Understanding Time Study Concepts

Time study is a work measurement technique used to record the times of performing a task or its elements by a qualified worker, at a defined level of performance. The main goal is to determine the time it should take to complete the task under given conditions.

Key terms in this problem include:

• Cycle Time: The time taken to complete one full cycle of the operation. Multiple observations are usually taken.
• Performance Rating: A factor that represents the worker's pace compared to a standard or normal pace (often considered 100%). A worker performing faster than normal would have a rating above 100%, and slower workers below 100%.
• Normal Time: The time required by a qualified worker working at a normal pace to complete a task. It is calculated by multiplying the average observed cycle time by the performance rating.
• Allowance: Extra time added to the normal time to account for personal needs (like restroom breaks), fatigue, and unavoidable delays. Allowances are often expressed as a percentage or a fraction.
• Standard Time: The total time in which a task should be completed by a qualified worker working at a normal pace, including allowances.

Calculating Standard Time

To calculate the standard time from the given time study data, we follow these steps:

Step 1: Calculate Average Cycle Time

We are given the cycle times recorded for the machinery operation: 7.0, 6.0, 7.0, 8.0 minutes.

The average cycle time is the sum of the observed times divided by the number of observations.

Average Cycle Time = $\frac{\text{Sum of Cycle Times}}{\text{Number of Observations}}$

Average Cycle Time = $\frac{7.0 + 6.0 + 7.0 + 8.0}{4} = \frac{28.0}{4} = 7.0 \text{ minutes}$

Step 2: Calculate Normal Time

The normal time accounts for the worker's performance rating. The performance rating is given as 95%, which is 0.95 as a decimal.

Normal Time = Average Cycle Time $\times$ Performance Rating

Normal Time = $7.0 \text{ minutes} \times 0.95 = 6.65 \text{ minutes}$

Step 3: Calculate Standard Time

The standard time includes an allowance for personal needs, fatigue, and delays. The allowance fraction is given as 0.1 (or 10%). There are two common ways allowance is applied: as a percentage of normal time, or as a percentage of standard time. Based on the options provided, the allowance is likely applied as a fraction of the standard time. The formula is:

Standard Time = $\frac{\text{Normal Time}}{1 - \text{Allowance Fraction}}$

Here, Normal Time = 6.65 minutes and Allowance Fraction = 0.1.

Standard Time = $\frac{6.65}{1 - 0.1} = \frac{6.65}{0.9}$

Standard Time = $7.3888... \text{ minutes}$

Rounding to two decimal places, the standard time is approximately 7.39 minutes.

Let's compare this result with the given options:

• 15.65 minutes
• 7.39 minutes
• 4.66 minutes
• 2.87 minutes

The calculated standard time of approximately 7.39 minutes matches one of the options.