Manufacturing System Design Decomposition™
The decomposition of FR-DP113, “Meet customer expected lead time” and “Mean throughput time reduction,” focuses on identifying predictable sources of delays and prescribing general solutions for elimination (see Figure 1). A delay is defined as time that a part spends in the manufacturing system when it is not being processed. Throughput time is defined as the total time that a part spends in the manufacturing system, from the time it enters as raw material to the time it leaves as a finished product. A relationship exists between the time a part spends in the manufacturing system and the total number of parts in the system. This relationship, known as Little’s Law (Little, 1961), can be expressed as follows:
where the variables and their units are the following:
L: Average quantity of parts in the system (i.e. total inventory) [parts]
λ: Average rate parts enter and leave the system [parts / time]
W: Average time spent in system (i.e. throughput time) [time]
This relationship assumes that the manufacturing system is operating at a steady state, so that the rate parts enter the system is, on average, equal to the rate at which parts leave the system. If these rates are not equal, parts will either accumulate in the system (arrival rate > departure rate) or the number of parts in the system will go to zero (arrival rate < departure rate). Little’s Law has been used to develop quantitative relationships between inventory and throughput time for the delays mentioned in this decomposition branch.
The delays identified in the MSDD include: lot delay, process delay, run size delay, transportation delay, and systematic operational delays (Figure 1).
Figure 1: Components of delays for throughput time reduction
To illustrate the first four delay requirements, Figure 2 illustrates a basic serial manufacturing line capable of producing two different types of parts (shown in the figure as cylinders and rectangles).
Figure 2 Types of delays in serial manufacturing operations
The MSDD has already dealt with uncertainties in the quality and time variation branches. Thus, the scope of the decomposition of DP-113 “Mean throughput time reduction” addresses the five delays that result in increased throughput time. The complete decomposition relative to delay reduction is shown in Figure 3. This section will provide further details regarding each type of delay and a formula that can be used to estimate the amount of delay. A simple, two-operation manufacturing system will be used to develop examples of the different types of delays. Assume there are two processing operations (op. 10 and op. 20) necessary, each with a cycle time of two minutes, with no variability in processing time, reliability, or quality. It is also assumed that the customer of this system will demand one part every two minutes. As a result, the amount of inventory kept in the system must be sufficient to prevent the starvation of any of the operations. If an operation is idle in this scenario, demand will go unfulfilled
Figure 3: The MSDD distinguishes five types of delays
FR-T1 “Lot delay”
Lot delay (FR-T1) occurs when parts are transported between operations in lots (also known as transfer batches) of greater than one. While one part in the lot is being processed, all other parts in the lot must wait in storage, either before or after the operation. For the example system, suppose that parts are transported from op. 10 to op. 20 in containers that hold 20 parts each (see Figure 4). Parts are moved only when a container is full. Thus, the first part completed at op. 10 and placed into an empty container must wait for the next 19 parts to be processed before it can be moved to op. 20. The 20th part produced and placed in the container can be moved to the next operation immediately, but upon arrival it must wait for the other 19 parts to be processed, assuming a first-in, first-out processing sequence. Other sequences (such as last-in, first-out) may be used, but the average waiting time over all of the parts in a container will be the same. Neglecting for now the time it takes to transport a full container from op. 10 to op. 20, we can see that the total number of parts stored between these operations is one less than the container size.
Figure 4: Lot delay example
Because transportation time is neglected, part #1 could be loaded into op. 20 immediately after part #20 is completed in op. 10. According to Little’s law, the throughput time added by this transportation lot size is given by:
W = L / λ = 19 parts / 0.5 parts/min. = 38 minutes
Or, more generally,
Lot delay = (Transfer batch size - 1) / Production rate
The means for reducing lot delay is simply to transfer parts in smaller batches, ideally with a transfer batch size of one piece (DP-T1). The design matrix at this level shows that reducing transfer batch size (with the ideal goal being single-piece flow) can have an impact on the ability to reduce process delay (FR-T2) and transportation delay (FR-T4), as reducing the transfer batch size will affect the frequency and quantity of material handling from one operation to the next.
