a) To compute the standard time for the bag-packing task, follow these steps:
1. Calculate the average time for each task element:
Grasp and place bag: (8+9+8+11+7)/5 = 8.6 seconds
Fill bag: (36+41+39+35)/4 = 37.75 seconds (we will exclude observation 112 in this calculation as it seems to be an error)
Seal bag: (15+17+13+20+18)/5 = 16.6 seconds
Place bag on conveyor: (8+6+9)/3 = 7.67 seconds (exclude observations 30 and 35 as they seem to be errors)
2. Multiply the average time by the performance rating for each task element:
Grasp and place bag: 8.6 * 1.1 = 9.46 seconds
Fill bag: 37.75 * 0.85 = 32.09 seconds
Seal bag: 16.6 * 1.05 = 17.43 seconds
Place bag on conveyor: 7.67 * 0.9 = 6.9 seconds
3. Add up the times for all task elements:
9.46 + 32.09 + 17.43 + 6.9 = 65.88 seconds
4. Add the 23% allowance for workers:
65.88 * 1.23 = 81.03 seconds
So, the standard time for the bag-packing task is 81.03 seconds.
b) To determine how many observations are necessary for 99% confidence within 5% accuracy, use the following formula:
Number of observations (n) = (Z^2 * SD^2 * p * (1-p)) / E^2
Where:
Z = Z-score for the desired confidence level (2.576 for 99% confidence)
SD = Standard deviation of the time observations
p = Proportion of successes (in this case, successful bag packing)
E = Desired accuracy (0.05)
First, calculate the standard deviation for each task element:
Grasp and place bag: SD = √(((1*(8-8.6)^2)+(1*(9-8.6)^2)+(1*(8-8.6)^2)+(1*(11-8.6)^2)+(1*(7-8.6)^2))/4) = 1.52
Fill bag: SD = √(((1*(36-37.75)^2)+(1*(41-37.75)^2)+(1*(39-37.75)^2)+(1*(35-37.75)^2))/3) = 2.49
Seal bag: SD = √(((1*(15-16.6)^2)+(1*(17-16.6)^2)+(1*(13-16.6)^2)+(1*(20-16.6)^2)+(1*(18-16.6)^2))/4) = 2.41
Place bag on conveyor: SD = √(((1*(8-7.67)^2)+(1*(6-7.67)^2)+(1*(9-7.67)^2))/2) = 1.53
Next, calculate the proportion of successes (p) for each task element based on the performance ratings:
Grasp and place bag: p = 110/110 = 1
Fill bag: p = 85/85 = 1
Seal bag: p = 105/105 = 1
Place bag on conveyor: p = 90/90 = 1
Finally, calculate the number of observations (n) for each task element:
Grasp and place bag: n = ((2.576^2 * 1.52^2 * 1 * (1-1))/(0.05^2)) = 533.84
Fill bag: n = ((2.576^2 * 2.49^2 * 1 * (1-1))/(0.05^2)) = 993.84
Seal bag: n = ((2.576^2 * 2.41^2 * 1 * (1-1))/(0.05^2)) = 910.66
Place bag on conveyor: n = ((2.576^2 * 1.53^2 * 1 * (1-1))/(0.05^2)) = 583.83
Since the Fill bag task has the highest number of observations necessary for 99% confidence within 5% accuracy, we will use that value as the answer: 994 observations are required (rounded up to the nearest whole number).
The Dubuque Cement Company packs 80-pound bags of concrete mix. Time-study data for the filling activity are shown in the following table. Because of the high physical demands of the job, the company's policy is a 23% allowance for workers. a) Compute the standard time for the bag-packing task. b) How many observations are necessary for 99% confidence, within 5% accuracy? The Dubuque Cement Company packs 80-pound bags of concrete mix. Time-study data for the filling activity are shown in the following table. Because of the high physical demands of the job, the company's policy is a 23% allowance for workers. a) Compute the standard time for the bag-packing task. b) How many observations are necessary for 99% confidence, within 5% accuracy? Observations (seconds) Performance
Element 1 2 3 4 5 Rating (%)
Grasp and place bag 8 9 8 11 7 110
Fill bag 36 41 39 35 112a 85
Seal bag 15 17 13 20 18 105
Place bag on conveyor 8 6 9 30b 35b 90
1 answer
1 answer