
a)
To determine: The normal time for the operation.
Introduction: The time study is the basis that helps set the standard time; it would time a sample of the performance of the worker.
a)

Answer to Problem 28P
The normal time is calculated as 77.8 minutes.
Explanation of Solution
Given information:
The observed time and performance rating for each element is given as follows:
Element | Performance rating | Observation (minutes) | ||||
1 | 2 | 3 | 4 | 5 | ||
Prepare daily reports | 120 | 35 | 40 | 33 | 42 | 39 |
Photocopy results | 110 | 12 | 10 | 36a | 15 | 13 |
Label and package reports | 90 | 3 | 3 | 5 | 5 | 4 |
Distribute reports | 85 | 15 | 18 | 21 | 17 | 45b |
a refers to the photocopying machine being broken
b refers to the delay in allowance factor
Formulae to calculate normal time:
Calculate normal time:
Element | Performance rating | Observation (minutes) | Average time | Normal time | ||||
1 | 2 | 3 | 4 | 5 | ||||
Prepare daily reports | 120% | 35 | 40 | 33 | 42 | 39 | 37.8 | 45.36 |
Photocopy results | 110% | 12 | 10 | 36a | 15 | 13 | 12.5 | 13.75 |
Label and package reports | 90% | 3 | 3 | 5 | 5 | 4 | 4 | 3.6 |
Distribute reports | 85% | 15 | 18 | 21 | 17 | 45b | 17.75 | 15.09 |
Calculate the average time to prepare daily reports:
The average time is calculated by taking an average of the observation given, which is a summation of 35, 40, 33, 42, and 39 and dividing the result by 5. Hence, the average is 37.8 minutes.
Calculate the average time to photocopy results:
The average time is calculated by taking an average of the observation given, which is a summation of 12, 10, 15, and 13 and dividing the result by 4. Hence, the average is 12.5 minutes.
Note: The observation with (Xa) should not be considered while calculating the average time.
Calculate the average time to label and package reports:
The average time is calculated by taking an average of the observation given, which is a summation of 3, 3, 5, 5, and 4 and dividing the result by 5. Hence, the average is 4 minutes.
Calculate the average time to distribute reports:
The average time is calculated by taking an average of the observation given, which is a summation of 15, 18, 21, and 17 and dividing the result by 4. Hence, the average is 17.75 minutes.
Note: The observation with (Xb) should not be considered while calculating the average time.
Calculate the normal time to prepare daily reports:
The normal time is calculated by multiplying average time and performance rating. The average time is calculated as 37.8 minutes, and performance rating is given as 120%. Hence, the normal time is 45.36 minutes.
Calculate the normal time to photocopy results:
The normal time is calculated by multiplying average time and performance rating. The average time is calculated as 12.50 minutes, and performance rating is given as 110%. Hence, the normal time is 13.75 minutes.
Calculate the normal time to label and package reports:
The normal time is calculated by multiplying average time and performance rating. The average time is calculated as 4.0 minutes, and performance rating is given as 90%. Hence, the normal time is 3.6 minutes.
Calculate the normal time to distribute reports:
The normal time is calculated by multiplying average time and performance rating. The average time is calculated as 17.75 minutes, and performance rating is given as 85%. Hence, the normal time is 15.09 minutes.
Calculate the total normal time:
The normal time is calculated by adding the normal time to prepare daily reports, photocopy results, label and package reports, and distribute reports.
Hence, the total normal time is 77.8 minutes.
b)
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.
b)

Answer to Problem 28P
Thestandard time is calculated as 91.53 minutes.
Explanation of Solution
Given information:
The allowance is given as 15%. The observed time and performance rating for each element is given as follows:
Element | Performance rating | Observation (minutes) | ||||
1 | 2 | 3 | 4 | 5 | ||
Prepare daily reports | 120 | 35 | 40 | 33 | 42 | 39 |
Photocopy results | 110 | 12 | 10 | 36a | 15 | 13 |
Label and package reports | 90 | 3 | 3 | 5 | 5 | 4 |
Distribute reports | 85 | 15 | 18 | 21 | 17 | 45b |
a refers to the photocopying machine being broken
b refers to the delay in allowance factor
Formula to calculate standard time:
Calculate standard time:
The standard time is calculated by dividing the normal time with the value attained by subtracting the allowance factor from 1. Normal time is calculated as 77.8 minutes and allowance factor is calculated as 15%
Hence, standard time is 91.53 minutes.
c)
To determine: The number of the
Introduction: The sample size is required to determine the number of observations that are necessary to find the true cycle time.
c)

