Time study: how many observations do you need?
In one sentence
Plan the observation count using the chosen error target for the mean and measurement variation; recheck the initial recommendation with new data and the appropriate t factor.
By the end of this lesson
- Calculate the planning count, rounded up, using a given z, sample standard deviation and absolute error.
- Check the planned count with a t factor and determine additional observations needed.
- Convert absolute and relative error targets using the correct units.
- Reject certainty claims due to dependence or representation problems even when the count appears sufficient.
Why it matters
We cannot judge whether work has been measured enough from the cycle count alone. The same number of observations can give a narrow interval for the mean with low variation and a wide one with high variation. The measurement plan must clearly state which mean is to be estimated and with what precision. Absolute error can be stated in seconds, relative error as a percentage of the mean. They are different targets. Observation count calculations assume comparable records from a defined method. If the method keeps changing, increasing the count does not solve the problem. First establish the method and measurement boundaries, then calculate the preliminary study's mean and sample standard deviation. These are the basic inputs carried forward from the statistics lesson.
The z factor used in preliminary planning gives an initial estimate of measurement workload. This lesson uses z=1.96 for the 95% level; z is for planning only. When process standard deviation is unknown and estimated from a small sample, use a t factor for the final sufficiency check. This distinction matters: reaching the planned count does not prove that the target interval has definitely been achieved. New data can change sample standard deviation. The t factor also depends on observation count. The recommendation determines the next measurement step under specified assumptions. Once measurement is complete, recalculate using all comparable records and compare the achieved half-width with the target.
Precision does not mean that individual cycles remain in the same narrow band. The quantity checked here is the half-width of the confidence interval for the mean. More independent observations can estimate the mean more precisely; they do not remove long process cycles. Delay risk in an individual cycle requires separate examination of the cycle sequence and events. Similarly, a narrow interval does not prove representation of all product variants. If measurement covers only easy conditions, the result applies to those conditions. Assess numerical sufficiency and representative scope together. Treating one as the other can produce a wrong decision despite a correct calculation.
Observation independence is especially important. Measuring the same cycle several times or counting subdurations derived from one event as separate cycles artificially increases the apparent information. Consecutive cycles may share warm-up, fatigue or material problems. Ordered records allow these effects to be investigated. When variation is high, return to causes instead of merely requesting more numbers. Plan separately for multiple methods; if usual conditions within the same method vary, establish a sampling arrangement that represents the scope. The result document must explain both the required total and where and under what conditions additional data will be collected.
Formula
Preliminary planning total n = ⌈(z × s ÷ E)²⌉
Achieved half-width H (s) = t(n−1
95%) × s ÷ √n
Relative half-width (%) = 100 × H ÷ x̄
Additional observations = max(0, Target total − Current observation count)
E (s) = Relative target rate × Planning mean (s)
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- Step-by-step instructions
- Worked example with real numbers
- Where the method misleads
- Common mistakes