# How to Calculate Percentage Improvement Between 2 Numbers by aim42794

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activity effi
alculates
provement c
Process im

by merwan mehta

The pursuit of lean principles of waste reduction                    In conducting a VSM exercise, lean implementers calculate
and throughput improvement are the chief means adopted            the percentage of value-added time and the inventory efficien-
by businesses all over the world after the spectacular story      cy for manufacturing, transactional and administrative pro-
of Toyota and its production system. In implementing lean         cesses. In VSM, the percentage of value-added time (%VAT)
principles, Toyota uses value stream mapping (VSM), which         is calculated as follows:
analyzes the entire value stream for a product from the raw
material to the finished state. VSM also finds use in analyz-      [total operation time or total activity time for the process /
ing service, transactional and administrative processes, from                 total lead-time for the process] * 100
the point of need identified by a customer until the service is
satisfactorily performed. As Mike Rother and John Shook’s           It is used as a metric along with inventory efficiency. Inven-
book, Learning to See, states, VSM captures material and infor-   tory efficiency is defined as:
mation flow simultaneously to allow lean practitioners to see
the flow of the entire product or service steps in a graphical      total operation time or total activity time for the process /
form to facilitate the application of manufacturing principles       [total inventory in the system / inventory usage per day],
in a systematic manner.                                                             converted into a percentage

28   Industrial Engineer
allows operators to see how well they are working together to
keep the product moving through the value stream. A tool that
can tremendously help to balance a process and simultane-
ously let operators know how well they are working as a team
is activity efficiency (AE). AE can equally well be applied to
manufacturing and service processes where throughput and
teamwork are essential.

The concept of activity efficiency
To understand the concept of AE, consider a simple process
as shown in Figure 1. Operations or activities A, B and C that
take 15 minutes, 25 minutes and 50 minutes, respectively, are
sequentially completed to get one output from the process.
The product can equally be a manufactured item or a service
that will be delivered as 15 + 25 + 50 = 90 minutes, after the
process is started.
Say we operate the process for an eight-hour shift with
two 10-minute breaks. This makes the available time for the
process equal to (8 hours x 60 minutes) – (2 x 10) = 460
minutes. The total capacity in terms of the people-minutes
available to conduct the process if there is one person man-
ning each of the three activities for the shift will be equal to
(3 x 460), or 1,380 minutes. Now as each unit needs 90 min-
utes of total work, we can calculate how many products can
be produced in an ideal situation if the entire available time
was converted into value-added time. This comes out to 1,380
minutes / 90 minutes = 15.33 units.
The cycle time (C/T) for the entire process consisting of
the three operations A, B and C will be 50 minutes because
Operation C is the bottleneck operation. Here, cycle time is
defined as the average time interval after which one product
will result from the process as it is continuously running. As
Although %VAT and inventory efficiency help improve the       we saw earlier, once the process begins to operate, the first
value-added time and reduce the amount of inventory in the      unit will be done in 90 minutes. Hence, of the 460 minutes
process, they do not do much to improve the throughput of       total available in the process, we would be left with 370 min-
the process. To improve throughput, the operations need to      utes (460 - 90) after the first product. In these 370 minutes,
be balanced well and there needs to be a metric in place that   the process will be able to produce (370 divided by 50), or 7.4

basic oPerations outPut

Figure 1. simple process with three operations

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a+e=lean

PrimeD Process

I                                I                          I                            I

Figure 2. A primed process ends with inventory in between each operation.