FR-T2 “Process Delay”
Process delay (FR-T2) results when the arrival rate of parts, ra, is greater than the service rate, rs (i.e., the rate at which parts are processed). Unlike the other four types of delays described in this section, process delay cannot occur in a steady-state condition. If the average arrival rate of parts is greater than the average service rate, the amount of inventory in the system will tend towards infinity. Assuming that the long-term average arrival rate is equal to the average service rate, process delay occurs only during shorter time intervals during which ra > rs. Essentially, process delay occurs when parts are processed in excess of demand. The processed parts must then wait until they are demanded by the customer. Returning to the two-operation example described earlier, suppose we look at process delay in the context of operation 20, as shown in Figure 5 and Figure 6.
Figure 5: Production state at the beginning of a shift
In the previous example, each operation had a cycle time of two minutes. Now suppose that op. 10’s cycle time has been decreased to 1.5 min., and that neither operation is ever starved for parts. Customer demand remains the same at one part every two minutes, for a total of 240 parts per 8-hour shift. After 6 hours of operation, op. 10 will have produced the necessary 240 parts for the shift (6 hrs * 60 min/hr / 1.5 min/part = 240 parts). Op. 20, however, will have only processed 180 parts (6 hrs * 60 min/hr / 2 min/part = 180 parts), resulting in an increase in in-process inventory of 60 parts. Assuming op. 10 stops producing parts when it has met demand for the shift, op. 20 will catch up at the end of the shift, customer demand will be fulfilled, and the amount of inventory in the system will return to its previous level. Note that although reducing the cycle time of operation 20 could eliminate the need to run overtime, it would not reduce the amount of process delay. Instead of waiting before operation 20, the parts would simply have to wait at a point further downstream in the system. The root cause of process delay is production ahead of demand, not insufficient capacity.
Figure 6: Production state four hours into the shift
The decomposition prescribes “production designed for takt time” (DP-T2) as the means to eliminate process delay. Achieving this condition requires that the pace of customer demand (i.e., the takt time) be defined (FR-T21) and that the service rate and arrival rate of the system be matched to this takt time (FR’s T-22 and T-23, respectively). The takt time for a system can be calculated by dividing the total number of available production hours in a given time interval (e.g., one week) by the total number of parts demanded during that time. In calculating takt time, it is important that factors such as machine downtime, setup time, and worker allowances be considered in determining how many hours of production can be expected. Matching the service rate to the takt time requires that the system have sufficient capacity to meet customer demand. Overproduction is avoided by ensuring that the arrival of parts at downstream operations is balanced to takt time (DP-T23). In this way, operations producing at a pace faster than the takt time will become starved for incoming materials, and the transfer of materials from one operation to the next will serve as the means to pace production.
FR-T3 “Run Size Delay”
Run size delay (FR-T3) occurs when multiple part types are produced and the sequence of production does not match the sequence of products demanded by the customer. For example, suppose that our two-operation system produces two part types, A and B, and the customer demands 200 of part type A and 40 of type B every day. Assuming that the system runs one shift per day, five days per week, weekly demand will be 1000 of part A and 200 of part B. Suppose that, in order to reduce machine downtime due to changeovers, the system is scheduled to produce all 1000 type A parts first (requiring 2 min/part * 1000 parts / 60 min/hour / 8 hours/day = 4.2 days) and then changeover and produce part type B for the remaining 0.8 days each week. The result will be that customer demand is met on a weekly basis. However, excess inventory of each part type will have to be kept in the system in order to meet the customer’s daily requirements, as shown in Figure 7. The upwards-sloping portions of the lines represent times when that product is being produced. The steep declines represent the daily shipment of the demanded parts to the customer. On average, an inventory of about 180 type A parts and 100 type B parts are kept in the system.
