Stochastic Process Costing Models Author(s): A. Wayne Corcoran and Wayne E. Leininger Source: The Accounting Review, Vol. 48, No. 1 (Jan., 1973), pp. 105-114 Published by: American Accounting Association Stable URL: http://www.jstor.org/stable/245193 . Accessed: 12/06/2014 22:05 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp
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Stochastic Process Costing Models A. Wayne Corcoran and Wayne E. Leininger
INTRODUCTION HE pattern of the cost flows within a
process costing system is a function of product flows within the corresponding production system. In a deterministic production system, all units would pass in a common sequence through the processes and exit the system as final product. However, many mass production systems cannot be classified as deterministic. Any unit entering a production system can generally be expected to exit the system in one of several forms. Even units that exit the system in the same form may not have cycled through the production processes in identical sequences. The process costing models developed in this paper are based on the premise that product flows within a mass production system can be described stochastically. Time will be handled in two ways resulting in two models. Standard costs will be integrated into the models for the purpose of costing output and inventories. In the final sections cost analysis based on the models will be treated. T
TRANSFER PERIOD MODEL'
Assume a multiple process production system with n processes and m output states. For example, a system might have three processes and two output states. Output from the system is either final product from the third process or defective units from the second and third processes. In our example, let the probability asso-
ciated with transferring units from the first process to the second process equal one. From the second process, if the probability of a unit being transferred to the third process is 0.75 and from the third process the probability of a unit exiting the system as a completed unit is 0.75, then we can represent the system as an absorbing Markov chain. The stochastic matrix describing such a system is: G
0
0
0 0 3/4i
0
1/4
0
.0
1
0 0
0
3/4
1/4
00
O
1
0
0
0
1
0
where each element pij represents the probability of a unit being transferred from
process i to processj2. The P matrix could 1 The transfer period model is based on material developed by: R. M. Cyert, H. J. Davidson and G. L. Thompson, "Estimation of the Allowance for Doubtful Accounts by Markov Chains," MANAGEMENTSCIENCE (April, 1962), pp. 287-303. The proofs of the formulas in this study are similar to the proofs of Cyert, Davidson, and Thompson. 2 In a stochastic matrix the values of all the elements are in the range O
