Sunday, June 28, 2015

Time Study by F.W. Taylor

Content from F.W. Taylor, Shop Management

Time Study

When work is to be repeated many times, the time study should be minute and exact. Each job should be carefully subdivided into its elementary operations, and each of these unit times should receive the most thorough time study. In fixing the times for the tasks, and the piece work rates on jobs of this class, the job should be subdivided into a number of divisions, and a separate time and price assigned to each division rather than to assign a single time and price for the whole job. This should be done for several reasons, the most important of which is that the average workman, in order to maintain a rapid pace, should be given the opportunity of measuring his performance against the task set him at frequent intervals. Many men are incapable of looking very far ahead, but if they see a definite opportunity of earning so many cents by working hard for so many minutes, they will avail
themselves of it.

As an illustration, the steel tires used on car wheels and locomotives
were originally turned in the Midvale Steel Works on piece work, a
single piece-work rate being paid for all of the work which could be
done on a tire at a single setting. A fixed price was paid for this
work, whether there was much or little metal to be removed, and on the
average this price was fair to the men. The apparent advantage of fixing
a fair average rate was, that it made rate-fixing exceedingly simple,
and saved clerk work in the time, cost and record keeping.

A careful time study, however, convinced the writer that for the reasons given above most of the men failed to do their best. In place of the single rate and time for all of the work done at a setting, the writer subdivided tire-turning into a number of short operations, and fixed a proper time and price, varying for each small job, according to the amount of metal to be removed, and the hardness and diameter of the tire. The effect of this subdivision was to increase the output, with the same men, methods, and machines, at least thirty-three per cent.

As an illustration of the minuteness of this subdivision, an instruction
card similar to the one used is reproduced in Figure 1 on the next page.
(This card was about 7 inches long by 4 inches wide.)

The cost of the additional clerk work involved in this change was so insignificant that it practically did not affect the problem. This principle of short tasks in tire turning was introduced by the writer in
the Midvale Steel Works in 1883 and is still in full use there, having survived the test of over twenty years' trial with a change of management.

In another establishment a differential rate was applied to tire turning, with operations subdivided in this way, by adding fifteen per cent to the pay of each tire turner whenever his daily or weekly piece
work earnings passed a given figure.


This, as already explained, is the most important element of the system advocated by the writer. Without it, the definite, clear-cut directions given to the workman, and the assigning of a full, yet just, daily task, with its premium for success, would be impossible; and the arch without
the keystone would fall to the ground.

In 1883, while foreman of the machine shop of the Midvale Steel Company of Philadelphia, it occurred to the writer that it was simpler to time with a stop watch each of the elements of the various kinds of work done in the place, and then find the quickest time in which each job could be
done by summing up the total times of its component parts, than it was to search through the time records of former jobs and guess at the proper time and price. After practicing this method of time study himself for about a year, as well as circumstances would permit, it became evident that the system was a success.

The writer then established the time-study and rate-fixing department, which has given out piece work prices in the place ever since.

This department far more than paid for itself from the very start; but it was several years before the full benefits of the system were felt, owing to the fact that the best methods of making and recording time observations, as well as of determining the maximum capacity of each of the machines in the place, and of making working tables and time tables, were not at first adopted.

It has been the writer's experience that the difficulties of scientific
time study are underestimated at first, and greatly overestimated after
actually trying the work for two or three months. The average manager
who decides to undertake the study of unit times in his works fails at
first to realize that he is starting a new art or trade. He understands,
for instance, the difficulties which he would meet with in establishing
a drafting room, and would look for but small results at first, if he
were to give a bright man the task of making drawings, who had never
worked in a drafting room, and who was not even familiar with drafting
implements and methods, but he entirely underestimates the difficulties
of this new trade.

The art of studying unit times is quite as important and as difficult as that of the draftsman. It should be undertaken seriously, and looked upon as a profession. It has its own peculiar implements and methods, without the use and understanding of which progress will necessarily be slow, and in the absence of which there will be more failures than successes scored at first.

