Having difficulties to create a feature based on the some groupby conditions

The data that I've looks similar to

I want to groupby at ir_id such that I can create err_flag column which is:

• type1: atleast 1 row having value "UNKNOWN" in err_type column, and also "yes" in pli_missing

• type2: atleast 1 row having value "UNKNOWN" in err_type column, and also "no" in pli_missing

• type3: no row having value "UNKNOWN" in err_type column, and also "no" in pli_missing

• both_type: both type1 and type2 error flag, i.e.

Which results in final O/p as:

dataset used:

custom_df = pd.DataFrame.from_dict({
    'ir_id':['name1', 'name1', 'name1', 'name1', 'name2', 'name2', 'name2', 'name3', 'name3', 'name3', 'name3', 'name4', 'name4', 'name4', 'name5', 'name5', 'name5', 'name5']
    , 'pli': [1,       2,       3,       np.nan,  4,       5,       np.nan,  6,       7,       8,       9,       10,      11,      12,      np.nan,  np.nan,  np.nan,  np.nan]
    , 'pli_missing': ["no","no","no","yes","no","no","yes","no","no","no","no","no","no","no","yes","yes","yes","yes"]
    , 'err_type': ["UNKNOWN",np.nan,np.nan,"UNKNOWN",np.nan,np.nan,"UNKNOWN",np.nan,np.nan,np.nan,"UNKNOWN",np.nan,np.nan,np.nan,"UNKNOWN","UNKNOWN","UNKNOWN","UNKNOWN"]
    , 'err_flag': ["both_type", "both_type", "both_type", "both_type", "type1", "type1", "type1", "type2", "type2", "type2", "type2", "type3", "type3", "type3", "type1", "type1", "type1", "type1"]
})

custom_df

PS Earlier