Principles Of Operations Management
Principles Of Operations Management
11th Edition
ISBN: 9780135173930
Author: RENDER, Barry, HEIZER, Jay, Munson, Chuck
Publisher: Pearson,
Question
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Chapter 10, Problem 29P

a)

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.

a)

Expert Solution
Check Mark

Answer to Problem 29P

Thestandard time is calculated as 85.56 seconds.

Explanation of Solution

Given information:

The allowance factor is given as 23%. The observed time and performance rating for each element is given as follows:

Element Performance rating Observation (seconds)
1 2 3 4 5
Grasp and place bag 110% 8 9 8 11 7
Fill bag 85% 36 41 39 35 112a
Seal bag 105% 15 17 13 20 18
Place bag on conveyor 90% 8 6 9 30b 35b

a refers to the bag breaking open

b refers to the conveyor getting jammed

Formulae to calculate standard time:

Average time=Observationsn

Normal time=Average time×Performance rating

Standard time=Normal time1Allowance factor

Calculate normal time:

Element Performance rating Observation (seconds) Average time Normal time
1 2 3 4 5
Grasp and place bag 110% 8 9 8 11 7 8.6 9.46
Fill bag 85% 36 41 39 35 112a 37.75 32.0875
Seal bag 105% 15 17 13 20 18 16.6 17.43
Place bag on conveyor 90% 8 6 9 30b 35b 7.67 6.9

Calculate the average time to grasp and place bag:

The average time is calculated by taking an average of the observation given, which is the summation of 8, 9, 8, 11, and 7 and dividing the result by 5. Hence, the average is 8.6 seconds.

Average time=Observationn=8+9+8+11+75=435=8.6 seconds

Calculate the average time to fill bag:

The average time is calculated by taking an average of the observation given, which is the summation of 36, 41, 39, and 35 and dividing the result by 4. Hence, the average is 37.75 seconds.

Average time=Observationn=36+41+39+354=1514=37.75 seconds

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

Calculate the average time to seal bag:

The average time is calculated by taking an average of the observation given, which is the summation of 15, 17, 13, 20, and 18 and dividing the result by 5. Hence, the average is 16.6 seconds.

Average time=Observationn=15+17+13+20+185=835=16.6 seconds

Calculate the average time to place bag on conveyor:

The average time is calculated by taking an average of the observation given, which is the summation of 8, 6, and 9 and dividing the result by 3. Hence, the average is 7.67 seconds.

Average time=Observationn=8+6+93=233=7.67 seconds

Note: The observations with (Xa and Xb) should not be considered while calculating the average time.

Calculate the normal time to grasp and place bag:

The normal time is calculated by multiplying average time and performance rating. Average time is calculated as 8.60 seconds, and performance rating is given as 110%. Hence, the normal time is 9.46 seconds.

Normal time=Average time×Performance rating=8.60×110%=8.60×1.1=9.46 seconds

Calculate the normal time fill bag:

The normal time is calculated by multiplying average time and performance rating. Average time is calculated as 37.75 seconds, and performance rating is given as 85%. Hence, the normal time is 32.09 seconds.

Normal time=Average time×Performance rating=37.75×85%=37.75×0.85=32.09 seconds

Calculate the normal time to seal bag:

The normal time is calculated by multiplying average time and performance rating. Average time is calculated as 16.60 seconds, and performance rating is given as 105%. Hence, the normal time is 17.43 seconds.

Normal time=Average time×Performance rating=16.60×105%=16.60×1.05=17.43 seconds

Calculate the normal time to place bag on conveyor:

The normal time is calculated by multiplying average time and performance rating. Average time is calculated as 7.67 seconds, and performance rating is given as 90%. Hence, the normal time is 6.90 seconds.

Normal time=Average time×Performance rating=7.67×90%=7.67×0.90=6.90 seconds

Calculate the total normal time:

The normal time is calculated by adding the normal time to grasp and place bag, fill bag, seal bag, and place bag on conveyor.

Normal time=Sum of normal times=9.46+32.09+17.43+6.90=65.88 seconds

Hence, the total normal time is 65.88 seconds.