When, on the other hand, an energetic, determined man goes at time study as if it were his life's work, with the determination to succeed, the results which he can secure are little short of astounding. The
difficulties of the task will be felt at once and so strongly by any one who undertakes it, that it seems important to encourage the beginner by giving at least one illustration of what has been accomplished.

Mr. Sanford E. Thompson, C. E., started in 1896 with but small help from the writer, except as far as the implements and methods are concerned, to study the time required to do all kinds of work in the building trades. In six years he has made a complete study of eight of the most important trades--excavation, masonry (including sewer-work and paving), carpentry, concrete and cement work, lathing and plastering, slating and roofing and rock quarrying. He took every stop watch observation himself and then, with the aid of two comparatively cheap assistants, worked up and tabulated all of his data ready for the printer. The magnitude of this undertaking will be appreciated when it is understood that the tables and descriptive matter for one of these trades alone take up
about 250 pages. Mr. Thompson and the writer are both engineers, but neither of us was especially familiar with the above trades, and this work could not have been accomplished in a lifetime without the study of elementary units with a stop watch.

In the course of this work, Mr. Thompson has developed what are in many respects the best implements in use, and with his permission some of them will be described. The blank form or note sheet used by Mr. Thompson, contains essentially:

(1) Space for the description of the work and notes in regard to it.

(2) A place for recording the total time of complete operations--that
is, the gross time including all necessary delays, for doing a whole job
or large portions of it.

(3) Lines for setting down the "detail operations, or units" into which
any piece of work may be divided, followed by columns for entering the
averages obtained from the observations.

(4) Squares for recording the readings of the stop watch when observing
the times of these elements. If these squares are filled, additional
records can be entered on the back. The size of the sheets, which should
be of best quality ledger paper, is 8 3/4 inches wide by 7 inches long,
and by folding in the center they can be conveniently carried in the
pocket, or placed in a case (see Fig. 3, page 153) containing one or
more stop watches.

This case, or "watch book," is another device of Mr. Thompson's. It
consists of a frame work, containing concealed in it one, two, or three
watches, whose stop and start movements can be operated by pressing with
the fingers of the left hand upon the proper portion of the cover of the
note-book without the knowledge of the workman who is being observed.
The frame is bound in a leather case resembling a pocket note-book, and
has a place for the note sheets described.

The writer does not believe at all in the policy of spying upon the
workman when taking time observations for the purpose of time study. If
the men observed are to be ultimately affected by the results of these
observations, it is generally best to come out openly, and let them know
that they are being timed, and what the object of the timing is. There
are many cases, however, in which telling the workman that he was being
timed in a minute way would only result in a row, and in defeating the
whole object of the timing; particularly when only a few time units are
to be studied on one man's work, and when this man will not be
personally affected by the results of the observations. In these cases,
the watch book of Mr. Thompson, holding the watches in the cover, is
especially useful. A good deal of judgment is required to know when to
time openly, or the reverse.

The operation selected for illustration on the note sheet shown in Fig. 2, page 151, is the excavation of earth with wheelbarrows, and the values given are fair averages of actual contract work where the
wheelbarrow man fills his own barrow. It is obvious that similar methods of analyzing and recording may be applied to work ranging from unloading coal to skilled labor on fine machine tools.

The method of using the note sheets for timing a workman is as follows:

After entering the necessary descriptive matter at the top of the sheet, divide the operation to be timed into its elementary units, and write these units one after another under the heading "Detail operations." If the job is long and complicated, it may be analyzed while the timing is going on, and the elementary units entered then instead of beforehand.
In wheelbarrow work as illustrated in the example shown on the note
sheet, the elementary units consist of "filling barrow," "starting"
(which includes throwing down shovel and lifting handles of barrow),
"wheeling full," etc. These units might have been further
subdivided--the first one into time for loading one shovelful, or still
further into the time for filling and the time for emptying each
shovelful. The letters a, b, c, etc., which are printed, are simply for
convenience in designating the elements.

