How to Calculate the Number of Observations Required for Time Study

Time study is one of the most important activities in industrial engineering. It is the foundation for manpower calculation, capacity planning, line balancing, costing, incentive calculation, and productivity improvement.

But in many factories, time study is misunderstood.

Some people take 3 readings and decide the cycle time.
Some people take 5 readings and calculate manpower.
Some take one “average-looking” reading and use it for planning.
Some take more readings only when someone questions the result.

This creates a serious problem.

If the observed time is not reliable, the standard time will not be reliable. If the standard time is not reliable, manpower calculation will also become wrong.

In simple words:

Cycle time wrong → Standard time wrong → Manpower wrong → Capacity wrong → Costing wrong

That is why every industrial engineer should understand one important question:

How many observations are required in a time study?

This article explains the concept in a simple and practical way.

Why One Observation Is Not Enough in Time Study

Let us say we observe one operator doing an operation and the stopwatch reading is:

18 seconds

Can we immediately say the operation time is 18 seconds?

No.

Because if we observe the same operation again, the next readings may be:

18 seconds, 19 seconds, 20 seconds, 18 seconds, 21 seconds

This happens because every operation has natural variation.

The variation may come from many reasons:

Operator movement variation
Part location variation
Material handling variation
Machine response variation
Tool condition
Part orientation
Fatigue
Minor delays
Measurement error
Difference in work rhythm

So time study is not just about holding a stopwatch. It is about collecting enough observations to find a reliable average.

What Are We Trying to Find in Time Study?

In time study, we are trying to find the representative average time for each element of work.

For example, an operation may be divided into elements like:

Pick the part
Load the part
Press the switch
Wait for machine cycle
Unload the part
Keep the part in tray

Each element may have a different level of variation.

Machine time may be very stable. Manual handling time may vary more. Searching, positioning, checking, walking, or aligning may vary even more.

So the number of observations required may not be the same for every element.

This is the key idea:

The more the variation, the more observations are required.

What Decides the Number of Observations?

The number of observations required in a time study mainly depends on three factors:

1. Variation in readings
2. Confidence level
3. Accuracy or margin of error

These three points are connected, but they are not the same. Let us understand them clearly.

1. Variation in Readings

Variation means how much the observed times are changing from cycle to cycle.

If the readings are very close to each other, fewer observations may be enough.

Example:

18, 18, 19, 18, 19

This is low variation. The operation looks stable.

But if the readings are like this:

12, 18, 25, 14, 30

This is high variation. The operation is not stable, or the method may not be consistent. In such cases, more observations are required.

In simple words:

Low variation = fewer observations may be enough.
High variation = more observations are required.

2. Confidence Level

Confidence level means how sure we want to be about our result.

A simple way to understand this is:

If we repeat the same time study 100 times under similar conditions, around 95 studies should give a result within the accepted error range (margin or error or accuracy – explained in next session).

In time study, we take some observations and calculate an average. But that average is only an estimate. It may not be exactly equal to the true average time of the operation.

For example, suppose we observe an operation 10 times and get an average of:

20 seconds

Can we say the true average is exactly 20 seconds?

Not exactly.

If we take more observations, the average may become 19.8 seconds or 20.3 seconds. So the observed average is only an estimate of the true average.

Confidence level tells us how much trust (if we repeat study how many times average will fall under accuracy range) we want to place on that estimate.

How sure do we want to be?

Common confidence levels used in time study are:

95%
95.45%

Higher confidence means we are asking for stronger proof. To get stronger proof, we usually need more observations.

Example:

95% confidence needs fewer observations than 99% confidence.

But in practical shop floor time study, 95% or 95.45% confidence is commonly used because it gives a good balance between reliability and effort.

3. Accuracy or Margin of Error

Accuracy or margin of error means how close we want our calculated average to be to the true average.

Confidence level tells us how sure we want to be.
Margin of error tells us how close the result should be.

