When designing service systems and considering the progression from mail$/$email contact to phone contact to face$-$to$-$face interaction with total customization, the appropriateness of each method depends on various factors including the nature of the service, customer preferences, complexity of the service, and cost considerations.

Here's how each method may be appropriate in different contexts:

$1.**$Mail$/$Email Contact$**$: This method is suitable for services where written communication suffices, such as simple inquiries, providing basic information, or handling straightforward transactions. It's often cost$-$effective for the service provider and convenient for customers who prefer asynchronous communication.

$2.**$Phone Contact$**$: Phone contact becomes more appropriate when customers require more immediate assistance or when the service interaction necessitates a real$-$time conversation. It allows for quicker resolution of issues, clearer communication of complex information, and a more personalized touch compared to email or mail.

$3.**$Face$-$to$-$Face Total Customization$**$: This approach is most appropriate for services that require highly personalized or complex solutions, such as consulting, financial planning, or certain healthcare services. Face$-$to$-$face interaction allows for deeper understanding of customer needs, building trust, and providing tailored solutions that address specific requirements effectively.

Therefore, the most appropriate method depends on the level of personalization and complexity required by the service and the preferences of the customers. It's essential to offer multiple channels of communication to accommodate different customer needs and preferences effectively.