We are now ready for the stop watch, which, to save clerical work,
should be provided with a decimal dial similar to that shown in Fig. 4.
The method of using this and recording the times depends upon the
character of the time observations. In all cases, however, the stop
watch times are recorded in the columns headed "Time" at the top of the
right-hand half of the note sheet. These columns are the only place on
the face of the sheet where stop watch readings are to be entered. If
more space is required for these times, they should be entered on the
back of the sheet. The rest of the figures (except those on the
left-hand side of the note sheet, which may be taken from an ordinary
timepiece) are the results of calculation, and may be made in the office
by any clerk.

As has been stated, the method of recording the stop watch observations
depends upon the work which is being observed. If the operation consists
of the same element repeated over and over, the time of each may be set
down separately; or, if the element is very small, the total time of,
say, ten may be entered as a fraction, with the time for all ten
observations as the numerator, and the number of observations for the

In the illustration given on the note sheet, Fig. 2, the operation
consists of a series of elements. In such a case, the letters
designating each elementary unit are entered under the columns "Op.,"
the stop watch is thrown to zero, and started as the man commences to
work. As each new division of the operation (that is, as each
elementary unit or unit time) is begun, the time is recorded. During
any special delay the watch may be stopped, and started again from the
same point, although, as a rule, Mr. Thompson advocates allowing the
watch to run continuously, and enters the time of such a stop,
designating it for convenience by the letter "Y."

In the case we are considering, two kinds of materials were handled sand
and clay. The time of each of the unit times, except the "filling," is
the same for both sand and clay; hence, if we have sufficient
observations on either one of the materials, the only element of the
other which requires to be timed is the loading. This illustrates one of
the merits of the elementary system.

The column "Av." is filled from the preceding column. The figures thus
found are the actual net times of the different unit times. These unit
times are averaged and entered in the "Time" column, on the lower half
of the right-hand page, preceded, in the "No." column, by the number of
observations which have been taken of each unit. These times, combined
and compared with the gross times on the left-hand page, will determine
the percentage lost in resting and other necessary delays. A convenient
method for obtaining the time of an operation, like picking, in which
the quantity is difficult to measure, is suggested by the records on the
left-hand page.

The percentage of the time taken in rest and other necessary delays,
which is noted on the sheet as, in this case, about 27 per cent, is
obtained by a comparison of the average net "time per barrow" on the
right with the "time per barrow" on the left. The latter is the quotient
of the total time shoveling and wheeling divided by the number of loads

It must be remembered that the example given is simply for illustration.
To obtain accurate average times, for any item of work under specified
conditions, it is necessary to take observations upon a number of men,
each of whom is at work under conditions which are comparable. The total
number of observations which should be taken of any one elementary unit
depends upon its variableness, and also upon its frequency of occurrence
in a day's work.

An expert observer can, on many kinds of work, time two or three men at
the same time with the same watch, or he can operate two or three
watches--one for each man. A note sheet can contain only a comparatively
few observations. It is not convenient to make it of larger size than
the dimensions given, when a watch-book is to be used, although it is
perfectly feasible to make the horizontal rulings 8 lines to the inch
instead of 5 lines to the inch as on the sample sheet. There will have
to be, in almost all cases, a large number of note sheets on the same
subject. Some system must be arranged for collecting and tabulating
these records. On Tables 2A and 2B (pages 160 and 161) is shown the form
used for tabulating. The length should be either 17 or 22 inches. The
height of the form is 11 inches. With these dimensions a form may be
folded and filed with ordinary letter sheets (8 1/2 inches by 11
inches). The ruling which has been found most convenient is for the
vertical divisions 3 columns to 1 1/8 inches, while the horizontal lines
are ruled 6 to the inch. The columns may, or may not, have printed

The data from the note sheet in Fig. 2 (page 151) is copied on to the
table for illustration. The first columns of the table are descriptive.
The rest of them are arranged so as to include all of the unit times,
with any other data which are to be averaged or used when studying the
results. At the extreme right of the sheet the gross times, including
rest and necessary delay, are recorded and the percentages of rest are

Formulae are convenient for combining the elements. For simplicity, in
the example of barrow excavation, each of the unit times may be
designated by the same letters used on the note sheet (Fig. 2) although
in practice each element can best be designated .by the initial letters
of the words describing it.


a = time filling a barrow with any material.

b = time preparing to wheel.

c = time wheeling full barrow 100 feet.

d = time dumping and turning.

e = time returning 100 feet with empty barrow.

f = time dropping barrow and starting to shovel.

p = time loosening one cubic yard with the pick.

