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Availability Modelling.md

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+# Availability Modelling
+
+# Introduction
+
+sdvsv
+
+# Model Parameters
+
+## Performance Time ($$t_p$$)
+
+The average time a T-Stick performance lasts given in hours.
+
+## Performer Intensity ($$j_p$$)
+
+The intensity of the performance, rough indicator of the impact of a performance on the reliability of certain components.
+
+## Simulation Parameters
+
+These additional parameters may be used for simulation, when wanting to take into account technician availability. It is not used for PIR calculations for the T-Stick evaluation though.
+
+### 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*.**
+
+### 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.
+
+### Technician Turnaround ($$t_{tech}$$)
+
+The average amount of business days it takes for the technician/luthier to return the instrument to the artist/musician.
+
+## Model Inputs
+
+### Maintenance Time between performances ($$t_m$$)
+
+The amount of time an artist/musician spends maintaining the T-Stick in between performances, given in hours.
+
+### Mean time to repair for T-Stick Components ($$MTTR_c$$)
+
+Mean time to repair/replace for T-Stick components in hours
+
+### Mean time between failure for T-Stick Components ($$MTBF_c$$)
+
+Mean time between failure of T-Stick components in hours
+
+### Maintenance actions between performance
+
+The actions the artist/musicians take when maintaining their instrument.
+
+### Available tools (T)
+
+The available equipment an artist has on hand for maintaining and fixing their instrument.
+
+# Compute Practice Interruption Rate (PIR)
+
+## 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.
+
+$$$
+\begin{equation}
+\lambda_{tstick} = \lambda_{esp32} + \lambda_{fsr}+\lambda_{imu}+\lambda_{button}+\lambda_{capsense}+\lambda_{resistor}+\lambda_{touchsensor}+\lambda_{battery}+\lambda_{connectors}
+\end{equation}
+$$$
+
+where $$\lambda_i$$ is the failure rate of component *i*.
+
+The failure rates for several components such as:
+
+* FSR
+* Resistor
+* IMU
+* Capsense Board
+* ESP32 Board
+* Battery
+
+can be estimated using a combination of the [FIDES reliability prediction too](https://www.fides-reliability.org/)l, the [MIL-217F Handbook](https://drive.google.com/file/d/1QNUiTOAwJebwC-bk0FJWB0jD3I6XFxFi/view?usp=drive_link), and the [NPRD-91](https://drive.google.com/file/d/1QPMqClW2nHY4U9tmMO5Lzc11RDF2Oeoc/view?usp=sharing). The MTBF of the connectors is taken from the performance model.
+
+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 (**$$t_P$$)
+
+$$$
+\begin{equation}
+MPBF = \frac{MTBF_{tstick}}{t_p}
+\end{equation}
+$$$
+
+## 4. Compute PIR
+
+We calculate the practice interruption rate by taking the reciprocal of $$MPBF$$.
+
+$$$
+\begin{equation}
+PIR = \frac{1}{MPBF}
+\end{equation}
+$$$
+
+Using Eq.5, Eq.6 and Eq.7 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 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.
+
+$$$
+\begin{equation}
+T_m =  \sum_{c=0}^n \frac{\lambda_c}{\lambda_{tstick}}(MTTR_c)
+\end{equation}
+$$$
+
+## Compute PMR
+
+To compute PMR we divide the $$MTBF_{tstick}$$ by the average maintenance time ($$T_m$$).
+
+$$$
+\begin{equation}
+PMR = \frac{MTBF_{tstick}}{T_m}
+\end{equation}
+$$$
+
+# Compute Direct Maintenance Costs (DMC)
+
+We can also look at the direct maintenance cost of the T-Stick which we define as the dollars spent on maintaining the T-Stick per performance hour.
+
+## 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.
+
+$$$
+\begin{equation}
+MRC_{tstick} = \sum_{c=0}^n \frac{\lambda_c}{\lambda_{tstick}}(MRC_c)
+\end{equation}
+$$$
+
+## Compute DMC
+
+To compute DMC we divide the mean repair cost by the mean time between failure of the T-Stick ($$MTBF_{tstick}$$)
+
+$$$
+\begin{equation}
+DMC = \frac{MRC_{tstick}}{MTBF_{tstick}}
+\end{equation}
+$$$
+
+

Gesture Algorithms.md

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+# Gesture Algorithms
+
+# Introduction
+
+Many different gesture algorithms have been used in the T-Stick. This section will list links to documentation for these algorithms. Check the [T-Stick Designs](./T-Stick%20Designs.md) to find out which algorithm is compatible with which T-Stick version.