odoo-survey-addons/survey_input_dates/models/survey_user_input.py

from odoo import models, fields, api


class SurveyUserInput(models.Model):
    _inherit = 'survey.user_input'

    date_start = fields.Datetime(string="Start date", readonly=True, help="This date is set when the user clicks on \"Start survey\" button for the first time.")
    date_done = fields.Datetime(string="Date done", readonly=True, help="This date is set when the user input is set ton \"Done\" status.")

    @api.multi
    def write(self, vals):
        if vals.get('state', False) == 'done':
            vals.update({
                'date_done': fields.Datetime.now(),
            })
        return super(SurveyUserInput, self).write(vals)