Why ring oscillator showing irregular graph ?
I don't have access to CADENCE.

But the first thing that hits me in the head right away is that your PMOS widths need to be twice (or more?) the width of your NMOS due to mobility. You probably want 20:1 on the PMOS and 10:1 on the NMOS, or something about like that. So when using \$\textrm{w}=2\:\mu\$ for your NMOS then use \$\textrm{w}=4\:\mu\$ for your PMOS.

Other than that, I don't yet see other problems. But I don't have your models and levels, either. (I use LTspice, only.)



Here is an example of my run using 9 stages:



Here's the schematic in LTspice I used:





Another possibility is the underlying models you are using. The detailed models I'm using are here:

.model  N_50n  nmos  level = 54
+binunit = 1            paramchk= 1            mobmod  = 0          
+capmod  = 2            igcmod  = 1            igbmod  = 1            geomod  = 0          
+diomod  = 1            rdsmod  = 0            rbodymod= 1            rgatemod= 1          
+permod  = 1            acnqsmod= 0            trnqsmod= 0          
+tnom    = 27           toxe    = 1.4e-009     toxp    = 7e-010       toxm    = 1.4e-009   
+epsrox  = 3.9          wint    = 5e-009       lint    = 1.2e-008   
+ll      = 0            wl      = 0            lln     = 1            wln     = 1          
+lw      = 0            ww      = 0            lwn     = 1            wwn     = 1          
+lwl     = 0            wwl     = 0            xpart   = 0            toxref  = 1.4e-009   
+vth0    = 0.22         k1      = 0.35         k2      = 0.05         k3      = 0          
+k3b     = 0            w0      = 2.5e-006     dvt0    = 2.8          dvt1    = 0.52       
+dvt2    = -0.032       dvt0w   = 0            dvt1w   = 0            dvt2w   = 0          
+dsub    = 2            minv    = 0.05         voffl   = 0            dvtp0   = 1e-007     
+dvtp1   = 0.05         lpe0    = 5.75e-008    lpeb    = 2.3e-010     xj      = 2e-008     
+ngate   = 5e+020       ndep    = 2.8e+018     nsd     = 1e+020       phin    = 0          
+cdsc    = 0.0002       cdscb   = 0            cdscd   = 0            cit     = 0          
+voff    = -0.15        nfactor = 1.2          eta0    = 0.15         etab    = 0          
+vfb     = -0.55        u0      = 0.032        ua      = 1.6e-010     ub      = 1.1e-017   
+uc      = -3e-011      vsat    = 1.1e+005     a0      = 2            ags     = 1e-020     
+a1      = 0            a2      = 1            b0      = -1e-020      b1      = 0          
+keta    = 0.04         dwg     = 0            dwb     = 0            pclm    = 0.18       
+pdiblc1 = 0.028        pdiblc2 = 0.022        pdiblcb = -0.005       drout   = 0.45       
+pvag    = 1e-020       delta   = 0.01         pscbe1  = 8.14e+008    pscbe2  = 1e-007     
+fprout  = 0.2          pdits   = 0.2          pditsd  = 0.23         pditsl  = 2.3e+006   
+rsh     = 3            rdsw    = 150          rsw     = 150          rdw     = 150        
+rdswmin = 0            rdwmin  = 0            rswmin  = 0            prwg    = 0          
+prwb    = 6.8e-011     wr      = 1            alpha0  = 0.074        alpha1  = 0.005      
+beta0   = 30           agidl   = 0.0002       bgidl   = 2.1e+009     cgidl   = 0.0002     
+egidl   = 0.8          
+aigbacc = 0.012        bigbacc = 0.0028       cigbacc = 0.002
+nigbacc = 1            aigbinv = 0.014        bigbinv = 0.004        cigbinv = 0.004
+eigbinv = 1.1          nigbinv = 3            aigc    = 0.017        bigc    = 0.0028