P = percentage of a day required to rest and necessary delays.

L = load of a barrow in cubic feet.

B = time per cubic yard picking, loading, and wheeling any given kind of
earth to any given distance when the wheeler loads his own barrow.

[Transcriber's note -- formula  and Tables omitted]

This general formula for barrow work can be simplified by choosing
average values for the constants, and substituting numerals for the
letters now representing them. Substituting the average values from the
note sheet on Fig. 2 (page 151), our formula becomes:
[Transcriber's note -- formula omitted]

In classes of work where the percentage of rest varies with the
different elements of an operation it is most convenient to correct all
of the elementary times by the proper percentages before combining them.
Sometimes after having constructed a general formula, it may be solved
by setting down the substitute numerical values in a vertical column for
direct addition.

Table 3 (page 164) gives the times for throwing earth to different
distances and different heights. It will be seen that for each special
material the time for filling shovel remains the same regardless of the
distance to which it is thrown. Each kind of material requires a
different time for filling the shovel. The time throwing one shovelful,
on the other hand, varies with the length of throw, but for any given
distance it is the same for all of the earths. If the earth is of such a
nature that it sticks to the shovel, this relation does not hold. For
the elements of shoveling we have therefore:

s = time filling shovel and straightening up ready to throw.

t = time throwing one shovelful.

w = time walking one foot with loaded shovel.

w1 = time returning one foot with empty shovel.

L = load of a shovel in cubic feet.

P = percentage of a day required for rest and necessary delays.

T = time for shoveling one cubic yard.

Our formula, then, for handling any earth after it is loosened, is:
[Transcriber's note -- omitted]

Where the material is simply thrown without walking, the formula

If weights are used instead of volumes:
[Transcriber's note -- omitted]

The writer has found the printed form shown on the insert, Fig. 5
(opposite page 166), useful in studying unit times in a certain class of
the hand work done in a machine shop. This blank is fastened to a thin
board held in the left hand and resting on the left arm of the observer.
A stop watch is inserted in a small compartment attached to the back of
the board at a point a little above its center, the face of the watch
being seen from the front of the board through a small flap cut partly
loose from the observation blank. While the watch is operated by the
fingers of the left hand, the right hand of the operator is at all times
free to enter the time observations on the blank. A pencil sketch of the
work to be observed is made in the blank space on the upper left-hand
portion of the sheet. In using this blank, of course, all attempt at
secrecy is abandoned.

The mistake usually made by beginners is that of failing to note in
sufficient detail the various conditions surrounding the job. It is not
at first appreciated that the whole work of the time observer is useless
if there is any doubt as to even one of these conditions. Such items,
for instance, as the name of the man or men on the work, the number of
helpers, and exact description of all of the implements used, even those
which seem unimportant, such, for instance, as the diameter and length
of bolts and the style of clamps used, the weight of the piece upon
which work is being done, etc.

It is also desirable that, as soon as practicable after taking a few
complete sets of time observations, the operator should be given the
opportunity of working up one or two sets at least by summing up the
unit times and allowing the proper per cent of rest, etc., and putting
them into practical use, either by comparing his results with the actual
time of a job which is known to be done in fast time, or by setting a
time which a workman is to live up to.

The actual practical trial of the time student's work is most useful,
both in teaching him the necessity of carefully noting the minutest
details, and on the other hand convincing him of the practicability of
the whole method, and in encouraging him in future work.

In making time observations, absolutely nothing should be left to the
memory of the student. Every item, even those which appear self-evident,
should be accurately recorded. The writer, and the assistant who
immediately followed him, both made the mistake of not putting the
results of much of their time study into use soon enough, so that many
times observations which extended over a period of months were thrown
away, in most instances because of failure to note some apparently
unimportant detail.

