. **SIMULATION ONLY** | ## Model Inputs | **Inputs** | **Symbol** | **Description** | @@ -28,15 +27,15 @@ TBD ### 1. Computing MTBF and failure rate of T-Stick -To compute the Practice interruption rate we must first compute the failure rate of the T-Stick ($$ \lambda_{tstick}$$). We do this by adding the failure rate of each component. +To compute the Practice interruption rate we must first compute the failure rate of the T-Stick ($ \lambda_{tstick}$). We do this by adding the failure rate of each component. -$$$ +$$ \begin{equation} \lambda_{tstick} = \lambda_{esp32} + \lambda_{fsr}+\lambda_{imu}+\lambda_{button}+\lambda_{capsense}+\lambda_{resistor}+\lambda_{touchsensor}+\lambda_{battery}+\lambda_{connectors} \end{equation} -$$$ +$$ -where $$\lambda_i$$ is the failure rate of component *i*. +where $\lambda_i$ is the failure rate of component $i$. The failure rates for several components such as: @@ -51,78 +50,78 @@ can be estimated using a combination of the [FIDES reliability prediction too](h We compute the MTBF of the t stick by taking the reciprocal of the failure rate. -$$$ +$$ \begin{equation} MTBF_{tstick} = \frac{1}{\lambda_{tstick}} \end{equation} -$$$ +$$ ### 3. Compute Mean Performances between failure (MPBF) -We can then compute the mean performances between failure ($$MTBF_{tstick}$$) by dividing the $$MTBF_{tstick}$$ by the **performance time (**$$t_P$$) +We can then compute the mean performances between failure ($MTBF_{tstick}$) by dividing the $MTBF_{tstick}$ by the performance time ($t_P$) -$$$ +$$ \begin{equation} MPBF = \frac{MTBF_{tstick}}{t_p} \end{equation} -$$$ +$$ ### 4. Compute PIR -We calculate the practice interruption rate by taking the reciprocal of $$MPBF$$. +We calculate the practice interruption rate by taking the reciprocal of $MPBF$. -$$$ +$$ \begin{equation} PIR = \frac{1}{MPBF} \end{equation} -$$$ +$$ -Using Eq.5, Eq.6 and Eq.7 we can simplify the PIR expression. +Using Eq.3 and Eq.6 we can simplify the PIR expression. -$$$ +$$ \begin{align*} PIR &= t_p(\frac{1}{MTBF_{tstick}}) \tag{Using Eq.3}\\ &= t_p(\lambda_{tstick}) \tag{Using Eq.6} \\ \end{align*} -$$$ +$$ Hence an alternative expression for the Practice Interruption rate is: -$$$ +$$ \begin{equation} PIR = t_p(\lambda_{tstick}) \end{equation} -$$$ +$$ In simple words the **Practice Interruption Rate** is the: -$$$ +$$ \text{average performance time} \times \text{failure rate of the t-stick} -$$$ +$$ ## Compute Performance/Maintenance Ratio (PMR) -Computing the Performance/Maintenance Ratio (PMR) is a matter of taking the $$MTBF_{tstick}$$ computed in the PIR model and dividing that by the average maintenance time. +Computing the Performance/Maintenance Ratio (PMR) is a matter of taking the $MTBF_{tstick}$ computed in the PIR model and dividing that by the average maintenance time. ### Computing Average Maintenance time ($$T_m$$) -To compute average maintenance time we consider the mean time to repair ($$MTTR_c$$) of each component and the failure rate of each component ($$\lambda_c$$). We can then take a weighted average of all the repair by taking into account each components contribution to the total failure rate. +To compute average maintenance time we consider the mean time to repair ($MTTR_c$) of each component and the failure rate of each component ($\lambda_c$). We can then take a weighted average of all the repair by taking into account each components contribution to the total failure rate. -$$$ +$$ \begin{equation} T_m = \sum_{c=0}^n \frac{\lambda_c}{\lambda_{tstick}}(MTTR_c) \end{equation} -$$$ +$$ ### Compute PMR -To compute PMR we divide the $$MTBF_{tstick}$$ by the average maintenance time ($$T_m$$). +To compute PMR we divide the $MTBF_{tstick}$ by the average maintenance time ($T_m$). -$$$ +$$ \begin{equation} PMR = \frac{MTBF_{tstick}}{T_m} \end{equation} -$$$ +$$ ## Compute Direct Maintenance Costs (DMC) @@ -130,22 +129,22 @@ We can also look at the direct maintenance cost of the T-Stick which we define a ### Compute Mean Repair Cost of the T Stick -The mean repair cost of the T-Stick ($$MRC_{tstick}$$) is computed the same way the average maintenance time, by using a weighted average of the mean repair cost of each component. +The mean repair cost of the T-Stick ($MRC_{tstick}$) is computed the same way the average maintenance time, by using a weighted average of the mean repair cost of each component. -$$$ +$$ \begin{equation} MRC_{tstick} = \sum_{c=0}^n \frac{\lambda_c}{\lambda_{tstick}}(MRC_c) \end{equation} -$$$ +$$ ### Compute DMC -To compute DMC we divide the mean repair cost by the mean time between failure of the T-Stick ($$MTBF_{tstick}$$) +To compute DMC we divide the mean repair cost by the mean time between failure of the T-Stick ($MTBF_{tstick}$) -$$$ +$$ \begin{equation} DMC = \frac{MRC_{tstick}}{MTBF_{tstick}} \end{equation} -$$$ +$$ diff --git a/docs/Images/IDMIL-logo-icon.png b/docs/Images/IDMIL-logo-icon.png new file mode 100644 index 0000000..fb4ac4c Binary files /dev/null and b/docs/Images/IDMIL-logo-icon.png differ diff --git a/docs/Images/favicon.ico b/docs/Images/favicon.ico new file mode 100644 index 0000000..37ed033 Binary files /dev/null and b/docs/Images/favicon.ico differ diff --git a/docs/index.html b/docs/index.html index 7da59f5..df1ec38 100644 --- a/docs/index.html +++ b/docs/index.html @@ -7,8 +7,9 @@ content="width=device-width, initial-scale=1, minimum-scale=1.0, shrink-to-fit=no, viewport-fit=cover"> -