This paper provides a model and an analytical study of replication as a technique to detect and correct silent errors, as well as to cope with both silent and fail-stop errors on large-scale platforms. Fail-stop errors are immediately detected, unlike silent errors for which a detection mechanism is required. To detect silent errors, many application-specific techniques are available, either based on algorithms (ABFT), invariant preservation or data analytics, but replication remains the most transparent and least intrusive technique. We explore the right level (duplication, triplication or more) of replication for two frameworks: (i) when the platform is subject only to silent errors, and (ii) when the platform is subject to both silent and fail-stop errors. A higher level of replication is more expensive in terms of resource usage but enables to tolerate more errors and to correct some silent errors, hence there is a trade-off to be found. Replication is combined with checkpointing and comes with two flavors: process replication and group replication. Process replication applies to message-passing applications with communicating processes. Each process is replicated, and the platform is composed of process pairs, or triplets. Group replication applies to black-box applications, whose parallel execution is replicated several times. The platform is partitioned into two halves (or three thirds). In both scenarios, results are compared before each checkpoint, which is taken only when both results (duplication) or two out of three results (triplication) coincide. If not, one or more silent errors have been detected, and the application rolls back to the last checkpoint, as well as when fail-stop errors have struck. We provide a detailed analytical study for all of these scenarios, with formulas to decide, for each scenario, the optimal parameters as a function of the error rate, checkpoint cost, and platform size. We also report a set of extensive simulation results that nicely corroborates the analytical model.