MGT635-1003B-04 International Business Operations Management
Assignment Name: Unit 5 Individual Project
Deliverable Length: 6-7 body pages
Details: As the production manager for an electronic circuit company you have encountered the following situation.
Part 1
A process for producing electronic circuits has achieved very high yield levels. An average of only 10 defective parts per million is currently produced.
1.What are the upper and lower control limits for a sample size of 100?
2.Recompute the upper and lower control limits for a sample size of 10,000?
3.Which of these two sample sizes would you recommend? Explain.
Part 2
Management has reconsidered the method of quality control and has decided to use process control by variables instead of attributes. For variables control a circuit voltage will be measured based on a sample of only five circuits. The past average voltage for samples of size 5 has been 3.1 volts, and the range has been 1.2 volts.
1.What would the upper and lower control limits be for the resulting control charts (average and range)?
2.Five samples of voltage are taken with the results in the table below. What action should be taken if any?
3.Discuss the pros and cons of using this variables control chart versus the control chart discussed in the first part of the assignment. Which do you prefer?
Sample 1 2 3 4 5
x 3.6 3.3 2.6 3.9 3.4
R 2.0 2.6 0.7 2.1 2.3
Please be aware that no one here will do your work for you. However, we will be happy to read over whatever you come up with and make suggestions and/or corrections.
Please post what you think.
To solve this assignment, we need to calculate the upper and lower control limits for both Part 1 and Part 2 of the problem. I will explain the process for each part and show you how to calculate the control limits.
Part 1:
1. To calculate the control limits for a sample size of 100, we will use the formula for the control limits of a sample mean:
Upper control limit (UCL) = x̄ + 3σ/√n
Lower control limit (LCL) = x̄ - 3σ/√n
Here, x̄ represents the average number of defective parts per million, σ represents the standard deviation, and n represents the sample size.
Given that the average number of defective parts per million is 10, and since we don't have the standard deviation, we can assume that the process is in control, and therefore, the population standard deviation can be estimated using the average range of the samples.
2. To calculate the control limits for a sample size of 10,000, follow the same formula as above, but replace the sample size with 10,000.
3. To determine which sample size is recommended, we need to consider the trade-off between the precision of the estimate and the cost and effort associated with obtaining a larger sample size. Generally, a larger sample size provides a more precise estimate of the population parameter, but it also requires more resources and time. In this case, since the process has already achieved very high yield levels with a sample size of 100, it may not be necessary to increase the sample size to 10,000.
Part 2:
1. To calculate the control limits for the variables control chart (average and range), we will use the formulas:
Average control limits:
UCL = x̄ + A2 * R
LCL = x̄ - A2 * R
Range control limits:
UCL = D4 * R
LCL = D3 * R
Here, x̄ represents the average voltage, R represents the range, A2, D3, and D4 are constants based on the sample size (n=5).
Given that the past average voltage is 3.1 volts and the range is 1.2 volts, we can calculate the control limits using these formulas.
2. For the given sample results in the table, we need to plot them on the variables control chart and determine if any action is needed. On the control chart, we compare the average voltage (x̄) and the range (R) of each sample with their respective control limits. If any points fall outside the control limits or exhibit non-random patterns, it indicates that the process is out of control and corrective action may be needed.
3. Finally, we need to discuss the pros and cons of using variables control chart versus attributes control chart (used in Part 1). We can compare factors such as the type of data being collected, the ease of measurement, the ability to detect and locate process variations, and the sensitivity to small changes. Based on these factors, we can express a preference for one control chart over the other.
This explanation should help you to understand how to solve the given assignment. If you have any specific questions or need further assistance, please feel free to ask.