Erratum: On modelling poor quality costs in part manufacturing operation
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Corrigenda: On modelling poor quality costs in part manufacturing operation In the original paper by Feiring et al.1 of which I was coauthor, the internal and external failure costs are modeled by a ®ve-state Markov chain. Their State 0 and State 3 involve compound activities. As a consequence, the activity-based quality costs associated with inspection and reworking= repairing activities cannot be separately estimated. Similarly, the customer's inspection and ®eld testing activity costs cannot be separated. In order to avoid this dif®culty, we must de®ne two additional states to de-couple the compound activities. Figure 1 below illustrates the corrected seven-state transition diagram. The revised state de®nitions for individual activities are given as follows. State 0 factory's inspection, State 1 factory's rework=repair, State 2 customer's inspection, State 3 ®eld test, State 4 passing customer acceptance, State 5 scrapping, and State 6 UAI=RAP. For certain parts in a batch, some quality cost-driving activities may not be required at all, while other activities may be performed at least once. The proportion of a given batch of parts requiring a certain activity is the probability that a random part may reach the corresponding state for the ®rst time. This ®rst-passage probability is therefore important for ®nding the expected number of parts that require a given operation, for example, ®eld test. The original paper, however, did not consider the ®rst-passage probability for the transient states. As a consequence, the total number of parts rejected by the customer for a given batch (denoted by M) was much smaller than the true value. Let rij be the probability that a part reaches State j for the ®rst time, given that it is initially in transient State i. Such probability can be determined by
rij pij
P k6j
pij rjk
State i, the following results are obtained: p01
1 ÿ p23 p02 ; r02 ; 1 ÿ p01 1 ÿ p23 ÿ p02 p20 p20 p23
1 ÿ p01 ; r23 1 ÿ p23 1 ÿ p01 ÿ p02 p20
r01 r20
Z r02 M ; X r01 M ; T r23 Z r02 r23 M F1 w01 r01 MD1 ;
Y r20 Z r02 r20 M ;
F2 u05 MV ;
3
F3 u06 MW ;
F5 w20 r02 r20 MS; F4 w20 r02 r20 MR; F7 v0 MU ; F6 w23 TD2 ;
4
where the seven failure costs, in $ per batch, for the quality system are de®ned as follows: F1 factory's rework= repair cost, F2 factory's scrapping cost, F3 UAI=RAP AP cost, F4 warranty, claims, and compensation cost, F5 factory's shipping and handling cost for returned parts, F6 customer's ®eld testing cost for parts that failed the inspection, and F7 factory's record updating cost. In this case study it is assumed that the total number of acceptable parts (G) to be delivered to the customer is 139 000. The absorption probability (u04 for both studies) is 0.925 when the factory's quality level is equal to 90%. The batch size M G=u04 150 270 parts for both studies. The number of parts that re
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