The man-hour and the man-day
A non-system unit · quantity: labour input, the number of workers times the time
In 1975 Frederick Brooks, who had led the making of the operating system for IBM's machines, set down a conclusion that had cost him dearly: adding people to a late project makes it later still. The cause lies in the very unit by which he and his superiors measured the work. The man-month adds up beautifully and divides just as easily, and that ease is exactly the trap.
The quantity is as plain as can be: one person working one hour spends one man-hour, and eight such hours are taken for a man-day. Out of this product grows its whole double nature. As a measure of labour already spent it is honest and irreplaceable: wages are reckoned by it, cost is computed, output is rated and the productivity of workshops compared.
01 · Definition
The man-hour is the labour input of one worker over one hour of work; the quantity comes from multiplying the number employed by the time worked, and therefore it expresses equally eight people for an hour and one person for a working day. A man-day equals eight man-hours, and a man-year is taken as about 1720 man-hours — the same figure that stands behind one full-time equivalent.
The worth of this unit lies in its additivity: labour input from different sections, shifts and trades adds up without any reservation, and so by it cost is computed, pay is reckoned, output is rated and the productivity of workshops compared with one another. Here the man-hour behaves as a full physical quantity, and nothing in the arithmetic betrays the trouble waiting on the other side.
The difficulty appears when the same product is read backwards and divided by the number of workers to obtain a term. Such a division is lawful only under two conditions: the work must break into independent parts, and the workers must be interchangeable. On earthworks both conditions are nearly met; in designing, in writing or in agreeing on anything at all they are not met even approximately.
Strictly speaking, this unit measures neither work in the physical sense nor time: it records the presence of a person in the appointed place for an hour. Hence it cannot be checked against an instrument nor verified on a specimen — it can only be compared with the timesheet, and how far the timesheet answers to what was actually done is a question outside metrology.
One and the same work of a hundred and sixty man-hours is handed out to an ever greater number of workers. The blue curve is the calendar term: at first it falls almost in inverse proportion, then runs into the indivisible share, and after that goes upward, because the talking eats more than an extra pair of hands gives. The crimson one is the labour input by the timesheet: it only grows.
The number of links grows not as the number of people but as their pairings: three workers have three links, five already have ten, ten have forty-five. Hence each next person costs the group more than the one before, and on paper none of this shows, since man-hours add up evenly no matter how many people are set to the task.
02 · Conversion
Labour input, staff, work order
Enter a labour input in any units, and the sheet will convert it into the rest, show what it turns into when reckoned as headcount, and what it turns into under rate-setting and pay. The first family is exact by convention, the second depends on the yearly fund adopted, the third on the grade and the rate.
The yearly fund is taken by default as 1720 man-hours; in the finer settings it can be changed to 2080 — a calendar year with no leave taken out.
The man-hour is convenient for a report by the very thing that makes it dangerous for a plan: it adds up regardless of what a person is doing and how skilled he is. Hence in an estimate twenty man-days of an apprentice and twenty man-days of a master look the same, though the work will come out different — and that is what grade coefficients were invented for.
| Value | Note | ||
|---|---|---|---|
| {u} | {name} | {value} | {note} |
03 · Orders of magnitude
logarithmic scale: from an hour to a pyramid04 · Measuring instruments
What counts the hours worked
The chief document from which man-hours are taken: a mark of attendance for every shift, and at the end of the month a total on the line. It feels awkward to call it an instrument, yet it is precisely what plays the part of a standard, since there is nothing else to check labour input against: what is measured is not the work but the presence in the appointed place.
Frank and Lillian Gilbreth, stopwatch in hand, took the bricklayer's work apart into separate motions and, removing the needless ones, cut the laying almost threefold. From this came time rates: the man-hour ceased to be a mere mark of attendance and acquired a content — so many pieces, metres or characters an hour.
A work order sets down how many man-hours are allotted for the job by the standard, and by the same order it is signed off. Here the unit works backwards, setting not the fact but the obligation, and therefore behind the standards stand whole handbooks where for every operation a grade and a time per unit of output are given.
Today's timesheet is kept in software, and the same software counts the time booked to tasks, projects and clients. The precision of the marks is deceptive: a person enters them from memory at the end of the day, and so a six-figure sum of man-hours is made up of rounded half-hours and rests on conscientiousness exactly as far as it goes.
05 · Writing rules
The hyphen, the abbreviation and the dot
Written with a hyphen, abbreviated as «man·h» and «man·d», and in Russian only the second part takes the plural. The number of workers and the time are given separately if the term matters, since it cannot be recovered from the product alone. Putting a unit of time in place of labour input is not allowed: an hour and a man-hour are different quantities.
The first writing confuses the term with the labour input, and from it one cannot tell whether a week of work by a crew of four was meant or four days of a crew of five. The second declines the first part, which is not done in this compound. The third turns the product into a term by division, and such a division is lawful only when the work divides. The fourth drops the unit altogether.
06 · Neighbouring units
Beside it stand the units that measure the same work differently: the full-time equivalent turns labour input into a number of permanent staff, an estimate in arbitrary points deliberately refuses hours, and the standard hour sets not the fact but the time allotted by the rate.
1720 man·h a year
allotted, not spent
without a unit of time
Of the Simetrium data sheets nearby stand hour and day, of which the unit is made, week with its working and its off time, yr, which sets the yearly fund, and clock cycle, where the same trouble holds: adding is easy, dividing is not always possible.
07 · Historical section
A unit that adds up but does not divide
Frederick Taylor began to measure how much time each operation in truth took, and found that the piece rates in the workshops came from custom and not from observation. The work was broken into elements, the elements were given times, and labour input became for the first time a quantity that is counted rather than judged by eye.
The Gilbreths filmed bricklayers and took the laying apart element by element, hunting for needless bends and regrips. Removing them and raising the pallet to a convenient height, they tripled the output — and thereby showed that the man-hour is no constant but depends on how the workplace is arranged.
Brooks, examining a delay of several years in an operating system, named the cause in the make-up of the unit itself: by equating people with months, the management took them for interchangeable. Hence the conclusion that became a law: adding hands to a late undertaking makes the lateness greater still, for newcomers must be taught, and teaching them takes those who already know.
In accounting and in reporting the man-hour has gone nowhere: by it cost, load and the employment statistics of whole countries are computed. But planning terms by it has been given up — where work divides badly, arbitrary points are taken instead of hours, deliberately stripped of a unit of time so that nobody is tempted to divide them by people.
A quantity whose arithmetic works in one direction only
The man-hour is built as an ordinary product and therefore looks entirely harmless, yet the harmlessness is one-sided. Addition here is faultless: labour from different shifts, sections and trades sums up, and the figure obtained says honestly how much resource has been spent. Division, however, demands what the product does not contain — the knowledge of whether the work breaks into parts at all.
So this unit serves as an example of how a form of notation prompts the wrong operation. Nobody would divide degrees by instruments, yet man-hours are divided by people all the time, because the dimension allows it and the calculator raises no objection. Brooks, examining his own failure, called such a reckoning a myth — and the name stuck to the whole unit.
Catalogue · units of measurement
A data sheet for every quantity
Seven SI base units, twenty-two derived ones with names of their own, and the non-SI quantities that neither science nor daily life does without. Each gets its own sheet: definition, conversion, instruments, writing rules, history. In 36 languages.