Time Study Sample Size Calculator
How many cycles must a time study measure? Enter a few pilot readings and a target precision, and get the number of observations you need. Free, instant and entirely in your browser.
One reading per line, or separated by spaces or semicolons. A comma or a period works as the decimal mark.
Observations needed in total
18
8 more readings to take
The target precision of ±10% is not reached yet. Take the additional readings shown.
- Readings entered
- 10
- Mean
- 33.6 s
- Standard deviation
- 6.54 s
- Coefficient of variation (CV)
- 19.5%
- Precision of your readings now
- ±13.9%
precision = t(n−1) × CV ÷ √n, needed n = first n that reaches the target
Precision is the half-width of the 95% confidence interval of the mean as a share of the mean, with the sample standard deviation. Outliers are neither removed nor flagged: review unusual readings before you enter them.
The same check inside every study
You calculated this from estimates. Measure the real one from shop-floor video.
A worked example
Ten pilot readings of one cycle, in seconds, and a target precision of ±10% at 95% confidence.
precision = t(n−1) × CV ÷ √n
- Readings (s)
- 30, 42, 25, 38, 33, 29, 45, 27, 36, 31
- Mean
- 33.6 s
- Standard deviation
- 6.54 s
- Coefficient of variation
- 6.54 ÷ 33.6 = 19.5%
- Precision with 10 readings
- 2.262 × 19.5% ÷ √10 = ±13.9%
- Precision with 18 readings
- 2.110 × 19.5% ÷ √18 = ±9.7%
- Observations needed in total
- 18, which is 8 more than taken
±13.9% is above the ±10% target, so the 10 readings are not enough yet. 18 is the first count that reaches the target; with 17 readings the precision still just misses it.
How many observations does a time study need?
The mean of a few cycle times is only an estimate. Its uncertainty is the precision: t(n−1) × CV ÷ √n, the half-width of the 95% confidence interval as a share of the mean, where CV is the coefficient of variation of the readings. The more the readings scatter, the more of them you need. Because the t-value itself depends on n, there is no closed formula: the calculator tries 8, 9, 10 … up to 30 readings and returns the first count that reaches your target. Three rules apply, the same as in Yamazo Studio: at least 8 readings, a coefficient of variation of at most 25%, and the target precision.
How to calculate it
- 1
Enter the pilot readings
Type the cycle times you have measured so far, in seconds, for one and the same method and condition.
- 2
Set the target precision
The relative error you accept in the mean, at 95% confidence. ±10% is the default in Yamazo Studio; tighten it for a critical job.
- 3
Read the number and the verdict
You get the observations needed in total, how many are still to take, the precision your readings carry now, and whether the sample is enough, too small or too scattered.
Frequently asked questions
How many cycles should a time study measure?
It depends on the spread of your readings: at least 8, and enough that the precision of the mean reaches your target. Tightly clustered readings reach it at 8; scattered ones need more.
Why is the coefficient of variation limited to 25%?
In Yamazo Studio a spread above 25% is called high variation. The first thing to check then is whether the cycles differ in method or conditions, rather than simply taking more readings.
Why is there no simple formula for the count?
The t-value used for the confidence interval depends on the number of readings itself. So the calculator tries 8, 9, 10 … up to 30 readings and returns the first count whose precision reaches the target.
Is this the same computation as in Yamazo Studio?
Yes. The precision formula, the t-values, the 8-reading minimum and the 25% limit are the ones behind the reliability verdict in Yamazo Studio. Here they run on the readings you type; nothing leaves your browser.