**Appendix A**

In the table below, the rows and columns describe individual production shifts. The probability of the machine failure during a given shift is derived from the matrix by setting the shift number in a given row against an appropriate column, e.g., for Machine *M*6, the probability that the machine failure will occur after shift 1 during shift 2 is 0.593 (first row, second column). The procedure of machine failure probability calculation is described in detail in Section 3.3 (Definition 4).

**Table A1.** The transition rate matrix for each machine in the production system. Bold numbers represent the highest probability of the machine failure.


#### **References**


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