+cigc    = 0.002        aigsd   = 0.017        bigsd   = 0.0028       cigsd   = 0.002
+nigc    = 1            poxedge = 1            pigcd   = 1            ntox    = 1
+xrcrg1  = 12           xrcrg2  = 5          
+cgso    = 6.238e-010   cgdo    = 6.238e-010   cgbo    = 2.56e-011    cgdl    = 2.495e-10     
+cgsl    = 2.495e-10    ckappas = 0.02         ckappad = 0.02         acde    = 1          
+moin    = 15           noff    = 0.9          voffcv  = 0.02       
+kt1     = -0.21        kt1l    = 0.0           kt2     = -0.042        ute     = -1.5
+ua1     = 1e-009       ub1     = -3.5e-019     uc1     = 0             prt     = 0
+at      = 53000
+fnoimod = 1            tnoimod = 0          
+jss     = 0.0001       jsws    = 1e-011       jswgs   = 1e-010       njs     = 1          
+ijthsfwd= 0.01         ijthsrev= 0.001        bvs     = 10           xjbvs   = 1          
+jsd     = 0.0001       jswd    = 1e-011       jswgd   = 1e-010       njd     = 1          
+ijthdfwd= 0.01         ijthdrev= 0.001        bvd     = 10           xjbvd   = 1          
+pbs     = 1            cjs     = 0.0005       mjs     = 0.5          pbsws   = 1          
+cjsws   = 5e-010       mjsws   = 0.33         pbswgs  = 1            cjswgs  = 5e-010     
+mjswgs  = 0.33         pbd     = 1            cjd     = 0.0005       mjd     = 0.5        
+pbswd   = 1            cjswd   = 5e-010       mjswd   = 0.33         pbswgd  = 1          
+cjswgd  = 5e-010       mjswgd  = 0.33         tpb     = 0.005        tcj     = 0.001      
+tpbsw   = 0.005        tcjsw   = 0.001        tpbswg  = 0.005        tcjswg  = 0.001      
+xtis    = 3            xtid    = 3          
+dmcg    = 0e-006       dmci    = 0e-006       dmdg    = 0e-006       dmcgt   = 0e-007     
+dwj     = 0e-008       xgw     = 0e-007       xgl     = 0e-008     
+rshg    = 0.4          gbmin   = 1e-010       rbpb    = 5            rbpd    = 15         
+rbps    = 15           rbdb    = 15           rbsb    = 15           ngcon   = 1
*
.model  P_50n  pmos  level = 54
+binunit = 1            paramchk= 1            mobmod  = 0          
+capmod  = 2            igcmod  = 1            igbmod  = 1            geomod  = 0          
+diomod  = 1            rdsmod  = 0            rbodymod= 1            rgatemod= 1          
+permod  = 1            acnqsmod= 0            trnqsmod= 0          
+tnom    = 27           toxe    = 1.4e-009     toxp    = 7e-010       toxm    = 1.4e-009   
+epsrox  = 3.9          wint    = 5e-009       lint    = 1.2e-008   
+ll      = 0            wl      = 0            lln     = 1            wln     = 1          
+lw      = 0            ww      = 0            lwn     = 1            wwn     = 1          
+lwl     = 0            wwl     = 0            xpart   = 0            toxref  = 1.4e-009   
+vth0    = -0.22        k1      = 0.39         k2      = 0.05         k3      = 0          
+k3b     = 0            w0      = 2.5e-006     dvt0    = 3.9          dvt1    = 0.635        
+dvt2    = -0.032       dvt0w   = 0            dvt1w   = 0            dvt2w   = 0          
+dsub    = 0.7          minv    = 0.05         voffl   = 0            dvtp0   = 0.5e-008     
+dvtp1   = 0.05         lpe0    = 5.75e-008    lpeb    = 2.3e-010     xj      = 2e-008     
+ngate   = 5e+020       ndep    = 2.8e+018     nsd     = 1e+020       phin    = 0          
+cdsc    = 0.000258     cdscb   = 0            cdscd   = 6.1e-008     cit     = 0          
+voff    = -0.15        nfactor = 2            eta0    = 0.15         etab    = 0          
