This paper presents a domino model for a failure process which can occur in the units of an insulator string. It extends the standard independent failure reliability assessment to the case of sequential failures, where failure of one unit increases the risk that its neighbours will also fail. The statistical properties of the resulting distribution of number of failed units per string are derived, and procedures given for estimating the model parameters from observed failure data. Examples of the use of the model are given and its results are compared with those of an alternative model based on a negative binomial distribution.