The Customer Responsiveness Index (CRI) is designed for government departments that want to focus on their "customers" only. For many government departments there are no direct competitors in the traditional sense, so the CRI is designed to narrow the focus onto customers, their environment and the internal factors necessary to deliver a great service to the government's "customers".
The MRI has also been used successfully in government departments that acknowledge they have competition from external service providers or the threat of being outsourced due to poor performance. In these cases the MRI can be a better solution in order to emphasize the fact that they do not have a monopoly and there are consequences for not delivering the service levels expected by customers.