Are there salary related schemes that are not based on final salary?

Yes.

The commonest alternative is a career average salary scheme. These are not as good for people who get promoted and end up with a big pay packet at the end of their careers, but can be better for people whose earnings vary (because of changes in their hours) or decline (as may happen to manual workers). 

Replacing a final salary scheme with a career average scheme is one of the ways that employers with pension fund deficits are trying to reduce the cost of pensions. There will certainly be many losers from such a change. Whether there are any winners will depend on the detail, in particular how much the employer is cutting in contributions to the scheme.

Career average schemes don't just take all your pay slips and find their average. Instead your pay for previous years will be uprated by some inflation measure so that it is expressed in today's money before the average is taken.

In other words, your last year's pay will be uprated by about 3.5 per cent (more or less the average annual rise in earnings in recent years). Your pay from two years ago will be uprated by 3.5 per cent twice.

Once this is done the pension is worked out in the same way as a final salary scheme, except the salary used is your career average.