Calculate the standard time:

The standard time is calculated by dividing normal time with the value attained by subtracting allowance factor from 1. Normal time is calculated as 65.88 seconds and allowance factor is calculated as 23%

Standard time=Normal time1Allowance factor=65.88 seconds10.23=65.88 seconds0.77=85.56 seconds

Hence, standard time is 85.56 seconds.

b)

Summary Introduction

To determine: The number of sample sizes required.

Introduction: Thesample size is required to determine the number of observations that are necessary to find the true cycle time.

b)

Expert Solution
Check Mark

Answer to Problem 29P

Thesample size to grasp and place bag is 83, to fill bag is 14, to seal bag is 70, and to place bag on conveyor is 107 samples.

Explanation of Solution

Given information:

Confidence level is 99% and accuracy is ±5%.

Element Performance rating Observation (seconds)
1 2 3 4 5
Grasp and place bag 110% 8 9 8 11 7
Fill bag 85% 36 41 39 35 112a
Seal bag 105% 15 17 13 20 18
Place bag on conveyor 90% 8 6 9 30b 35b

Formula to determine the required number of observations:

n=(zshx¯)2

n refers to the number of observations required

z refers to the table value for confidence level

s refers to the standard deviation

h refers to accuracy level

x(bar) refers to the average observed time

Determine the proper number of observations required:

Element Mean observed time s Sample
Grasp and place bag 8.6 1.52 8
Fill bag 37.75 2.75 14
Seal bag 16.6 2.7 70
Place bag on conveyor 7.67 1.54 107

Calculate the standard deviation to grasp and place bag:

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 result should be square rooted. The standard deviation to grasp and place bag is 1.52.

s=(Sample observationx¯)2n1=(88.6)2+(98.6)2+(88.6)2+(118.6)2+(78.6)251=9.24=1.52

Calculate the standard deviation to fill bag:

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 resultant should be square rooted. The standard deviation to fill bag is 2.75.

s=(Sample observationx¯)2n1=(3637.75)2+(4137.75)2+(3937.75)2+(3537.75)241=22.753=2.75

Calculate the standard deviation to seal bag:

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 resultant should be square rooted. The standard deviation to seal bag is 1.

s=(Sample observationx¯)2n1=(1517.43)2+(1717.43)2+(1317.43)2+(2017.43)2+(1817.43)251=32.64454=2.70

Calculate the standard deviation to place bag on conveyor:

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 resultant should be square rooted. The standard deviation to place bag on conveyor is 1.54.

s=(Sample observationx¯)2n1=(87.67)2+(67.67)2+(97.67)231=4.66672=1.54

Calculate the sample size to grasp and place bag:

It is calculated by multiplying the z value of 2.58, the standard deviation that is given as 1.52, and dividing the result with the multiple of the accuracy level and average observed time that is given as 0.05 and 8.6, respectively. Hence, the required number of observations is 83 samples.

n=(zshx¯)2=(2.58×1.520.05×8.6)2=(3.92160.43)283 samples

Calculate the sample size to fill bag:

It is calculated by multiplying the z value of 2.58, the standard deviation that is given as 2.75, and dividing the result with the multiple of the accuracy level and average observed time that is given as 0.05 and 37.75, respectively. Hence, the required number of observations is 14 samples.

n=(zshx¯)2=(2.58×2.750.05×37.75)2=(7.0951.8875)214 samples

Calculate the sample size to seal bag:

It is calculated by multiplying the z value of 2.58, the standard deviation that is given as 2.7, and dividing the result with the multiple of the accuracy level and average observed time that is given as 0.05 and 16.6, respectively. Hence, the required number of observations is 70 samples.

n=(zshx¯)2=(2.58×2.70.05×16.6)2=(6.9660.83)270 samples

Calculate the sample size to place bag on conveyor:

It is calculated by multiplying the z value of 2.58, the standard deviation that is given as 1.54, and dividing the resultant with the multiple of the accuracy level and average observed time that is given as 0.05 and 7.67, respectively. Hence, the required number of observations is 107 samples.

n=(zshx¯)2=(2.58×1.540.05×7.67)2=(3.97320.3835)2107 samples

Hence, the standard time for the process is 85.56 seconds. Sample size to grasp and place bag is 83, to fill bag is 14, seal bag is 70, and to place bag on conveyor is 107 samples.

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