How to ensure scrum adherence and alignment between products and teams?

Is there a sense of urgency for change in the company? Why not offer to work with the CEO, in order to plan and better communicate it?

If you have three teams working on separate software products, but those products have interdependencies, then you don't have three separate software products. Since you mention that there needs to be some alignment around the customer experience and operational infrastructure, it sounds like you have a product portfolio. However, your organizational structure with teams belonging to separate departments responsible for the operations side of each product doesn't align with portfolio management.

Just from what you describe, the underlying problem is this lack of portfolio management. But to get here, you'll need to tear down the departmental silos and get product development into a more appropriate structure that includes product management, user experience design, development, test, and operations from all of the products. It's probably going to be a long process, but the silos are going to hold you back from making real progress here.

Many thanks for your reply Ian. I would say that there is currently insufficient or no sense of urgency, mainly due to lack of understanding. It speaks to working with top management, as you suggest. The question that has occupied my mind is how to convince them that we actually have a problem. I have begun to gather concrete examples of inefficiency and how things have been close to going completely wrong. However, I would also like to offer some kind of solution suggeston. My experience is mainly in web development, where product management and the formation of a development organization have been quite clear-cut. Here maybe product portfolio management is an option, as Thomas Owens suggests. However, I wonder who would shoulder the Product Portfolio Manager role and whether a portfolio management team could consist of representatives from the various departments. Do you have any advice here?

What about the Scrum adherence question, could this be driven by the formation of a Scrum Master guild or something similar? Is something more compelling / binding needed in your experience (which, however, feels contrary to Scrum values)? Or is there something else that could be done to facilitate Scrum adherence?

The question that has occupied my mind is how to convince them that we actually have a problem. I have begun to gather concrete examples of inefficiency and how things have been close to going completely wrong. However, I would also like to offer some kind of solution suggeston.

Suppose you did all of that. Would those facts evidence a problem, as far as senior management is concerned? What you highlight as inefficiency they might call established practice, which has worked so far, even if it means bringing things back from the brink at the last minute.

My advice is to zero in on the forces that have lead to experimentation with Scrum in the first place. Who in the organization wants Scrum at all, and why? What would constitute evidence, to management, of the need for change? If you want to offer some kind of "solution" at this point, why not propose EBM indicators, such as current value, unrealized value, time to market, and ability to innovate?

You said that the CIO has identified the problem and then ask who should shoulder the Product Portfolio Management duties.  That sounds like a question for the CIO to answer but only if one of the solutions the CIO is considering includes Product Portfolio Management.  If I were in your situation, I would be offering myself to the CIO as willing to help in any way possible and make it known that you are also willing to provide suggestions.  Notice I said suggestions and not answers. You don't have answers, you have information that can help arrive at answers. 

There is no continuous alignment (e.g. Scrum of Scrums) between the teams.

Or is there something else that could be done to facilitate Scrum adherence?

Why should there be alignment between teams? It sounds like you have self-managing, self-organizing teams so why is that not considered adherence to Scrum? The way you phrase your questions related to the adherence almost sounds like you want to have a standardized way of doing things for all teams which sounds like a Project Management Office which isn't really a "scrum thing". 

I am going to agree with @Thomas Owens' assessment that you do not have 3 products.  You have 1 product with a number of parts which could easily number more than 3. And @Ian Mitchell points to the fact that this isn't a team issue as much as it is an organizational issue.  In order for any kind of agile mindset to be successful, it requires that the organization as a whole understands and supports it.  Your CIO has interpreted a problem and it sounds like you think there is a problem. But so far we only have evidence of 2 individuals in a larger group interpreting that there are any issues. In order for anything to change it is going to require a much larger group of individuals to acknowledge and welcome changes.  You have a challenge and you need to work with the CIO to start proving there are problems and facilitate changes across the organization. 

Good luck. 

@Daniel Wilhite Many thanks for insightful advice. In regards to Scrum adherence

The way you phrase your questions related to the adherence almost sounds like you want to have a standardized way of doing things for all teams which sounds like a Project Management Office which isn't really a "scrum thing".

I meant adhering to the Scrum framework (roles, events, artifacts, and rules), not a standardized way of doing things. Sorry for phrasing the question poorly. Any thoughts on this given my clarification?

In regards to alignment between the teams I was thinking along the lines of Scrum of Scrums for scaling Daily stand-ups, i.e. the purpose being uncovering dependencies and mutual obstacles. You seem to question why this is needed, can you please explain why?

Suppose dependencies were identified during Product Backlog refinement, and managed by teams accordingly. What impact would that have on the need for a scaling mechanism such as the one you describe?

Ok, you mean that proper Product Backlog refinement would allow the teams to self-organize and thereby remove the need for Scrum of Scrums?