Answer to Problem 28P
The sample size to prepare reports is 15, to photocopy results is 44, label, and package reports is 96, and to distribute reports is 31 samples.
Explanation of Solution
Given information:
The confidence level is 95% and accuracy is ±5%.
Element | Performance rating | Observation (minutes) | ||||
1 | 2 | 3 | 4 | 5 | ||
Prepare daily reports | 120 | 35 | 40 | 33 | 42 | 39 |
Photocopy results | 110 | 12 | 10 | 36a | 15 | 13 |
Label and package reports | 90 | 3 | 3 | 5 | 5 | 4 |
Distribute reports | 85 | 15 | 18 | 21 | 17 | 45b |
Formula to determine the required number of observation:
n refers to the number of observations required
z refers to the table value for the confidence level
s refers to the standard deviation
h refers to an accuracy level
x(bar) refers to the average observed time
Determine a proper number of observation required:
Element | Mean observed time | s | Sample |
Prepare daily reports | 37.8 | 3.7 | 15 |
Photocopy results | 12.5 | 2.1 | 44 |
Label and package reports | 4 | 1 | 96 |
Distribute reports | 17.75 | 2.5 | 31 |
Calculate the standard deviation to prepare daily reports:
The standard deviation can be calculated by dividing two values. The first value can be calculated by adding the square of the value attained by subtracting the mean observed value from each observation. The second value can be attained by subtracting 1 from the number of samples and the results should be square rooted. The standard deviation to prepare the daily report is 3.7.
Calculate the standard deviation to photocopy results:
The standard deviation can be calculated by dividing two values. The first value can be calculated by adding the square of the value attained by subtracting the mean observed value from each observation. The second value can be attained by subtracting 1 from the number of samples and the results should be square rooted. The standard deviation to photocopy results is 2.1.
Calculate the standard deviation to label and package reports:
The standard deviation can be calculated by dividing two values. The first value can be calculated by adding the square of the value attained by subtracting the mean observed value from each observation. The second value can be attained by subtracting 1 from the number of samples and the results should be square rooted. The standard deviation to label and package reports is 1.
Calculate the standard deviation to distribute reports:
The standard deviation can be calculated by dividing two values. The first value can be calculated by adding the square of the value attained by subtracting the mean observed value from each observation. The second value can be attained by subtracting 1 from the number of samples and the results should be square rooted. The standard deviation to distribute reports is 2.5.
Calculate the sample size to prepare daily reports:
It is calculated by multiplying the z value of 1.96, the standard deviation that is given as 3.7, and dividing the result with the multiple of the accuracy level and average observed time that is given as 0.05 and 37.8, respectively. Hence, the required number of observations is 15 samples.
Calculate the sample size to photocopy results:
It is calculated by multiplying the z value of 1.96, the standard deviation that is given as 2.1, and dividing the result with the multiple of the accuracy level and average observed time that is given as 0.05 and 12.5, respectively. Hence, the required number of observations is 44 samples.
Calculate the sample size to label and package reports:
It is calculated by multiplying the z value of 1.96, the standard deviation that is given as 1, and dividing the result with the multiple of the accuracy level and average observed time that is given as 0.05 and 4, respectively. Hence, the required number of observations is 96 samples.
Calculate the sample size to distribute reports:
It is calculated by multiplying the z value of 1.96, the standard deviation that is given as 2.5, and dividing the result with the multiple of the accuracy level and average observed time that is given as 0.05 and 17.75, respectively. Hence, the required number of observations is 31 samples.
Hence, the normal time for the process is 77.8 minutes and standard time for the process is 91.53 minutes. The sample size to prepare reports is 15, to photocopy results is 44, label and package reports are 96, and to distribute reports is 31 samples.
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Chapter 10 Solutions
Principles Of Operations Management
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