resistor production resistor production trial -...
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ContentsInitial Problem Statement 2 Narrative 3-11 Notes 12 Appendices 13-15
Resistor ProductionHow can the outcomes be analysed to optimise the process?
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How can the outcomes be analysed to optimise the process?
Modern manufacturing plants make use of
engineering quality control to ensure that a
product’s quality meets a specified standard and
that rejection rates are minimised. When aiming
to produce resistors to a specified value the
process invariably produces a range of values.
Often products are graded depending on how
close they are to the nominal specification; those
that are closer can have a higher sale price.
Resistor ProductionInitial Problem Statement
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Narrative IntroductionAn electronics component plant manufactures electrical resistors. For such components all manufactured units are tested and graded according to their tolerance, i.e. how close the manufactured value is to the stated value. Those that are closest to the specified value can by sold at a higher price as being precision items.
Discussion DiscussionIf you were in charge of the manufacturing process what would you measure and how? How would you use this information to grade the components?
It is stated that every component is tested. Is this sensible? What is the alternative and what consequences does this have?
DiscussionWhat else might the information you gather tell you?
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2. Measured dataLooking at a particular machine responsible for manufacturing 100 Ω resistors the following data are collected for a production run of 10 000 components. The resistor values have been measured to the nearest whole number of Ohms.
These data are plotted below
Resistor value (Ω) Number of components
<90 1
90 3
91 8
92 19
93 41
94 83
95 154
96 262
97 410
98 593
99 790
190 969
101 1096
102 1142
103 1096
104 969
105 790
106 593
107 410
108 262
109 154
110 83
>110 72
TOTAL 10 000
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Resistance values are recorded as a whole number but in fact the data are continuous so anything from 99.5 to
100.4999… is recorded as 100.
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0
200
400
600
800
1000
1200
<90 90 91 92 93 94 95 96 97 98 99 100
101
102
103
104
105
106
107
108
109
110
>11
0
Number
Measured resistance recorded to nearest integer
Figure 1.
DiscussionDoes it matter as much whether the resistors produced have a resistance value of greater than 100 Ω as it does if they have a value of less than 100 Ω.
DiscussionWhat information about how the production process is working do these data tell you?
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3. Calibrating the machineLook again at the production characteristics.
0
200
400
600
800
1000
1200
<90 90 91 92 93 94 95 96 97 98 99 100
101
102
103
104
105
106
107
108
109
110
>11
0
Number
Measured resistance recorded to nearest integer
Figure 1.
DiscussionIt is clear that the machine is not operating as intended. If you were recalibrating the machine what production characteristics would you address?
DiscussionIs it worth recalibrating the machine?
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4. Grading the productsFor resistor production high precision is not usually required. However, they are not all sold as a single product. Instead the resistors are graded into 4 possible types depending on their tolerance (how close they are to 100 Ω) and sold at a price according to their quality. This allows a high yield from the machine without requiring a high precision process.
The tolerance bands are summarised below. In this case, when assigning resistors to the bands the recorded values of the resistance are used which are to the nearest whole number.
Tolerance Description Unit price
Within 1% Premium quality product £0.016
Within 2% High quality product £0.012
Within 5% Standard product £0.005
Within 10% Low quality product £0.001
Outside 10% Reject -
DiscussionThese unit prices are given to one-thousandth of a pound. Is this possible? What does it mean and why would a company do this?
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Activity 1Look again at the production data.
Resistor value (Ω) Number of components
<90 1
90 3
91 8
92 19
93 41
94 83
95 154
96 262
97 410
98 593
99 790
190 969
101 1096
102 1142
103 1096
104 969
105 790
106 593
107 410
108 262
109 154
110 83
>110 72
TOTAL 10 000
What are the yields for each of the categories of product? Remember that each product can belong to only one category. Use the information to fill in the following table.
Per 10 000 produced
Tolerance Number Sales value
Within 1%
Within 2%
Within 5%
Within 10%
Outside 10%
Total
Discussion DiscussionLook at the total row in the table. What do the totals tell you?
How shall you decide whether or not to recalibrate the machine?
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5. Predicted behaviour of the calibrated machineFor a nominal 100 Ω resistor the expected distribution of resistance values when measured to the nearest whole value per 10,000 components manufactured are summarised in the table below.
Resistor value (Ω) Number of components
<90 12
90 19
91 41
92 83
93 154
94 262
95 410
96 593
97 790
98 969
99 1096
190 1142
101 1096
102 969
103 790
104 593
105 410
106 262
107 154
108 83
109 41
110 19
>110 12
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These data are plotted below.
0
200
400
600
800
1000
1200
<90 90 91 92 93 94 95 96 97 98 99 100
101
102
103
104
105
106
107
108
109
110
>110
Number
Measured resistance recorded to nearest integer
Figure 2.
DiscussionIs this distribution reasonable?
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These data are plotted below.
Activity 2What are the yields for each of the categories of product in the recalibrated machine? Remember that each product can belong to only one category. Use the information to fill in the following table and compare the values with the previous results
Per 10 000 produced
Tolerance Number Sales value
Within 1%
Within 2%
Within 5%
Within 10%
Outside 10%
Total
The results for the measurements made prior to any calibration are
Per 10 000 produced
Tolerance Number Sales value
Within 1% 2855 45.680
Within 2% 1735 20.820
Within 5% 3681 18.405
Within 10% 1656 1.656
Outside 10% 73 0.000
Total 10 000 86.561
Discussion DiscussionWhat are the rejection rates for the current and predicted recalibrated operations? Give the answers in terms of a decimal, a fraction and a percentage.
What is the increase in sales income as a percentage? Would you fix the machine?
MultimediaThe resource Resistor Production Interactive is available to show how variations of mean and spread affect the results. See appendix 1.
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NotesResistor production numbersAt the time of writing the Sichuan Yongxing Electronics Co. based in China has the capacity to produce 5 billion resistors per year! These will be manufactured in a range of values and product types (high power, lower power, variable, etc) but the number still represents an enormous production quantity for any individual item.
The range of values produced is not random. It is designed to give the best possible range of products for use. The determination of the best spread of such “standard values” is covered in a separate resource.
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Appendix 1using the interactives
Resistor Production InteractiveThese are some guidelines for using the resource Resistor Production Interactive.
Figure 3.
Use the sliders to change the mean and standard deviation. Pressing the “random” button will select random values for these parameters. Pressing the “show” button at the bottom of the page will display the distribution. This allows you to guess the shape before viewing it.
Figure 4.
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Pressing the “show” button at the top of the page when a new distribution has been selected and shown (using the bottom “show” button” will reveal the value per 10 000 items for the selected distribution. Try to guess whether it will be larger or smaller than the previous case or the calibrated (nominal) case.
Figure 5.
If the “live update” box is ticked the distribution and value will change as the parameters are varied.
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Appendix 2mathematical coveragePL objectives
Use statistics to solve engineering problems• Display data using a bar chart• Extract numerical information from a data set• Calculate probability• Estimate probability as a relative frequency