units. In the entire eight-hour shift, we will get (1 + 7.4), or   throughput by working at 100 percent efficiency. An alter-
8.4 units. In this scenario, we started with no inventory in       nate way this can be achieved would be to use three stations
between the activities or operations, or with what we call an      with three operators and let them each complete the three
unprimed process or a dry process.                                 operations A, B and C. Depending on the capital require-
Say we keep the process filled with an available unit at        ment for the stations, this may or may or not be possible.
the start of the shift or have what is referred to as a primed        In the best-case scenario, we see that for an unprimed line
or a wet process. This scenario is shown in Figure 2. A            we can ideally only get 8.4 units, and the AE for the unprimed
primed process is ended with inventory in between each             line will be equal to 8.4 divided by 15.33, or 0.548, or AE
operation so that each operation in the next shift can be-         (unprimed line) = 54.8 percent. Similarly, the AE (primed
gin immediately and does not have to wait for the line to          line) will be 10.2 divided by 15.33 = 66.5 percent. The sum-
fill up. In a primed process, the first t will be done instant-    mary of the results for the example are shown in Figure 3.
ly after the production begins since a unit is completely             Observing the AE numbers, we see that the loss of ef-
ready after Operation C. Hence, in the 460 minutes avail-          ficiency from 100 percent to 66.5 percent is due to the
able in the shift, we can get 460 divided by 50, which is          imbalance in the process even when the process is run
9.2 units. Adding the one unit that we got at the very start       primed, and the loss of efficiency from 66.5 percent to
of the shift, in eight hours we will get (1 + 9.2), or 10.2        54.8 percent is due to running the line unprimed. No
units. Hence, the expected output for a primed line for our        matter how efficiently the employees in the process func-
scenario will be 10.2 units.                                       tion, it will be very difficult for them to produce better
In conducting this analysis, we have gotten three num-          results than these. Processes that are infrequently done
bers: ideal expected output = 15.33 units, expected output         can be considered unprimed processes, whereas repetitive
(unprimed line) = 8.4 units, and expected output (primed           processes that are constantly being carried out can be con-
line) = 10.2 units. We can now use these numbers to calcu-         sidered primed processes. If a process can be kept primed,
late the AE. If the process produces 15.33 units, we can say       the efficiency of the process will be higher. Production,
that the work cell is running at an ideal efficiency of 100        administrative and transactional business processes can
percent. This can only happen if the operations are perfectly      all be run as primed or unprimed processes depending on
balanced and if the operators are working to maintain the          the specific application.

outPut measurement

Expected output units                 Activity efficiency (%)
ideal                                     15.33                                      100

unprimed                                      8.4                                     54.80

Primed                                      10.2                                    66.50

Figure 3. summary of results for activity efficiency

30   Industrial Engineer
Applying AE to a work cell                                       we see that all the rest of the operations except operations
Now let’s apply the concept of AE to a more complex work         WS-4 and WS-8 take less than or equal to 12 minutes. Sta-
cell. Figure 4 shows an assembly (hypothetical) process          tion WS-4 takes 22 minutes and Station WS-8 takes 25
where nine operations (with times for each shown in min-         minutes. To accommodate these, we will definitely have to
utes) complete the assembly, and the 10th operation in-          provide two stations each for both to bring down their cycle
spects the product.                                              times to 11 minutes and 12.5 minutes, respectively: (cycle
The total time needed to complete one product is 114 min-
utes, which means that if we set up the assembly as a line
hyPothetical assembly
and pass the product from station to station with all opera-
tors present, one unit will take 114 minutes to be completely    Process
assembled and tested. Now say the customer requires 32
products in one shift. The available time in one shift is (8
hours x 60 minutes) – (two 10-minute breaks) = 460 min-
utes. Hence, the customer is buying one unit every (460
minutes divided by 32), or 14.4 minutes. This is also called
the takt time, which is the average rate at which the customer
buys the product. Takt time is used in the process to make
sure that the cycle time of each operation does not exceed
the takt time, or the process will not be able to make all the
products needed. Since our takt time is 14.4 minutes, the
maximum cycle time for any operation in the process, as a
rule of thumb, should not exceed 90 percent of 14.4 minutes
or 13 minutes.
Studying the individual operations, we see that opera-
tions WS-5 and WS-6, which are close to one another, take a
total of only 12 minutes, and hence these two can be merged      Figure 4. operation times for assembly of a plant with
into one operation taking 12 minutes. With this change,          nine operations

