By Kenneth P. Gee
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While state 4 is limiting, it is not absorbing - all pounds must ultimately pass from it either to be paid or to enter into bad debt. Stryford Ltd 31 Hence only P and B are absorbing states. The approach to computing hp may be expressed in words as follows : Amount paid from state 4 = (Opening balance in state 4 + amount assumed to enter state 4) - (Closing balance in state 4 + amount leaving state 4 as bad debt) The transition probability of payment is given by the amount paid from state 4 divided by the opening balance in that state.
Here, the relatively small number for Process 0 is attributable to the discarding of defective units at the ends of Processes A-C. A similar explanation may be advanced for the remaining three rows of the matrix, where (for example) the small number in the first column of the second row arises from the fact that a unit starting in Process B can pass through Process A only in the relatively rare event of the reworking of that process being required. To establish the volume of RDA units undergoing each process at any given time, it is necessary to define a row vector k , which for the general case of n processes will be of dimension 1 x n, Th is vector contains the new elements started into production at the beginning of each transfer period (which is here each shift).
Economics of the 'zero defects' approach Suppose that, by extensive expenditure of time and money on quality control, a 'zero defects' regime were to be established, in which all the RDA unit assemblies which entered Process A ultimately emerged from Process D as finished RDA units, and none were ever withdrawn from the manufacturing system as being beyond repair. It would then be possible to draw up a new version of the existing matrix Q, being conditional upon all of the units of output being good.
Advanced Management Accounting Problems by Kenneth P. Gee