+vfb     = 0.55         u0      = 0.0095       ua      = 1.6e-009     ub      = 8e-018     
+uc      = 4.6e-013     vsat    = 90000        a0      = 1.2          ags     = 1e-020     
+a1      = 0            a2      = 1            b0      = -1e-020      b1      = 0          
+keta    = -0.047       dwg     = 0            dwb     = 0            pclm    = 0.55       
+pdiblc1 = 0.03         pdiblc2 = 0.0055       pdiblcb = 3.4e-008     drout   = 0.56       
+pvag    = 1e-020       delta   = 0.014        pscbe1  = 8.14e+008    pscbe2  = 9.58e-007  
+fprout  = 0.2          pdits   = 0.2          pditsd  = 0.23         pditsl  = 2.3e+006   
+rsh     = 3            rdsw    = 250          rsw     = 160          rdw     = 160        
+rdswmin = 0            rdwmin  = 0            rswmin  = 0            prwg    = 3.22e-008  
+prwb    = 6.8e-011     wr      = 1            alpha0  = 0.074        alpha1  = 0.005      
+beta0   = 30           agidl   = 0.0002       bgidl   = 2.1e+009     cgidl   = 0.0002     
+egidl   = 0.8          
+aigbacc = 0.012        bigbacc = 0.0028       cigbacc = 0.002
+nigbacc = 1            aigbinv = 0.014        bigbinv = 0.004        cigbinv = 0.004
+eigbinv = 1.1          nigbinv = 3            aigc    = 0.69         bigc    = 0.0012
+cigc    = 0.0008       aigsd   = 0.0087       bigsd   = 0.0012       cigsd   = 0.0008
+nigc    = 1            poxedge = 1            pigcd   = 1            ntox    = 1
+xrcrg1  = 12           xrcrg2  = 5          
+cgso    = 7.43e-010    cgdo    = 7.43e-010    cgbo    = 2.56e-011    cgdl    = 1e-014     
+cgsl    = 1e-014       ckappas = 0.5          ckappad = 0.5          acde    = 1          
+moin    = 15           noff    = 0.9          voffcv  = 0.02       
+kt1     = -0.19        kt1l    = 0            kt2     = -0.052        ute     = -1.5
+ua1     = -1e-009      ub1     = 2e-018       uc1     = 0             prt     = 0
+at      = 33000
+fnoimod = 1            tnoimod = 0          
+jss     = 0.0001       jsws    = 1e-011       jswgs   = 1e-010       njs     = 1          
+ijthsfwd= 0.01         ijthsrev= 0.001        bvs     = 10           xjbvs   = 1          
+jsd     = 0.0001       jswd    = 1e-011       jswgd   = 1e-010       njd     = 1          
+ijthdfwd= 0.01         ijthdrev= 0.001        bvd     = 10           xjbvd   = 1          
+pbs     = 1            cjs     = 0.0005       mjs     = 0.5          pbsws   = 1          
+cjsws   = 5e-010       mjsws   = 0.33         pbswgs  = 1            cjswgs  = 5e-010     
+mjswgs  = 0.33         pbd     = 1            cjd     = 0.0005       mjd     = 0.5        
+pbswd   = 1            cjswd   = 5e-010       mjswd   = 0.33         pbswgd  = 1          
+cjswgd  = 5e-010       mjswgd  = 0.33         tpb     = 0.005        tcj     = 0.001      
+tpbsw   = 0.005        tcjsw   = 0.001        tpbswg  = 0.005        tcjswg  = 0.001      
+xtis    = 3            xtid    = 3          
+dmcg    = 0e-006       dmci    = 0e-006       dmdg    = 0e-006       dmcgt   = 0e-007     
+dwj     = 0e-008       xgw     = 0e-007       xgl     = 0e-008     
+rshg    = 0.4          gbmin   = 1e-010       rbpb    = 5            rbpd    = 15         
+rbps    = 15           rbdb    = 15           rbsb    = 15           ngcon   = 1   


The other thing is to provide the initial conditions to CADENCE. I've set the node called Osc to a volt, to start out.

LTspice is a little different in how it works, internally. So it could be something else.