It may be needless to state that when the results of time observations
are first worked up, it will take far more time to pick out and add up
the proper unit times, and allow the proper percentages of rest, etc.,
than it originally did for the workman to do the job. This fact need not
disturb the operator, however. It will be evident that the slow time
made at the start is due to his lack of experience, and he must take it
for granted that later many short-cuts can be found, and that a man with
an average memory will be able with practice to carry all of the
important time units in his head.

No system of time study can be looked upon as a success unless it
enables the time observer, after a reasonable amount of study, to
predict with accuracy how long it should take a good man to do almost
any job in the particular trade, or branch of a trade, to which the time
student has been devoting himself. It is true that hardly any two jobs
in a given trade are exactly the same and that if a time student were to
follow the old method of studying and recording the whole time required
to do the various jobs which came under his observation, without
dividing them into their elements, he would make comparatively small
progress in a lifetime, and at best would become a skilful guesser. It
is, however, equally true that all of the work done in a given trade can
be divided into a comparatively small number of elements or units, and
that with proper implements arid methods it is comparatively easy for a
skilled observer to determine the time required by a good man to do any
one of these elementary units.

Having carefully recorded the time for each of these elements, it is a
simple matter to divide each job into its elementary units, and by
adding their times together, to arrive accurately at the total time for
the job. The elements of the art which at first appear most difficult to
investigate are the percentages which should be allowed, under different
conditions, for rest and for accidental or unavoidable delays. These
elements can, however, be studied with about the same accuracy as the

Perhaps the greatest difficulty rests upon the fact that no two men work
at exactly the same speed. The writer has found it best to take his time
observations on first-class men only, when they can be found; and these
men should be timed when working at their best. Having obtained the best
time of a first-class man, it is a simple matter to determine the
percentage which an average man will fall short of this maximum.

It is a good plan to pay a first-class man an extra price while his work
is being timed. When work men once understand that the time study is
being made to enable them to earn higher wages, the writer has found
them quite ready to help instead of hindering him in his work. The
division of a given job into its proper elementary units, before
beginning the time study, calls for considerable skill and good
judgment. If the job to be observed is one which will be repeated over
and over again, or if it is one of a series of similar jobs which form
an important part of the standard work of an establishment, or of the
trade which is being studied, then it is best to divide the job into
elements which are rudimentary. In some cases this subdivision should be
carried to a point which seems at first glance almost absurd.

For example, in the case of the study of the art of shoveling earths,
referred to in Table 3, page 164, it will be seen that handling a
shovelful of dirt is subdivided into, s = "Time filling shovel and
straightening up ready to throw," and t = "Time throwing one shovelful."

The first impression is that this minute subdivision of the work into
elements, neither of which takes more than five or six seconds to
perform, is little short of preposterous; yet if a rapid and thorough
time study of the art of shoveling is to be made, this subdivision
simplifies the work, and makes time study quicker and more thorough.

The reasons for this are twofold:

First. In the art of shoveling dirt, for instance, the study of fifty or
sixty small elements, like those referred to above, will enable one to
fix the exact time for many thousands of complete jobs of shoveling,
constituting a very considerable proportion of the entire art.

Second. The study of single small elements is simpler, quicker, and more
certain to be successful than that of a large number of elements
combined. The greater the length of time involved in a single item of
time study, the greater will be the likelihood of interruptions or
accidents, which will render the results obtained by the observer
questionable or even useless.

There is a considerable part of the work of most establishments that is
not what may be called standard work, namely, that which is repeated
many times. Such jobs as this can be divided for time study into groups,
each of which contains several rudimentary elements. A division of this
sort will be seen by referring to the data entered on face of note
sheet, Fig. 2 (page 151).

In this case, instead of observing, first, the "time to fill a shovel,"
and then the time to "throw it into a wheelbarrow," etc., a number of
these more rudimentary operations are grouped into the single operation

a = "Time filling a wheelbarrow with any material."

This group of operations is thus studied as a whole.

