A u chart is to be used to control a corrugated paper product line. End product is produced in rolls of varying length 1 m wide. Nonconformities include surface imperfections, improper gluing, improper tension setting on the corrugated inner core, etc. The control statistic is nonconformities per 100 m with one roll constituting a sample. To determine the initial control limits, 20 rolls were inspected and the total count of nonconformities was 326 in a total of 9000 m.
(a) Find the value of ¯u in nonconformities per 100 m.
(b) The next roll inspected is of length 250 m and has 15 non conformities. Is there reason to believe that this roll is significantly worse than the other rolls?