Work Sampling: Formula, Sample Size and Worked Example

What is work sampling

Work sampling estimates the share of time that people or machines spend on each activity, based on instantaneous observations made at random moments. Instead of timing the whole shift, you take "snapshots" of the process and count how many show each activity.

The method was developed by L. H. C. Tippett in the British textile industry in the 1930s and is still used to measure idle time, waiting, rework and long or irregular tasks, where continuous time study would be expensive or impractical.

Work sampling visual map

The map summarizes the sample size formula, the step-by-step procedure and the worked example with 400 observations.

Number of observations formula

Each observation is a draw with two outcomes: the activity is happening or it is not. The proportion therefore follows the binomial distribution, and the number of observations needed is:

n = Z² × p × (1 − p) ÷ E²

• Z: 1.96 for 95% confidence.
• p: expected proportion of the activity (estimate it from a pilot sample; with no information, use 0.5).
• E: accepted absolute error, in percentage points (0.05 = ±5 points).

For the general statistics, see sample size. At 95% confidence and E = ±5 points:

If you want ±3 points with p = 30%, the error shrinks and the cost grows: n = 3.8416 × 0.21 ÷ 0.0009 = 897 observations. Halving the error quadruples the sample.

Step by step

1. Define the objective and the categories. Example: producing, waiting for material, setup, other. Categories must be exhaustive and mutually exclusive.
2. Define what and who to observe: one workstation, a cell, a team of forklift drivers.
3. Run a pilot sample (50 to 100 observations) to estimate p and calculate n.
4. Draw the observation times. Use a random number table or a spreadsheet; avoid fixed times such as "on the hour".
5. Walk the route at the drawn instant and record what each person or machine is doing at that moment, without waiting for the activity to finish.
6. Spread the rounds across all shifts and days of the period, including shift start and end.
7. Recalculate the confidence interval during the study and stop when the target error is reached.

Worked example: machining cell

Illustrative example: a cell with 5 operators, observed for 10 working days of 8 hours, with 8 rounds per day at drawn times (for example 08:12, 09:47, 10:31, 11:58, 13:24, 14:09, 15:36 and 16:02). Total: 5 × 8 × 10 = 400 observations, above the 385 required for ±5 points in the worst case (p = 50%).

Each row's error comes from 1.96 × √(p × (1 − p) ÷ n). For "producing": 1.96 × √(0.62 × 0.38 ÷ 400) = 1.96 × 0.0243 = 0.0476, or ±4.8 points. The interval runs from 57.2% to 66.8%.

Practical reading: the cell's total time is 5 × 8 × 10 = 400 hours. Waiting for material took about 16% of it, or 64 hours in two weeks. That is the first improvement target, before anyone talks about work pace.

From the result to standard time

When the study also records the period's output and the operator's pace, work sampling yields a standard time. In the example, the cell made 4,000 parts in the 400 hours.

The 105% rating and 15% allowance are example values; in practice the rating comes from the observer's assessment at each working observation and the allowance from company policy. The result feeds workforce sizing and production capacity.

When to use it and when not to

Use the technique to diagnose where time goes: it underpins productivity calculations and locates losses that OEE lumps into a single category. At stations with heavy physical load, combine it with an ergonomics assessment to separate waiting from needed recovery.

Common mistakes

• Predictable times. If people know when you walk by, behavior changes. Draw the times and do not announce them.
• Small sample for a rare category. A 2% activity needs far more observations to reach an acceptable relative error than a 40% one.
• Vague categories. "Other" cannot be the biggest slice. Break it down if it exceeds 15%.
• Shift or day bias. Observing only in the morning or only on Tuesdays distorts the proportion.
• Recording what the person is about to do rather than what they are doing. Note the state at the instant of observation.
• Neglecting communication. Explain the purpose to the team: the study measures the process, not the people.

Frequently asked questions

What is work sampling?

It is a technique that estimates the proportion of time spent on each activity through instantaneous observations at random times.

What is the formula for the number of observations?

n = Z² × p × (1 − p) ÷ E². With 95% confidence (Z = 1.96), p = 30% and ±5 points of error, n = 323.

How many observations are needed?

It depends on p and the accepted error. With no prior information, use p = 50%: at ±5 points that is 385 observations.

How does it differ from a time study?

A time study measures the duration of each element in a repetitive cycle. Work sampling estimates the proportion of time per activity and suits irregular work or many workstations.

Do the times have to be random?

Yes. Fixed times create bias because they coincide with routines such as shift start, breaks and changeovers.

Can you calculate standard time with work sampling?

Yes, if you record the period's output and rate the pace: standard time = (working proportion × total time ÷ parts) × rating × (1 + allowance).

About the author

Vagner Soares

Lean Manufacturing & Behavioral Management Specialist

Over 20 years in the automotive and metalworking industries (GM and Dana), Lean Manufacturing practitioner since 2006. SENAI instructor and mentor in Brazil’s Brasil Mais Produtivo program, delivering consulting, training and audits for 50+ companies, combining quality, productivity and people development.

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