Another illustration of the degree of subdivision which is desirable
will be found by referring to the inserts, Fig. 5 (opposite page 166).

Where a general study is being made of the time required to do all kinds
of hand work connected with and using machine tools, the items printed
in detail should be timed singly.

When some special job, not to be repeated many times, is to be studied,
then several elementary items can be grouped together and studied as a
whole, in such groups for example as:

(a) Getting job ready to set.

(b) Setting work.

(c) Setting tool.

(d) Extra hand work.

(e) Removing work.

And in some cases even these groups can be further condensed.

An illustration of the time units which it is desirable to sum up and
properly record and index for a certain kind of lathe work is given in
Fig. 6.

The writer has found that when some jobs are divided into their proper
elements, certain of these elementary operations are so very small in
time that it is difficult, if not impossible, to obtain accurate
readings on the watch. In such cases, where the work consists of
recurring cycles of elementary operations, that is, where a series of
elementary operations is repeated over and over again, it is possible to
take sets of observations on two or more of the successive elementary
operations which occur in regular order, and from the times thus
obtained to calculate the time of each element. An example of this is
the work of loading pig iron on to bogies. The elementary operations or
elements consist of:

(a) Picking up a pig.

(b) Walking with it to the bogie.

(c) Throwing or placing it on the bogie.

(d) Returning to the pile of pigs.

Here the length of time occupied in picking up the pig and throwing or
placing it on the bogie is so small as to be difficult to time, but
observations may be taken successively on the elements in sets of three.
We may, in other words, take one set of observations upon the combined
time of the three elements numbered 1, 2, 3; another set upon elements
2, 3, 4; another set upon elements, 3, 4, 1, and still another upon the
set 4,1, 2. By algebraic equations we may solve the values of each of
the separate elements.

If we take a cycle consisting of five (5) elementary operations, a, b,
c, d, e, and let observations be taken on three of them at a time, we
have the equations:

[Transcriber's Note: omitted]

The writer was surprised to find, however, that while in some cases
these equations were readily solved, in others they were impossible of
solution. My friend, Mr. Carl G. Barth, when the matter was referred to
him, soon developed the fact that the number of elements of a cycle
which may be observed together is subject to a mathematical law, which
is expressed by him as follows:

The number of successive elements observed together must be prime to the
total number of elements in the cycle.

Namely, the number of elements in any set must contain no factors; that
is, must be divisible by no numbers which are contained in the total
number of elements. The following table is, therefore, calculated by Mr.
Barth showing how many operations may be observed together in various
cases. The last column gives the number of observations in a set which
will lead to the determination of the results with the minimum of labor.

[Transcriber's note -- Table omitted]

When time study is undertaken in a systematic way, it becomes possible
to do greater justice in many ways both to employers and workmen than
has been done in the past. For example, we all know that the first time
that even a skilled workman does a job it takes him a longer time than
is required after he is familiar with his work, and used to a particular
sequence of operations. The practiced time student can not only figure
out the time in which a piece of work should be done by a good man,
after he has become familiar with this particular job through practice,
but he should also be able to state how much more time would be required
to do the same job when a good man goes at it for the first time; and
this knowledge would make it possible to assign one time limit and price
for new work, and a smaller time and price for the same job after being
repeated, which is much more fair and just to both parties than the
usual fixed price.

As the writer has said several times, the difference between the best
speed of a first-class man and the actual speed of the average man is
very great. One of the most difficult pieces of work which must be faced
by the man who is to set the daily tasks is to decide just how hard it
is wise for him to make the task. Shall it be fixed for a first-class
man, and if not, then at what point between the first-class and the
average? One fact is clear, it should always be well above the
performance of the average man, since men will invariably do better if a
bonus is offered them than they have done without this incentive. The
writer has, in almost all cases, solved this part of the problem by
fixing a task which required a first-class man to do his best, and then
offering a good round premium. When this high standard is set it takes
longer to raise the men up to it. But it is surprising after all how
rapidly they develop.

