Compute the requirement of spares for breakdown maintenance for an item that exhibits a Poissonian behavior for failure rates with a mean breakdown rate of five items per month. If the lead time for procuring these spares is one month and a service level of 90 per cent is to be used, what buffer stock of these items should be maintained? (A fixed re-order quantity system of inventory is being used). x28 Buffer stock is required to cover the lead time only, i.e. to cover one month's period. Mean consumption rate, = 5 per month Referring to the Poisson distribution table for a = 5, we have for X = 7... Cumulative probability = 0.867 x=8... Cumulative probability = 0.932 Thus, with seven items only 86.7 per cent service level is attained; with eight items 93.2 per cent service level is obtained. Since one would err on the higher side of the service level, the value of x = 8 is chosen. This means the amount of spares stock that has to be kept must correspond to a maximum demand rate Dmax of eight during the lead time. In other words we should keep a Buffer Stock =Dmax - Daverage during a lead time - 8-5 = 3 items. Thus, buffer stock desired is three numbers of the given spare part. The main shaft of an equipment has a very high reliability of 0.990. The equipment comes from Russia and has a high downtime cost associated with the failure of this shaft. This is estimated at 2 crore as the costs of sales lost and other relevant costs. However, this spare is quoted at 10 lakh at present. Should the shaft spare be procured along with the equipment and kept or not? The expected cost of down-time = (Probability of failure) (Cost when break-down occurs) = 11 -0.990) * (2 crore) = 72 lakh However, the cost of procuring the spare now is 10 lakh. Therefore, expected cost of downtime cost of spare; hence the spare need not be bought along with the equipment. less than the Sun. Illustration 7 PQR company has kept records of breakdowns of its machines for 300 days work year as shown below: No. of breakdown Frequency in days 0 40 1 150 2 70 3 30 4 10 300 The firm estimates that each breakdown costs 650 and is considering adopting a preventive maintenance program which would cost 200 per day and limit the number of breakdown to an average of one per day. What is the expected annual savings from preventive maintenance program