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Operations Management and Quality Control

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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.

What are the upper and lower control limits for a sample size of 100?
Recompute the upper and lower control limits for a sample size of 10,000?
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.

What would the upper and lower control limits be for the resulting control charts (average and range)?
Five samples of voltage are taken with the results in the table below. What action should be taken if any?
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

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Solution Summary

This solution contains step-by-step calculations to determine the upper and lower control limit for differing sample sizes as well as for per variable control chart. It also analyzes the results and provides a conclusion of the sample sizes using variable control charts.

Solution Preview

Part1:
As per attributes control chart formula:
For sample size of 100
UCL= .0001(average % defective 100 * 1 /10, 00,000) + 3 * sq.root of .0001*.9999/100

= .0001+ .002998497= .003098497
LCL= .0001- .002998497= - .002898497

For sample size of 10,000
UCL= .0001+3*SQ.RT. of .0001*.9999/10000= .000384604
LCL= .0001- .00028464= -.000184607
Sample size of 10,000 will be better because by 100 sample ...

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