The precise point between the average and the first-class, which is
selected for the task, should depend largely upon the labor market in
which the works is situated. If the works were in a fine labor market,
such, for instance, as that of Philadelphia, there is no question that
the highest standard should be aimed at. If, on the other hand, the shop
required a good deal of skilled labor, and was situated in a small
country town, it might be wise to aim rather lower. There is a great
difference in the labor markets of even some of the adjoining states in
this country, and in one instance, in which the writer was aiming at a
high standard in organizing a works, he found it necessary to import
almost all of his men from a neighboring state before meeting with

Whether the bonus is given only when the work is done in the quickest
time or at some point between this and the average time, in all cases
the instruction card should state the best time in which the work can be
done by a first-class man. There will then be no suspicion on the part
of the men when a longer "bonus time" is allowed that the time student
does not really know the possibilities of the case. For example, the
instruction card might read:

Proper time . . . . . 65 minutes

Bonus given first time job is done. 108 minutes

It is of the greatest importance that the man who has charge of
assigning tasks should be perfectly straightforward in all of his
dealings with the men. Neither in this nor in any other branch of the
management should a man make any pretense of having more knowledge than
he really possesses. He should impress the workmen with the fact that he
is dead in earnest, and that he fully intends to know all about it some
day; but he should make no claim to omniscience, and should always be
ready to acknowledge and correct an error if he makes one. This
combination of determination and frankness establishes a sound and
healthy relation between the management and men.

There is no class of work which cannot be profitably submitted to time study, by dividing it into its time elements, except such operations as take place in the head of the worker; and the writer has even seen a time study made of the speed of an average and first-class boy in solving problems in mathematics.

Clerk work can well be submitted to time study, and a daily task assigned in work of this class which at first appears to be very miscellaneous in its character.

One of the needs of modern management is that of literature on the subject of time study. The writer quotes as follows from his paper on "A Piece Rate System," written in 1895:

"Practically the greatest need felt in an establishment wishing to start a rate-fixing department is the lack of data as to the proper rate of speed at which work should be done. There are hundreds of operations which are common to most large establishments, yet each concern studies the speed problem for itself, and days of labor are wasted in what should be settled once for all, and recorded in a form which is available to all manufacturers.

"What is needed is a hand-book on the speed with which work can be done, similar to the elementary engineering handbooks. And the writer ventures to predict that such a book will before long be forthcoming. Such a book should describe the best method of making, recording, tabulating, and
indexing time observations, since much time and effort are wasted by the adoption of inferior methods."

Unfortunately this prediction has not yet been realized. The writer's chief object in inducing Mr. Thompson to undertake a scientific time study of the various building trades and to join him in a publication of this work was to demonstrate on a large scale not only the desirability
of accurate time study, but the efficiency and superiority of the method of studying elementary units as outlined above. He trusts that his object may be realized and that the publication of this book may be followed by similar works on other trades and more particularly on the details of machine shop practice, in which he is especially interested.

As a machine shop has been chosen to illustrate the application of such details of scientific management as time study, the planning department, functional foremanship, instruction cards, etc., the description would be far from complete without at least a brief reference to the methods
employed in solving the time problem for machine tools.

Methods employed in solving the time problem for machine tools

The study of this subject involved the solution of four important problems:

First. The power required to cut different kinds of metals with tools of various shapes when using different depths of cut and coarseness of feed, and also the power required to feed the tool under varying conditions.

Second. An investigation of the laws governing the cutting of metals with tools, chiefly with the object of determining the effect upon the best cutting speed of each of the following variables:

(a) The quality of tool steel and treatment of tools (i.e., in heating, forging, and tempering them).

(b) The shape of tool (i.e., the curve or line of the cutting edge, the lip angle, and clearance angle)

(c) The duration of cut or the length of time the tool is required to last before being re-ground.

(d) The quality or hardness of the metal being cut (as to its effect on cutting speed).

(e) The depth of the cut.

(f) The thickness of the feed or shaving

(g) The effect on cutting speed of using water or other cooling medium on the tool.

Third. The best methods of analyzing the driving and feeding power of machine tools and, after considering their limitations as to speeds and feeds, of deciding upon the proper counter-shaft or other general driving speeds.

