work sampling and structured estimating
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WORK SAMPLING AND STRUCTURED ESTIMATING. CHAPTER 12. Work sampling is a method of finding the percentage occurrence of a certain activity by statistical sampling and random observations.

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Work sampling is a method of finding the percentage occurrence of a certain activity by statistical sampling and random observations.

  • Work sampling is the process of making sufficient random observations of an operator’s activities to determine the relative amount of time the operator spends on the various activities associated with the job.

The major goal of work sampling is to determine how long, or how much of the work day, is spent on specific types of work.

  • Work sampling may identify the fact that certain operators spend a large portion of their time waiting for work, or performing paperwork tasks, or even performing activities that are not included in their job descriptions.
  • One of the basic foundations of statistical sampling theory is the concept that the larger the sample size, the results will be more accurate.
  • In work sampling, a sufficient number of observations must be made to be sure that the results accurately summarize the work performed. There are statistical formulas to help determine how many observations should be made.


  • It is recommended that a uniform procedure should be followed to perform a work sampling study is to

1. Establish the Purpose

  • First, the objective of the study should be established. Work sampling can be used to determine an overall perspective on the work done.

2. Identify the Subjects

  • Second, the people performing the task must be identified, i.e. general office work is being studied with the objective of determining overall productivity.

3. Identify the Measure of Output

  • The third step in making the study is the identification of the measure of the output produced or the types of activities performed on the jobs being studied. This step is especially important if the objective of the study is to measure productivity with the intent of setting a standard.

4. Establish a Time Period

  • Fourth, the time period during which the study will be conducted must be established. Starting and stopping points for the study must be defined as well.

5. Define the Activities

  • This step involves defining the activities that are performed by the people under study. For example, the definition used in a machine utilization study, including only the categories of working, idle, and idle-mechanical breakdown.

6. Determine the Number of Observations Needed

  • After the work elements are defined, the number of observations for the desired accuracy at the desired confidence level must be determined. If a reasonable guess cannot be made, then a trial study of perhaps 20 to 40 observations should be made to get an estimate.

7. Schedule the Observations

  • Once the number of required observations has been determined, either from appropriate statistical calculations or from tables, and the actual observations must be scheduled. Typically, the analyst will assign an equal number of observations each day during the course of the study. For example, if 800 observations are required and 20 work days are established as an appropriate observation time, 40 observations should be recorded each day.
  • A random number table can be used to establish the random times for each observation.

8. Inform the Personnel Involved

  • Before the study is actually performed, the personnel involved should be informed about the objective of the study and the methodology that will be employed.

9. Record the Raw Data

  • The next is the actual recording of the raw data. Although this recording can be performed by anyone, it is desirable that a trained analyst be employed.
  • It is also very important that the observations be made at exactly the same location every time.

10. Summarize the Data

  • After the data have been collected, they must be summarized.

A few words about sampling

  • Sampling is mainly based on probability. Probability has been defined as “the degree to which an event is likely to occur”.
  • A simple and often-mentioned example that illustrates the point is that of tossing a coin.
  • The law of probability says that we are likely to have 50 heads and 50 tails in every 100 tosses of the coin. The greater the number of tosses, the more chance we have of arriving at a ratio of 50 heads to 50 tails.
  • The size of the sample is therefore important, and we can express our confidence in whether or not the sample is representative by using a certain confidence level.

Establishing confidence levels

  • Let us go back to our previous example and toss five coins at a time, and then record the number of times we have heads and the number of times we have tails for each toss of these five coins. Let us then repeat this operation 100 times.

To make things easier, it is more convenient to speak of a 95 per cent confidence level than of a 95.45 per cent confidence level.

  • To achieve this we can change our calculations and obtain:
    • 95 per cent confidence level or 95 per cent of the area under the curve = 1.96σp
    • 99 per cent confidence level or 99 per cent of the area under the curve = 2.58σp
    • 99.9 per cent confidence level or 99.9 per cent of the area under the curve = 3.3σp
  • In this case we can say that if we take a large sample at random we can be confident that in 95 per cent of the cases our observations will fall within ± 1.96 σp

Determination of sample size

  • As well as defining the confidence level for our observations we have to decide on the margin of error that we can allow for these observations.
  • Let us look at our example about the productive time and the idle time of the machines in a factory. There are two methods of determining the sample size that would be appropriate for this example:
  • the statistical methodand the nomogram method.

