Formulae: Actual output Efficiency= Effective capacity Utilization = Actual output Design capacity TC-FC+VC (TC- Total cost; FC - Fixed costs; VC-Variable costs) Output rate = Operating time per day Cycle time Operating time per day Cycle time = Desired output rate N. min Cycle time (where Nmin - Theoretical minimum number of work stations and Sum of task times) Percentage of idle time = Idle time per cycle x100 (where Nactual = Actual number of stations) XCycle time Efficiency 100% - Percent idle time Header for task assignment chart: Revised Station Time Workstation Remaining Eligible Assign Task Time Idle Remaining Time Mean chart: UCL/LCL = xzo; (where z = normal standard deviate, = 0) UCL/LCL=x+4R (where A2 is given factor and R is the average of the range - a given) = Range chart: UCL =D&R and LCL DR (where D3 and D4 are given factors) p-chart: UCL, / LCL, = p where average fraction defective in the population Total Number of defectives p = Total number of observations P(1-p) and p is the estimated 11 c-chart: UCL/LCL =z (where c is the mean number of defects per unit). If c is unknown, the sample estimate e is used in place of c, using e-Number of defects /Number of samples Explanation: 1. A manufacturing plant produced 500 units in a day with an actual output of 480 units. What is the efficiency of the plant? 2. A machine has a design capacity of producing 100 units in an hour. If the machine operates for 45 minutes in an hour, what is the effective capacity of the machine? 3. A company has fixed costs of $10,000 and variable costs of $5 per unit produced. If the company produces 2,000 units, what is the total cost of production? 4. A manufacturing process has an output rate of 10 units per hour. If the cycle time is 6 minutes, what is the operating time per day required to produce 500 units? 5. A manufacturing process has a cycle time of 20 seconds and a desired output rate of 60 units per hour. What is the operating time per day required to meet the desired output rate? 6. A manufacturing process has a total of 10 tasks with task times of 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 minutes. What is the minimum number of workstations required to complete the tasks within a cycle time of 60 minutes? 7. A manufacturing process has 6 workstations and a cycle time of 5 minutes. If the idle time per cycle is 30 seconds, what is the efficiency of the process? 8. A mean chart for a manufacturing process has an upper control limit of 4.5 and a lower control limit of 3.5. If the average of the sample means is 4.0 and the standard deviation is 0.2, is the process under control? 9. A range chart for a manufacturing process has an upper control limit of 0.5 and a lower control limit of 0.2. If the average range is 0.3, is the process under control? 10. A company inspects 200 samples of a product and finds 20 defective units. What is the estimated average fraction defective in the population?