Fourth. After the study of the first, second, and third problems had resulted in the discovery of certain clearly defined laws, which were expressed by mathematical formulae, the last and most difficult task of all lay in finding a means for solving the entire problem which should be so practical and simple as to enable an ordinary mechanic to answer quickly and accurately for each machine in the shop the question, "What driving speed, feed, and depth of cut will in each particular case do the work in the quickest time?"

In 1881, in the machine shop of the Midvale Steel Company, the writer began a systematic study of the laws involved in the first and second problems above referred to by devoting the entire time of a large vertical boring mill to this work, with special arrangements for varying the drive so as to obtain any desired speed. The needed uniformity of the metal was obtained by using large locomotive tires of known chemical composition, physical properties and hardness, weighing from 1,500 to
2,000 pounds.

For the greater part of the succeeding 22 years these experiments were
carried on, first at Midvale and later in several other shops, under the
general direction of the writer, by his friends and assistants, six
machines having been at various times especially fitted up for this

The exact determination of these laws and their reduction to formulae
have proved a slow but most interesting problem; but by far the most
difficult undertaking has been the development of the methods and
finally the appliances (i.e., slide rules) for making practical use of
these laws after they were discovered.

In 1884 the writer succeeded in making a slow solution of this problem
with the help of his friend, Mr. Geo. M. Sinclair, by indicating the
values of these variables through curves and laying down one set of
curves over another. Later my friend, Mr. H. L. Gantt, after devoting
about 1 1/2 years exclusively to this work, obtained a much more rapid
and simple solution. It was not, however, until 1900, in the works of
the Bethlehem Steel Company, that Mr. Carl G. Barth, with the assistance
of Mr. Gantt and a small amount of help from the writer, succeeded in
developing a slide rule by means of which the entire problem can be
accurately and quickly solved by any mechanic.

The difficulty from a mathematical standpoint of obtaining a rapid and accurate solution of this problem will be appreciated when it is remembered that twelve independent variables enter into each problem, and that a change in any of these will affect the answer. The instruction card can be put to wide and varied use. It is to the art of management what the drawing is to engineering, and, like the latter, should vary in size and form according to the amount and variety of the information which it is to convey. In some cases it should consist of a pencil memorandum on a small piece of paper which will be sent directly to the man requiring the instructions, while in others it will be in the form of several pages of typewritten matter, properly varnished and mounted, and issued under the check or other record system, so that it can be used time after time. A description of an instruction card of
this kind may be useful.

After the writer had become convinced of the economy of standard methods and appliances, and the desirability of relieving the men as far as possible from the necessity of doing the planning, while master mechanic at Midvale, he tried to get his assistant to write a complete instruction card for overhauling and cleaning the boilers at regular periods, to be sure that the inspection was complete, and that while the work was thoroughly done, the boilers should be out of use as short a time as possible, and also to have the various elements of this work done on piece work instead of by the day. His assistant, not having undertaken work of this kind before, failed at it, and the writer was
forced to do it himself. He did all of the work of chipping, cleaning, and overhauling a set of boilers and at the same time made a careful time study of each of the elements of the work. This time study showed that a great part of the time was lost owing to the constrained position of the workman. Thick pads were made to fasten to the elbows, knees, and hips; special tools and appliances were made for the various details of the work; a complete list of the tools and implements was entered on the
instruction card, each tool being stamped with its own number for identification, and all were issued from the tool room in a tool box so as to keep them together and save time. A separate piece work price was fixed for each of the elements of the job and a thorough inspection of each part of the work secured as it was completed.

The instruction card for this work filled several typewritten pages, and described in detail the order in which the operations should be done and the exact details of each man's work, with the number of each tool required, piece work prices, etc.

The whole scheme was much laughed at when it first went into use, but the trouble taken was fully justified, for the work was better done than ever before, and it cost only eleven dollars to completely overhaul a set of 300 H.P. boilers by this method, while the average cost of doing the same work on day work without an instruction card was sixty-two dollars.

Updated 28 June 2015
First Posted on 3 August 2013

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