Q
Thus,
U = (100)(175,000 parts)/258,681 parts = 67.7%.
Additionally, a manufacturing system under repair may not be fully used. Thus, the availability of a system, expressed as a percentage, can be calculated. It is determined by the equation
A = 100(tmtbf − tmtbr)/tmtbf
where
| A | = | availability |
| t mtbf | = | mean time between failures (hr) |
| t mtbr | = | mean time to repair (hr). |
These two measures provide solid insight into a manufacturing system and can also help in identifying automation opportunities. Additionally, if utilization and availability information is known within a facility, realistic actual production values can be calculated. Consider the following example.
Example 2.10
A manufacturing system has a theoretical production capacity of 100,000 parts/ month. Typical utilization of the system is 80% and availability is 93%. What is the anticipated actual monthly production of the system?
Solution
Rearranging the equation for utilization and factoring in the availability of the system yields the following equation:
Q = UPcA.
Thus,
Q = (80%)(100,000 parts/month)(93%) = 74,400 parts/month.
Another important quantifying measure of production is manufacturing lead-time. Manufacturing lead-time is the total time it takes to convert raw material into a finished product. Thus, it is the summation of the time of each individual manufacturing process that the product passes through. Note, however, that a product is not processed continually. There is also non-operation time associated with each operation. Examples of non-operation times include those for moving and queuing of parts between operations, waiting for materials, waiting for tools, and so on. These must be accounted for in the calculation of manufacturing lead-time. Additionally, the time to set up the process, where appropriate, must also be considered. Accordingly, the equation for the manufacturing lead-time of a process manufacturing system consisting of operations (indexed by i) is
tmlt = sumi(tsu + Qtc + tnop)i,
where
| t mlt | = | manufacturing lead-time for batch |
| t su | = | setup time for a process |
| Q | = | number of parts in batch |
| t c | = | operational cycle time of a process |
| t nop | = | non-operation time of a process |
Note that this equation can be used for other types of manufacturing systems as well. However, some of the terms may be insignificant. Consider a quantity manufacturing system. The setup time and non-operation time may become very small compared to the batch size. Additionally, in the flow-line system the setup and non-operation time are essentially nonexistent.
Example 2.11
A part is routed through 4 machines in lot sizes of 500 parts/batch. Average non-operation time is 6 hr. Setup and operational cycle times are shown in the table below. Calculate the manufacturing lead-time for the part.
Solution
The governing equation is
tmlt = sumi(tsu + Qtc + tnop)i.
Calculate the manufacturing lead-time for each operation:
| t mlt1 | = | 1 hr/batch + (500 parts/batch)(3 min/part)(1 hr/60 min) + 6 hr/batch = 32 hr/batch |
| t mlt2 | = | 6 hr/batch + (500 parts/batch)(8 min/part)(1 hr/60 min + 6 hr/batch = 78.67 hr/batch |
| t mlt3 | = | 1.5 hr/batch + (500 parts)(4 min/part)(1 hr/60 min + 6 hr/batch = 40.83 hr/batch |
| t mlt4 | = | (4 hr/batch + 500 parts)(3 min/part)(1 hr/60 min) + 6 hr/batch = 35 hr/batch |
Summing operation lead-times gives
tmlt = tmlt1 + tmlt2 + tmlt3 + tmlt4 = 32 + 78.67 + 40.83 + 35 = 186.5 hr/batch.
It is relatively easy to visualize how improvements in productivity result in corresponding improvements in these measures. Therefore, such measures can also be used in making the case for automation.
2.4 Process Inputs and Manufacturing Costs
The previous section demonstrated how one would quantify the output of a process with a measure (production rate) that can be used in productivity calculations. In this section, methods of quantifying the input to the process are developed. As shown in Section 2.2, input into the productivity calculation (PI) is amount of money required for the process step under consideration, which is input into the process over the same time frame as that of the output measurement. Both measurements are in units of $/hr.
Inputs to a process are typically broken down into categories consisting of capital, energy, labor, and material. These categories are termed partial productivity measures. Consideration of a breakdown of the costs to manufacture a product is shown in Figure
