Consider the analysis of a thermocouple that will be used to measure the temperature of a gas stream (Ghosh and Olewnik, 2013). The time t0.99 that it will take the thermocouple to reach 0.99 of the gas stream temperature, under certain conditions, depends on the junction density 𝜌, the thermocouple diameter D, the specific heat capacity c, the convection coefficient h, the initial temperature Ti , and the gas temperature T∞ as follows:
All six inputs are uncertain, so there is uncertainty about the value of the time t0.99. Suppose that the uncertainties about all six inputs are modeled as normally distributed random quantities in which the standard deviation equals 4% of the mean. At their mean values, Use Monte Carlo sampling to determine a 95% confidence interval on the mean of t0.99.