Use different language. Reframe the idea of failure. Call it something else, like "Stuff we now know doesn't work" or "Ageless Wisdom," or something like that, so when people make mistakes, they might say to themselves or each other, "Now that's what I call ageless wisdom." You could take a bucket and call it the "Wisdom Bucket" and put it somewhere easily accessible. People could write failures down on scraps of paper and anonymously put them in the bucket and have a weekly reading.

You could also brainstorm with the group your working with to think of ways to get people to share more failures with each other. If people come up with their own solutions, they usually stick more anyway.

By the way, I don't think it's true that you learn more from failure. They can be equally valuable if you get into the juicy details. Maybe you can have people share both?

You should distinguish between doing something wrong under a correct hypothesis (failure) and doing something right under a wrong hypothesis (negative result). I assume you mean sharing negative results, not failures.

If the person passes through self-knowledge, this leads it to be prepared to take on a possible failure in the work with maturity.

Quality control circles (QCC), A Japanese HR Practice, is one of the best method to share failure, and rectify it. Another method is, one time failure/mistake should not be taken as negative point. Attitude of learning may also help.

Karl Weick's concept of Sensemaking seems to be something that is so important in teams and organisations yet it seems to be a concept that tends to overlooked in practice.  Sensemaking relates to the meaning that people give to an event and this may be incorporated in what can be termed as 'failures' ....... or an opportunity for learning and building expertise?

The method that can be created a sharing of failure at work is creating the good relationship between employees on the job and off the job.

In my opinion this can only happen if people feel safe and if joint responsibility is taken for failure, rather than attempting to find a scapegoat.

It's a great learning opportunity and we tend to remember failure more and longer than success.

Eleanor

Success and failure are the two sides of the same coin of work performance. Every activity one does is not the guarantee of success. However in case of failure one should not keep mum and come to own failure like success. One sound human relation precedent is 'praise in public but criticism in alone, similarly through 'word of mouth' mechanism, sharing of failure will win over one's confidence in the group while prove you good team member with potential leadership qualities. 

There are umpteen ways to share the same at work. Mentor - mentee, wherein a senior or PM can share his learning with team mates.

Allocate a day in a week, teammates should be encouraged to share their learnings, from the failures. Two to three issues could be discussed, once in a week for a fixed time slot.

Online employee portals to share their learning, over the intranet.

I think you can benefit from the abstract and the references of that article.

https://www.researchgate.net/publication/257913309_Interpersonal_competence_transfer_and_methods_in_organizations_A_qualitative_study_in_the_scope_of_inspectorship

Article Interpersonal competence transfer and methods in organizatio...

If we try to maintain simplicity, we understand that failure means we are closer to figuring out how to get it right.  So, in debriefing the hypothesis and the methodology - we can hone in on areas of that require improvement.  Failure is unfortunately a word that invokes discomfort for most - I agree that after examining the results then we use a portal as a reservoir to store our learning points.  

An article that covers similar ground is at http://www.adb.org/publications/embracing-failure. A Learning Charter, about which more is at http://www.adb.org/publications/drawing-learning-charters, might encourage team members to (i) appreciate that failure is not avoidable, objective, a single event, a stigma, the enemy, or final; (ii) understand why they made the decision they took based on the information they had; (iii) assess their decisions based on what they knew at the time; (iv) judge the systemic errors they committed in under- or overestimating difficulties, costs, timelines, abilities, etc.; (v) examine whether they had all the information they needed; (vi) investigate what successes are contained in the failure and draw dividends; (vii) plan to obtain more and better information to underpin future decisions; (viii) use the experience to build and work from strengths; and ix) set a new goal, order their plan, take action, reevaluate progress, and adjust continually.

There are some journals already addressing the publication of negative results:

Journal of Negative Results in BioMedicine

Journal of Pharmaceutical Negative Results

Journal of Negative Results (no activity since 2013)

The All Results Journals: Chem

I have not publish anything in these journals (I cannot say I do not have negative results in my work, though).

You can find one of the best answers in Aviation field. Look for ASRS, managed by NASA:

ASRS is a voluntary reporting system. To encourage reporting, ASRS establishes that the report guarantees immunity in the case that any other could have observed and informed the mistake. ASRS managers know that this feature could drive in some extent to fraud by the notifier but, even though, they prefer assuming that risk that having people hiding mistakes.

ASRS database is transparent. You can look for different events and nobody is going to ask why you are asking or if you are a researcher. Simply, the unidentified database is opened to anyone.

Another important feature is the personality of the system administrator. Why NASA? The most probable administrator in U.S.A. should be FAA, that is, the Aviation Federal Agency but, in that way, many notifiers could distrust any claimed non-punitive approach, especially since that approach should be in conflict with FAA functions.

NASA, then, is another firewall to guarantee safety to the notifier.

You can find different reporting systems in Aviation, NPPs and some other fields but, in my opinion, ASRS, summarizes the conditions that you should ask for in a system driven to share failures inside an organization.

What methods can be used to encourage the sharing of failure at work?

Every organization will have effective moments in business and they will also have moments of failure. There are steps to encourage sharing deconstructive situations with openness and honesty. Try to build a session using (1) Feedback; (2) Assessment; (3) Reconstruction; (4) Re-framing; (5) Negatives Boundaries. There are several resourceful methods available on re-framing and re-building organizations with positive constructs in organizational leadership. As a team building exercise, it may be appropriate to target deconstructive methods and constructive methods organizational behavior.

Reference:  Reframing Organizations: Artistry, Choice and Leadership. Boleman & Deal. (2008).

Great question!  Good luck with the team!