
a)
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)

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:
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.
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.
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.
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.
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.
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.
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.
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.
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.
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%
Hence, standard time is 85.56 seconds.
b)
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)

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 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.
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.
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.
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.
Calculate the
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.
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.
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.
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.
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.
Want to see more full solutions like this?
Chapter 10 Solutions
Principles Of Operations Management
- At Quick Car Wash, the wash process is advertised to take less than 6 minutes. Consequently, management has set a target average of 330 seconds for the wash process. Suppose the average range for a sample of 7 cars is 10 seconds. Use the accompanying table to establish control limits for sample means and ranges for the car wash process. Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. The UCLR equals seconds and the LCLR equals seconds. (Enter your responses rounded to two decimal places.)arrow_forwardIf Jeremy who is the VP for the operations, proceeds with their existing prototype (which is option a), the firm can then expect sales to be 120,000 units at $550 each. And with a probability of 0.52 and a 0.48 probability of 65,000 at $550. we However, he uses his value analysis team (option b), the firm expects sales of 75,000 units at $770, with a probability of 0.78 and a 0.22 probability of 65,000 units at $770. Value engineering, at a cost of $100,000, is only used in option b. Which option for this has the highest expected monetary value (EMV)? The EMV for option a is $? The EMV for option b is $? Which has the highest expected monetary value. A or B?arrow_forwardPart 1 of 2 Jim's Outfitters, Inc., makes custom western shirts. The shirts could be flawed in various ways, including flaws in the weave or color of the fabric, loose buttons or decorations, wrong dimensions, and uneven stitches. Jim randomly examined 10 shirts, with the following results shown to the right. Shirt Defects 1 7 2 1 4 13 3 10 2 8 5 9 10 8 7 a. Assuming that 10 observations are adequate for these purposes, determine the three-sigma control limits for defects per shirt. The UCLC equals and the LCL equals (Enter your responses rounded to two decimal places. If your answer for LCL is negative, enter this value as 0.)arrow_forward
- Management at Webster Chemical Company is concerned as to whether caulking tubes are being properly capped. If a significant proportion of the tubes are not being sealed, Webster is placing its customers in a messy situation. Tubes are packaged in large boxes of 144. Several boxes are inspected, and the following numbers of leaking tubes are found: Sample Tubes Sample Tubes Sample Tubes 1 7 8 7 15 7 2 7 9 8 16 9 3 6 10 7 17 3 4 4 11 1 18 7 5 8 12 8 19 7 6 7 2 9 13 14 1 20 6 7 Total 121 Calculate p-chart three-sigma control limits to assess whether the capping process is in statistical control. The UCLp equals and the LCLp equals (Enter your responses rounded to three decimal places. If your answer for LCLp is negative, enter this value as 0.)arrow_forwardAspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (in.) from the last six samples are Bottle Sample 1 2 3 4 1 0.624 0.586 0.602 0.591 2 0.613 0.599 0.578 0.618 3 0.606 0.585 0.587 0.623 4 0.581 0.623 0.571 0.610 5 0.609 0.610 0.623 0.617 6 0.605 0.573 0.570 0.602 Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. Suppose that the specification for the bottle neck diameter is 0.600 ± 0.050 in. and the population standard deviation is 0.014 in. a. What is the process capability index? The Cpk is (Enter your response rounded to two decimal places.)arrow_forwardHow would you handle the Apple 'batterygate' scandal as an operations manager? What quality measures would you take to fix the problem and prevent it from happening again? When would you implement these measures and communicate with the stakeholders?arrow_forward
- Perosnal Thoughts about the articlearrow_forwardRevenue retrieval for Brew Mini= $ round response to two decimal places What would be the best design alternative? Brew master or brew miniarrow_forwardThe revenue retrieval for PG Glass design is ?. Enter response as a whole number). The revenue retrieval for Glass Unlimited design is ? (enter your response as a whole number). What is The best design alternative? Glass unlimited or PG Glass?arrow_forward
- Foundations of Business (MindTap Course List)MarketingISBN:9781337386920Author:William M. Pride, Robert J. Hughes, Jack R. KapoorPublisher:Cengage LearningFoundations of Business - Standalone book (MindTa...MarketingISBN:9781285193946Author:William M. Pride, Robert J. Hughes, Jack R. KapoorPublisher:Cengage Learning
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,