For example, suppose our calculated average time is:

20 seconds

If we choose ±5% accuracy:

5% of 20 seconds = 1 second

So the acceptable range is:

19 seconds to 21 seconds

This means we are saying:

The true average should be within 1 second above or below 20 seconds.

Now suppose we choose ±10% accuracy:

10% of 20 seconds = 2 seconds

So the acceptable range is:

18 seconds to 22 seconds

Now compare both:

±5% accuracy gives a narrow range.
±10% accuracy gives a wider range.

So ±5% is stricter and more accurate. But because it is stricter, it needs more observations.

In simple words:

±10% accuracy is easier to achieve.
±5% accuracy is more reliable, but it needs more observations.

Difference Between Confidence Level and Margin of Error

Many people get confused between confidence level and margin of error.

Here is the simple difference:

Confidence level means how sure we want to be.
Margin of error means how close we want the result to be.

Let us take one example.

Average observed time = 20 seconds
Confidence level = 95%
Margin of error = ±5%

5% of 20 seconds = 1 second

So we are saying:

We want to be 95% confident that the true average time is between 19 seconds and 21 seconds.

Here:

95% = confidence level
19 to 21 seconds = accuracy range
±1 second = margin of error
±5% = margin of error in percentage

This does not mean every individual cycle will be between 19 and 21 seconds. Some cycles may be 18 seconds or 22 seconds.

It means the estimated average time is expected to be within that range.

Simple Shop Floor Understanding

Think of confidence level and margin of error like this:

Confidence level asks:

How sure do you want to be?

Margin of error asks:

How much difference can you accept?

Example:

If we say:

20 seconds ±5% at 95% confidence

It means:

We are 95% confident that the true average time is within 5% of 20 seconds.

That is:

Between 19 seconds and 21 seconds.

If we want higher confidence, we need more observations.
If we want tighter accuracy, we also need more observations.
If the operation has more variation, we again need more observations.

So the number of observations increases when:

Variation is high
Confidence level is high
Margin of error is small

For professional time study, a practical and reliable choice is usually:

95% or 95.45% confidence level
±5% margin of error

This gives a good balance between statistical reliability and practical shop floor effort.

Formula to Calculate Number of Observations in Time Study

For time study, the following formula is commonly used for calculating the required number of observations at approximately 95.45% confidence level and ±5% accuracy:

n = [ 40 × √(n′Σx² − (Σx)²) / Σx ]²

Where:

n = required number of observations
n′ = number of preliminary observations already taken
x = value of each observed reading
Σx = sum of observed readings
Σx² = sum of squares of observed readings

The formula may look difficult at first, but the calculation is simple when we do it step by step.

Simple Example: Calculating Number of Observations

Suppose we take 5 preliminary observations for one work element.

The readings are:

7, 6, 7, 7, 6

These readings may be in seconds, decimal minutes, or any other consistent time unit.

Now we calculate x² for each reading.

Reading x	x²
7	49
6	36
7	49
7	49
6	36

Now calculate:

Σx = 7 + 6 + 7 + 7 + 6 = 33

Σx² = 49 + 36 + 49 + 49 + 36 = 219

n′ = 5

Now apply the formula:

n = [ 40 × √(n′Σx² − (Σx)²) / Σx ]²

Substitute the values:

n = [ 40 × √(5 × 219 − 33²) / 33 ]²

n = [ 40 × √(1095 − 1089) / 33 ]²

n = [ 40 × √6 / 33 ]²

n = 8.81

Since the required number of observations cannot be in decimal, we round it up.

So:

n = 9 observations

This means, for this element, we need around 9 observations.

Since we already took 5 observations, we need to continue the study.

But we should not blindly say only 4 more readings are enough. When we add more readings, the values of Σx and Σx² will change. So after collecting additional readings, we should check again whether the sample size is adequate.

Why Different Elements Need Different Observations

A time study is usually done element by element.

Let us take one simple operation:

Element 1: Pick part
Element 2: Load part
Element 3: Press button
Element 4: Machine cycle
Element 5: Unload part
Element 6: Keep part in tray

Now suppose we calculate the required number of observations for each element.