Statistical method. The formula used in this method is:


Let us assume that some 100 observations were carried out as a preliminary study and at random, and that these showed the machine to be idle in 25 per cent of the cases (p = 25) and to be working 75 per cent of the time (q = 75).

  • We thus have approximate values for p and q; in order now to determine the value of n.
  • Let us choose a confidence level of 95 per cent with a 10 per cent margin of error (that is, we are confident that in 95 per cent of the cases our estimates will be ± 10 per cent of the real value).

Nomogram methodAn easier way to determine sample size is to read off the number of observations needed directly from a nomogram such as the one reproduced in figure 91.


Making random observations

  • To ensure that our observations are in fact made at random, we can use a random table such as the one in table 12.
  • Various types of random table exist, and these can be used in different ways. In our case let us assume that we shall carry out our observations during a day shift of eight hours, from 7 a.m. to 3 p.m. An eight-hour day has 480 minutes. These may be divided into 48 ten-minute periods.
  • We can start by choosing any number at random from our table, for example by closing our eyes and placing a pencil point somewhere on the table. Let us assume that in this case we pick, by simple chance, the number 11 which is in the second block, fourth column, fourth row (table 12).
  • We now choose any number between 1 and 10. Assume that we choose the number 2; we now go down the column picking out every second reading and noting it down, as shown below (if we had chosen the number 3, we should pick out every third figure, and so on).
  • 11 38 45 87 68 20 11 26 49 05

Looking at these numbers, we find that we have to discard 87, 68 and 49 because they are too high (since we have only 48 ten-minute periods, any number above 48 has to be discarded).

  • Similarly, the second 11 will also have to be discarded since it is a number that has already been picked out. We therefore have to continue with our readings to replace the four numbers we have discarded. Using the same method, that is choosing every second number after the last one (05), we now have 14 15 47 22
  • These four numbers are within the desired range and have not appeared before. Our final selection may now be arranged numerically and the times of observation throughout the eight-hour day worked out. Thus our smallest number (05) represents the fifth ten-minute period after the work began at 7 a.m. Thus our first observation will be at 7.50 a.m., and so on (table 13).

Example: Conducting the study

  • Determining the scope of the study. Before making our actual observations, it is important that we decide on the objective of our work sampling.
  • The simplest objective is that of determining whether a given machine is idle or working. In such a case, our observations aim at detecting one of two possibilities only:
  • We can, however, extend this simple model to try to find out the cause of the stoppage of the machine:

Making the observations

  • So far we have taken the first five logical steps in conducting a work sampling study.
    • selecting the job to be studied and determining the objectives of the study;
    • making a preliminary observation to determine the approximate values of p (idle) and q (working);
    • in terms of a chosen confidence level and accuracy range, determining n (the number of observations needed) determining the frequency of observations, using random tables;
    • designing record sheets to meet the objectives of the study.
    • There is one more step to take: that of making and recording the observations and analyzing the results.
advantages of work sampling
Advantages of Work Sampling
  • Can be used to measure activities that are impractical to measure by direct observation
  • Multiple subjects can be included
  • Requires less time and lower cost than continuous direct observation
  • Training requirements less than DTS or PMTS
  • Less tiresome and monotonous on observer than continuous observation
  • Being a subject in work sampling is less demanding than being watched continuously for a long time
disadvantages and limitations
Disadvantages and Limitations
  • Not as accurate for setting time standards as other work measurement techniques
  • Usually not practical to study a single subject
  • Work sampling provides less detailed information about work elements than DTS or PMTS
  • Since work sampling deals with multiple subjects, individual differences will be missed
  • Workers may be suspicious because they do not understand the statistical basis of work sampling