A manufacturing process uses a certain critical device. The device is in working order when first installed. If the device experiences a problem, it shuts down until it is either repaired or scrapped. After shutting down, a technician is summoned. The technician may either restore the device to working order, or may determine that the device is beyond repair and must be scrapped. While working, the device experiences problems that induce a shut down at a rate of 2 per annum. While shut down, the device is restored to working order at a rate of 1 per annum, or is scrapped at a rate of 2 per annum. Once scrapped, the device remains so. The three states of the device are to be modelled by a continuous time stochastic process. a) Carefully solve the Kolmogorov forward equations for PWORKING ORDER. (t), for each je{WORKING ORDER, SHUT DOWN, SCRAPPED}.