Erratum: On modelling poor quality costs in part manufacturing operation

In the original paper by Feiring et al. 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 0ˆ factory's inspection, State 1ˆ factory's rework=repair, State 2ˆ customer's inspection, State 3ˆ ®eld test, State 4ˆ passing customer acceptance, State 5ˆ scrapping, and State 6ˆ 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