Element	Required observations
Pick part	12
Load part	18
Press button	5
Machine cycle	3
Unload part	15
Keep part in tray	10

In this case, the highest required sample size is 18.

So, practically, we should observe 18 cycles for the full operation.

This is because one element needs 18 observations to become reliable. If we stop at 10 observations, that element may not be statistically reliable.

This is a very important point for industrial engineers:

Do not decide the number of observations only based on the total cycle time. Check the variation of individual elements also.

Practical Step-by-Step Method for Time Study Observation

Here is a practical method that can be followed on the shop floor.

Step 1: Define the operation clearly

Before starting time study, clearly define the operation.

Mention:

Part number
Operation name
Machine or workstation
Operator
Method followed
Tools and fixtures used
Start point and end point of the cycle

A time study without a defined method is weak.

Step 2: Break the job into elements

Do not time only the full cycle. Break the job into meaningful elements.

Example:

Pick component
Place in fixture
Clamp component
Start machine
Machine cycle
Remove component
Inspect visually
Place in output bin

Good element breakdown gives better understanding of variation.

Step 3: Take preliminary observations

Start with 5 or 10 preliminary readings.

For very short cycle operations, you may need more preliminary readings.

For highly manual or variable operations, 10 preliminary readings are better.

Step 4: Calculate required observations

For each element, calculate:

Σx
Σx²
n′
Required n

This will tell you how many observations are required for that element.

Step 5: Use the highest required sample size

If different elements show different required sample sizes, take the highest value as the required number of cycle observations.

Example:

Element-wise required observations:

8, 12, 6, 20, 14

Then required cycle observations = 20

Step 6: Continue observations if needed

If the required number is more than the observations already taken, continue taking readings.

After adding more readings, recalculate and confirm.

Step 7: Remove abnormal readings with proper reason

If an abnormal event happens, do not mix it blindly with normal readings.

Examples of abnormal events:

Tool falls down
Material not available
Operator talks to supervisor
Machine stops
Part is defective
Operator searches for tool
Fixture gets jammed

Such readings should be recorded separately with remarks.

Step 8: Calculate average observed time

Once sufficient observations are taken, calculate the average observed time for each element.

Step 9: Apply rating

Observed time is not yet normal time.

If the operator is working faster or slower than standard performance, apply performance rating.

Normal time = Observed time × Rating factor

Step 10: Add allowances

Normal time is not yet standard time.

Allowances must be added for:

Personal needs
Fatigue
Unavoidable delays
Special working conditions, if applicable

Standard time = Normal time + Allowances

Only after this should the time be used for manpower calculation, capacity planning, costing, and line balancing.

What If the Required Number of Observations Is Very High?

Sometimes, the calculation may show a very high number of observations.

For example:

Required observations = 75
Required observations = 100
Required observations = 150

Before blindly taking so many readings, check the method.

A high sample size usually means high variation. High variation may indicate that the operation is not stable.

Ask these questions:

Is the operator following the same method every cycle?
Is material location changing frequently?
Is the part orientation changing?
Is the workstation layout poor?
Is the element too broad?
Is waiting time mixed with manual work?
Is the operator searching for tools or parts?
Is the fixture or machine inconsistent?
Are abnormal readings included?

Time study should not become a blind statistical activity. If variation is very high, first stabilize the method.

A good industrial engineer does not only calculate time. A good industrial engineer questions the method behind the time.

Final Thoughts

Many manpower calculations fail not because the manpower formula is wrong, but because the input time is wrong.

Before asking:

How many operators are required?

We should first ask:

How was the cycle time observed?
How many observations were taken?
Was the sample size enough?
Was variation checked?
Was the method stable?
Were abnormal readings removed?
Was rating applied?
Were allowances added?

Time study is not just stopwatch work. It is a disciplined industrial engineering activity that combines observation, statistics, method understanding, and professional judgement.

When we calculate the right number of observations, we protect the factory from wrong manpower, wrong capacity, wrong cost, and wrong decisions.

That is where professional industrial engineering begins.