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a+e=lean

rise in ae With kanbans

Figure 5. Process setup for a prime line

time = operation times / number of stations). Looking at all      be 143 minutes as shown.
the operations again with two stations for operations WS-4           Now we can calculate the people requirements of the pro-
and WS-8, we see that all the operations have a cycle time of     cess as shown in the column with the heading “# of opera-
less than 12.5 minutes. Therefore, using 13 minutes as the        tors” in Figure 4. One operator is needed for all stations ex-
cycle time for the process that we calculated will work well.     cept for operations WS-5 and WS-6, which are combined as
Based on this example, we can calculate the planned opera-     one and need one operator, and operations WS- 4 and WS-8,
tion time (O/T) for each operation as shown in the column         which need two operators each. The total number of operators
with the heading “Planned O/T” in Figure 4. As the product        needed for the cell comes to 11.
will move every 13 minutes from one station to another, the          With this scenario, we can calculate the AE for the unprimed
planned operation time for all operations will be 13 minutes      line. In the unprimed line, the first part will be done in 114
except WS-4 and WS-8, which will have a planned operation         minutes. Every part after that will come out every 13 minutes,
time of 26 minutes (13 x 2) each. The total operation time will   which is the designed cycle time for the process. The expected
output after the first part is completed in 114 minutes will
be (460 minutes – 114 minutes) divided by the cycle time of
the process of 13 minutes, or 26 pieces (346 / 13). The total
expected output for the unprimed line in a shift will be 27.6
pieces (1 + 26.6).
Considering the line primed as shown in Figure 5, with a
finished part kept at the end of the inspection Operation 10,
the first part after the line has begun will be instantly supplied,
and every part after that will come out every 13 minutes. The
expected output after the first part will be 460 minutes di-
vided by 13, or 35.4 pieces. With the one piece delivered at the
very start of the process, the expected output for the primed
line would be 36.4 pieces (1 + 35.4).
Next, we calculate the ideal number of products that can
be produced in a shift by the line. At 100 percent efficiency,
all the operations are perfectly balanced and the operators
are working at their best, and in such a case the total people-
minutes available in the cell in a shift will all be converted into
value-added work. The total people-minutes in the cell is 460
minutes times the number of people in the cell (460 x 11 peo-
ple), or 5,060 people-minutes. Converting all of the 5,060
people-minutes into products, we should get 5,060 divided

32   Industrial Engineer
iDeal figures

Expected results

units                                     Efficiency (%)

ideal                                         44.38                                            100

unprimed                                          27.6                                             62

Primed                                          36.4                                             82

Figure 6. Expected results in terms of units and efficiency for process

by 114 minutes, or 44.38 units. Therefore, the ideal expected        on getting all the setups done simultaneously and focus on
output from the work cell is 44.38 pieces.                           conducting simultaneous preventive maintenance for all the
We have three numbers that we have calculated: ideal ex-           stations.
pected output (44.38 units), expected output – unprimed                 Analyzing and creating a process line as suggested also
(27.6 units) and expected output – primed line (36.4 units).         enables the implementation of a team-based incentive plan
Utilizing these, we can now calculate the AE (unprimed line)         to motivate all the operators in the process to perform at
= (expected output unprimed line) / (ideal expected output)          their best and constantly improve based on the AE numbers.
= 27.6 / 44.38 = 0.62, or 62 percent, and AE (primed line)           The other added advantage in analyzing a line using AE is
= (expected output primed line) / (ideal expected output)            also that bottleneck operations in the process become clear-
= 36.4 / 44.38 = 0.82, or 82 percent. These have been sum-           ly identified, and if a kaizen to improve a part of the process
marized in Figure 6.                                                 in terms of cycle time, setup time or quality is to be under-
taken or an investment made, it can be made to the opera-
Conclusions                                                          tion that has a cycle time that is closest to the takt time. In
What the results tell us is that no matter how well the op-          our case, that would be to improve operation WS-8 followed
erators in the process perform, they will not be able to use         by operation WS-10. d
more than 62 percent of the time they are present in the
cell to perform value-added work required to satisfy the             Merwan Mehta is an associate professor in the technology systems de-
customer. This is when they begin with an unprimed pro-              partment at East Carolina University in Greenville, N.C. He has more
cess. If the process is primed with an adequate number of            than 20 years experience in business and industry working as an in-
kanbans between the operations as shown in Figure 5, the             dustrial engineer, machine tool design engineer, manufacturing engineer
AE will be raised from 62 percent to 82 percent. The gain            and manager, project director, vice president and lean Six Sigma consul-
of 20 percent can solely be attributed to priming the line.          tant. Mehta has conducted two-day value stream mapping workshops
Further, no matter what the operators do, they will not be           for IIE’s Operational Excellence Conference and Expo since 2001 and
able to exceed an AE of 82 percent as the loss of 18 percent         at various companies all over the United States. He holds a Ph.D., is
from the ideal of 100 percent is entirely due to the imbal-          an SME-certified manufacturing engineer and is an ASQ-certified Six
ance within the operations.                                          Sigma black belt.
Metrics to monitor the AE for the unprimed or the primed
process as the case may be can then be implemented to allow
operators to see how well they are doing. Within a short time
after implementing a line as described above, employees will
learn that the only way to keep the efficiency high is to work
as a team to move the product from the first station to the
last consistently. Any hitch in one of the operations is a loss
in time for the entire process. This allows employees to focus

June 2009   33

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