I've been working with analysers for the cement plants for last nine years and have still a little doubt about the actual use of measurement of NO_x in the kiln inlet. If you can kindly send me some literature about the firing in the kiln and the advantages of measuring various gases at the kiln inlet.

The NO_x level at the kiln inlet is a very good indication of the burning zone temperature in the kiln. In turn this is one of the most important considerations in the control and optimisation of the kiln. NO_x arises from two sources,
(i) organic nitrogen in the fuel, and
(ii) oxidation of the atmospheric nitrogen in the combustion air drawn into the kiln. This oxidation of the atmospheric nitrogen rises in direct proportion to the temperature in the flame and the burning zone.

I would like to know how to get rid of the rings that occurs around upper transition zone without mechanically breaking by stopping the kilns

There are various options, but if you cannot avoid the problem by better control of the kiln feed chemistry or burning conditions in the kiln then there are two possibilities:
(i) install the equipment to fire Cardox charges in the region where you have persistent problems, and
(ii) by an industrial gun and shoot the rings out.