You're trying to estimate a proportion. You should read about doing Bayesian inference for proportions (for example here). If this is your first problem you might want to choose a simpler problem where the quantity you're trying to estimate is a discrete variable (that'll make the problem simpler). The particular mistake you've made is using a single value for your prior; the value I think you're trying to estimate (the proportion of shuttles that fail) is continuous so you should have a prior distribution over the real line [0,1].