Cost Month (x) Cumulative number of component Replace individually by month end Total Cost (TC) Average Cost = Tc Individual Group per month 1 200 600 2000 2600 2600 2 520 2000 3560 1780 3 1082 2000 1560 3246 5508.6 7607.76 5246 7508.6 4 1836.2 2000 1748.67 1877.15 1921.55 5 2535.92 2000 9607.76 Since the average cost is lowest in 3d month, the optimal interval i.e. replacement is 3 months. Also the average cost is less than ? 1791 of individual replacement, the group replacement policy is better. X30 (0) LEI de the cost of Individual Replacement Month Average Cost of Group Average cost of 'K' Value To obtai the value of K use Replacement Individual Replacement ) the equation Average cost 1 (2000 + 200 K)/1 597 K of Individual Replacement 5.04 = Average Cost of Group 2 (2000 + 520 K)/2 597 K 2.97 Replacement 3 (2000 + 1082 K]/3 597 K 2.82 4 (2000+ 1836.2 K)/4 597 K 3.62 5 (2000 + 2535.92 K}/5 597 K 4.45 If group replacement is anything smaller than 2.82, then Group Replacement would be uneconomical. (c) Let'a' be the unit cost of Group Replacement Policy Month Average cost of Group Average of Individual 'a' Value Replacement Replacement 1 (2000 a + 600)/1 ) 1791 0.60 2 (2000 a + 1560)/2 1791 1.01 3 (2000 a + 3246)/3 a 3 1791 1.06 (2000 a +5508.6)/4 1791 0.83 5 (2000 a + 7607.76)/5 1791 0.67 When unit cost is more than 1.06 then Individual Replacement policy would be better. 4 Illustration 10. An electric company which generates and distributes electricity conducted a study on the life of poles. The repatriate life data are given in the following table: Life data of electric poles Year after installation: 2 3 4 5 6 7 8 9 10 Percentage poles failing: 1 2 3 5 7 12 20 30 16 4 1 . if the company now installs 5.000 poles and follows a policy of replacing poles only when they fal, how many poles are expected to be replaced each year during the next ten years? To simplify the computation assume that failures occur and replacements are made only at the end of a year. if the cost of replacing individually is ? 160 per pole and if we have a common group replacement policy it costs 80 per pole, find out the optimal period for group replacement