Chapter 10, Problem 23P

Virginia College promotes a wide variety of executive- training courses for firms in the Arlington, Virginia, region. Director Wendy Tate believes that individually written letters add a personal touch to marketing. To prepare letters for mailing, she conducts a time study of her secretaries. On the basis of the observations shown in the following table, she wishes to develop a time standard for the whole job.

  The college uses a total allowance factor of 12%. Tate decides to delete all unusual observations from the time study. What is the standard time?

^aDisregard–secretary stopped to answer the phone.

^bDisregard–interruption by supervisor.

Summary Introduction

To determine: The standard time for the operation.

Introduction: Time study is the basis that helps set the standard time; it would time a sample of the performance of the worker.

Answer to Problem 23P

Thestandard time is calculated as 5.4 minutes.

Explanation of Solution

Given information:

The allowance factor is given as 12%. The observed time and performance rating for each element is given as follows:

Element	Performance rating	Observation (minutes)
		1	2	3	4	5	6
Typing letter	85	2.5	3.5	2.8	2.1	2.6	3.3
Typing envelope	100	0.8	0.8	0.6	0.8	3.1a	0.7
Stuffing envelope	95	0.4	0.5	1.9a	0.3	0.6	0.5
Sealing and sorting	125	1	2.9b	0.9	1	4.4b	0.9

^a refers to the secretary stopping to answer the phone

^b refers to the interruption by a supervisor

Formulae to calculate standard time:

$\text{Average time}=\frac{\text{Observations}}{n}$

$\text{Normal time}=\text{Average time}\times \text{Performance rating}$

$\text{Standard time}=\frac{\text{Normal time}}{1-\text{Allowance factor}}$

Calculate standard time:

Element	Performance rating	Observation (minutes)						Average time	Normal time
		1	2	3	4	5	6
Typing letter	85%	2.5	3.5	2.8	2.1	2.6	3.3	2.8	2.38
Typing envelope	100%	0.8	0.8	0.6	0.8	3.1a	0.7	0.74	0.74
Stuffing envelope	95%	0.4	0.5	1.9a	0.3	0.6	0.5	0.46	0.437
Sealing and sorting	125%	1	2.9b	0.9	1	4.4b	0.9	0.95	1.1875

Excel worksheet:

Calculate the average time for typing letters:

The average time is calculated by taking an average of the observation given, which is summation of 2.5, 3.5, 2.8, 2.1, 2.6, and 3.3 and dividing the result by 6. Hence, the average is 2.8 minutes.

$\begin{array}{c}\text{Average time}=\frac{\text{Observation}}{n}\\ =\frac{2.5+3.5+2.8+2.1+2.6+3.3}{6}\\ =\frac{16.8}{6}\\ =2.8\text{ minutes}\end{array}$

Calculate the average time for typing envelope:

The average time is calculated by taking an average of the observation given, which is summation of 0.8, 0.8, 0.6, 0.8, and 0.7 and dividing the result by 5. Hence, the average is 0.74 minutes.

$\begin{array}{c}\text{Average time}=\frac{\text{Observation}}{n}\\ =\frac{0.8+0.8+0.6+0.8+0.7}{5}\\ =\frac{3.7}{5}\\ =0.74\text{ minutes}\end{array}$

Note: The observation with (X^a) should not be considered while calculating the average time.

Calculate the average time for stuffing envelope:

$\begin{array}{c}\text{Average time}=\frac{\text{Observation}}{n}\\ =\frac{0.4+0.5+0.3+0.6+0.5}{5}\\ =\frac{2.3}{5}\\ =0.46\text{ minutes}\end{array}$

The average time is calculated by taking an average of the observation given, which is summation of 0.4, 0.5, 0.3, 0.6, and 0.5 and dividing the result by 5. Hence, the average is 0.46 minutes.

Note: The observation with (X^a) should not be considered while calculating average time.

Calculate average time for sealing and sorting:

$\begin{array}{c}\text{Average time}=\frac{\text{Observation}}{n}\\ =\frac{1.0+0.9+1.0+0.9}{4}\\ =\frac{3.8}{4}\\ =0.95\text{ minutes}\end{array}$

The average time is calculated by taking an average of the observation given, which is summation of 1.0, 0.9, 1.0, and 0.9 and dividing the result by 4. Hence, the average is 0.95 minutes.

Note: The observation with (X^a and X^b) should not be considered while calculating average time.

Calculate normal time for typing letter:

$\begin{array}{c}\text{Normal time}=\text{Average time}\times \text{Performance rating}\\ =2.8\times 85\%\\ =2.8\times 0.85\\ =2.38\text{ minutes}\end{array}$

Normal time is calculated by multiplying the average time and performance rating. The average time is calculated as 2.8 minutes, and performance rating is given as 85%. Hence, the normal time is 2.38 minutes.

Calculate normal time for typing envelope:

The normal time is calculated by multiplying the average time and performance rating. The average time is calculated as 0.74 minutes, and performance rating is given as 100%. Hence, the normal time is 0.74 minutes.

$\begin{array}{c}\text{Normal time}=\text{Average time}\times \text{Performance rating}\\ =0.74\times 100\%\\ =0.74\times 1\\ =0.74\text{ minutes}\end{array}$

Calculate normal time for stuffing envelope:

The normal time is calculated by multiplying the average time and performance rating. The average time is calculated as 0.46 minutes, and performance rating is given as 95%. Hence, the normal time is 0.437 minutes.

$\begin{array}{c}\text{Normal time}=\text{Average time}\times \text{Performance rating}\\ =0.46\times 95\%\\ =0.46\times 0.95\\ =0.437\text{ minutes}\end{array}$

Calculate normal time for sealing and sorting:

The normal time is calculated by multiplying the average time and performance rating. The average time is calculated as 0.95 minutes, and performance rating is given as 125%. Hence, the normal time is 1.1875 minutes.

$\begin{array}{c}\text{Normal time}=\text{Average time}\times \text{Performance rating}\\ =0.95\times 125\%\\ =0.95\times 1.25\\ =1.1875\text{ minutes}\end{array}$

Calculate the total normal time:

The normal time is calculated by adding the normal time for typing letter, typing envelope, stuffing envelope, and sealing and sorting.

$\begin{array}{c}\text{Normal time}=\text{Sum of normal times}\\ =2.38+0.74+0.437+1.1875\\ =4.75\text{ minutes}\end{array}$

Hence, the total normal time is 4.75 minutes.

Calculate the standard time:

The standard time is calculated by dividing the normal time with the value attained by subtracting the allowance factor from 1. The normal time is calculated as 4.75 minutes and the allowance factor is calculated as 12%

$\begin{array}{c}\text{Standard time}=\frac{\text{Normal time}}{1-\text{Allowance factor}}\\ =\frac{4.75\text{ minutes}}{1-0.12}\\ =\frac{4.75\text{ minutes}}{0.88}\\ =5.4\text{ minutes}\end{array}$

Hence, the standard time is 5.4 minutes.