Question

A workstation consisting of 12 machines in parallel, each having a mean process time of 2 hours. The station works 16 hours a day in 2 shifts; each is 8 hours. There is one hour break in each shift. You need to produce a lot of 48 jobs per day.

1. Calculate the capacity in jobs per day of this station.
2. A workstation with 12 machines in parallel, each having a mean process time of 2 hours. The station works 16 hours a day in 2 shifts; each is 8 hours. There is one hour break in each shift. The machines are subject to failure and have a mean time to failure of 100 hours with a mean time to repair of 8 hours. You need to produce a lot of 48 jobs per day. Calculate the capacity in jobs per day. Why it is lower or higher than part A?
3. A workstation with 12 machines in parallel, each having a mean process time of 2 hours. The station works 16 hours a day in 2 shifts; each is 8 hours. There is one hour break in each shift. The machines are subject to failure and have a mean time to failure of 100 hours with a mean time to repair of 8 hours. In addition, the machines are set up every 24 jobs, and the mean setup time is 3 hours. You need to produce a lot of 48 jobs per day. Calculate the capacity of the workstation in jobs per day. Why it is higher or lower than parts A and B?
4. For each case above, calculate the utilization of the workstation, and calculate the maximum production the station can make in each case as well.

Answer 1

Production time per shift of 1 machine = ( 16-2) =14 hours per day

Number of items made be each machine = 14/2 =7 per day

Number of output of 12 parallel machines = 7x12 =84 per day

(ii) Machine availability in this case = MTTF/(MTTF+MTTR) =100/(100+8) =0.925925

Net production now = capacity x availability = 84x0.925925 =77.77 per hour

It is lower than part A, because it has downtime related to repairs.

(iii) Number of jobs made by each machine per day = 7

if set up is done after 24 jobs, each set up time will come after 48 hours.

total efficiency = 48/(48+3)=0.941176

New production per day now = 77.77 x 0.941176 =73.1952

It is lower than in part B because it also comprises of set up time after every 24 jobs.

(iv) utilisation = utilised hours / total hours

Case I - 14/16 =0.875

Case II = 0.875*0.925925 =0.8101

Case III = 0.8101*0.941176 =0.7625