Work Sampling Calculator

Calculator Inputs

Study Name

Total Observations

Working Observations

Delay Observations

Confidence Level

Allowable Error (%)

Shift Hours Per Day

Study Days

Performance Rating (%)

Allowance (%)

Example Data Table

Study	Total Observations	Working	Delay	Idle	Utilization
Assembly Line A	240	186	21	33	77.50%
Machining Cell B	300	231	24	45	77.00%
Packaging Station C	180	129	18	33	71.67%

Formula Used

Observed utilization: p = Working Observations ÷ Total Observations

Idle proportion: Idle % = (Idle Observations ÷ Total Observations) × 100

Delay proportion: Delay % = (Delay Observations ÷ Total Observations) × 100

Standard error: SE = √[p(1 − p) ÷ n]

Confidence interval: p ± z × SE

Required samples: n = (z² × p × (1 − p)) ÷ e²

Observed working hours: Total Study Hours × p

Normal time: Observed Working Hours × Performance Rating

Standard time: Normal Time × (1 + Allowance)

This approach helps estimate how much time a worker or machine spends in productive, idle, or delayed states through random observations.

How to Use This Calculator

Enter a study name so your exported results are easier to identify.
Provide total observations collected during random checks.
Enter how many observations showed productive work.
Enter delay observations caused by waiting, stoppages, or interruptions.
Select the desired confidence level for interval estimation.
Choose an allowable error percentage for required sample planning.
Fill in shift hours, study days, performance rating, and allowance.
Press the calculate button to display results above the form.
Use the CSV and PDF buttons to save the computed report.

FAQs

1. What is work sampling?

Work sampling is a statistical method using random observations to estimate how often a worker, team, or machine is productive, idle, or delayed.

2. When should I use work sampling instead of time study?

Use work sampling when activities are irregular, long-cycle, or difficult to measure continuously. It works well for utilization, allowances, and multi-activity environments.

3. Why does the calculator ask for delay observations?

Delay observations separate stoppages from pure idle time. This helps engineers identify controllable process losses and distinguish waiting from non-working availability.

4. What does the confidence interval mean?

The confidence interval shows a likely range for the true utilization proportion. Higher sample counts usually narrow the interval and improve decision reliability.

5. How is required sample size estimated?

Required samples depend on observed utilization, selected confidence level, and allowable error. Smaller error targets or higher confidence levels increase sample needs.

6. What is performance rating used for here?

Performance rating adjusts observed working time to normal time. It helps convert raw utilization findings into a more standardized performance estimate.

7. Why include allowance percentage?

Allowance percentage expands normal time into standard time. It accounts for fatigue, personal needs, and unavoidable delays in practical engineering studies.

8. Can this calculator be used for machine studies?

Yes. The same method can estimate machine utilization, waiting time, and delay patterns, provided your observation categories are clearly defined beforehand.