Technico Ltd. has installed a machine costing Rs 4 lacs and is in the process of deciding on an appropriate number of a certain spare parts required for repairs. The spare parts cost Rs 4,000 each but are available only if they are ordered now. In case the machine fails and no spares are available, the cost to the company of mending the plant would be Rs 18,000. The plant has an estimated life of 8 years and the probability distribution of failures during this time, based on experience with similar machines, is as follows:

Ignoring any discounting for time value of money, determine the following:

(a) The optimal number of units of the spare part on the basis of (i) minimax principle, (ii) minim in principle, (iii) Laplace principle, (iv) Hurwicz principle (taking a= 0.7), and (v) expected cost principle.

(b) The expected number of failures in the 8-year period.

(c) The regret table, and the optimal choice on the basis of least expected regret criterion.

(d) EVPI.

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No. of failures during 8-yearly period Probability : 0 1 2 3 4 5 44 6+ : 0.1 20 0.2 0.3 0.2 -0 22 0.1 0.1 0