Figure 7: Inventory due to run size delay
To avoid run size delays, production must be matched to customer demand during each demand interval (DP-T3). The demand interval is defined here as the period of time between deliveries to the customer. In the example above, the demand interval is one day. In practice, the length of the demand interval can vary significantly. When transportation distances are long and transportation is expensive, the demand interval might be a week or longer. When transportation distances are short and inventory reduction is critical, the demand interval might be as short as a few hours or less. In order to produce according to customer demand, demand information must be known in advance (FR-T31), requiring frequent communication with the downstream customer, and the manufacturing system must be capable of producing in sufficiently small run sizes (FR-T32). The ability to rapidly changeover equipment from one part type to the next (DP-T33) is critical for achieving this objective. Figure 8 shows how the WIP in the system varies throughout the week when production in the example system is matched to customer demand on a daily basis. With this case, inventory is reduced to an average of 115 of part type A and only 4 of part type B. Run size delay has, by definition, been eliminated completely. The inventory that remains in the system is due to process delay (FR-T2). In this example system, there is a short-term mismatch between the production and shipment rates (i.e. during the day parts are produced at a rate of 0.5 parts / minute, but shipped at a rate of 0 parts / minute).
Figure 8: Reduced inventory – reduced run size delay
FR-T4 “Transportation Delay”
Let us now assume that the time to transport a container of parts from operation 10 to 20 is non-zero (see Figure 9). In this case, additional inventory is necessary to prevent part shortages at op. 20. The transportation delay time (FR-T4) is defined as the total time from the moment when a full transfer batch of parts is ready to be transported until these parts arrive at the downstream operation and are ready for processing. This time includes the time parts spend waiting to be transported, the time spent in transit, and any necessary loading and unloading time. The amount of inventory added to the system due to transportation time is given by:
Additional inventory =
Transportation time * Production rate
The transportation delay will be equal to the amount of transportation time. Continuing with the example system and assuming that it takes 6 minutes to transport parts from operation 10 to 20, the amount of additional inventory will be:
6 minutes * 0.5 parts/min = 3 parts
Figure 9: System state 4 minutes into the transportation time
The manufacturing system design decomposition advocates system layout design as the means for reducing transportation delays. By arranging equipment based on product flow (DP-T4) as opposed to grouping equipment by operation, transportation distance can be minimized. An alternative means for reducing transportation delay would be to speed up the means of transportation; however, this solution is not prescribed by the decomposition, as it does not address the root cause of the delay: long transportation distances. Another important factor for reducing transportation delay is ensuring that transportation resources arrive to pick up and deliver parts at the proper times. This timing aspect is covered in the decomposition of FR-T2, “Reduce process delay.” This information is reflected in the design matrix by a relationship between DP-T2, “Production designed for takt time,” and FR-T4, “Reduce transportation delay.”
FR-T5 “Systematic Operational Delays”
Routinely occurring delays caused by interferences among resources are referred to in the MSDD as systematic operational delays (FR-T5). The decomposition considers two categories of resources, production resources (workers and/or automation involved in the processing of parts) and support resources (workers and/or equipment supporting this production by supplying small purchased parts, removing chips from machine tools, etc.). Delays occur when one resource prevents another from performing its duties. The delay time is given by:
Systematic operational delay = Duration of interference among resources
For example, consider a workstation at which an operator manually performs several assembly tasks, including adding some screws, washers, etc. to a partially assembled product. Assuming that the operators have containers of each of these small purchased parts at their workstations, a support resource is necessary to periodically replenish the operators’ supply. If this replenishment requires operators to stop working and move away from their workstations, an interference has occurred between a support resource (the material replenisher) and a production resource (the operator). The part being processed is delayed by the amount of time it takes the replenisher to refill the necessary containers. The proposed means for reducing such delays is the coordination and separation of the work and access requirements of each resource (DP’s T51-T53).