$U_{\max }$

Maximal production rate

$\alpha (.)$

Continuous time and finite state Markov process

$\Theta (\cdot )$

System state

$\xi (\cdot )$

Stochastic process of machine states

$\Omega$

Set of system modes

$B(\cdot )$

Set of admissible production capacities for each

$Q(\cdot )$

Transition matrix

$\pi (\cdot )$

Probability limit

$\rho$

Discount rate

$g(\cdot )$

Instantaneous cost

$J(\cdot )$

Total cost function

$z_j$

Optimal inventory level of product type j

$c^{+}$

Inventory cost

$c^{-}$

Shortage cost

$c_r$

CM cost

$c_{LOTO}$

LOTO cost

$c^{\alpha }$

Operation cost under CM at state $\alpha (.)$

$q_{\alpha \beta }$

Rate of transition from state $\alpha (.)$ to $\beta (.)$

$r_{21}$

CM rate without human error (CM - WOHE) with demand d₁

$r_{31}$

CM rate with human error (CM - WHE) with demand d₁

$r_{54}$

CM rate without human error (CM - WOHE) with demand d₂

$r_{64}$

CM rate with human error (CM - WHE) with demand d₂

$h_x$

Increment of the variable x

${\vartheta }_x(\cdot )$

Value function of inventory x

${\vartheta }^h(\cdot )$

Approximation of the value function for $h_x$ increment