topic 4- control chart for attributes
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Control Chart for Attributes
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IntroductionMany quality characteristics cannot be conveniently represented numerically. In such cases, each item inspected is classified as either conforming or nonconforming to the specifications on that quality characteristic. Quality characteristics of this type are called attributes. Examples are nonfunctional semiconductor chips, warped connecting rods, etc,.
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p charts: proportion of units nonconforming.np charts: number of units nonconforming.c charts: count of nonconformities.u charts: count of nonconformities per unit.Control Charts for Variables DataX and R charts: for sample averages and ranges.Md and R charts: for sample medians and ranges.X and s charts: for sample means and standard deviations.X charts: for individual measures; uses moving ranges.Types of Control ChartsControl Charts for Attributes Datadefectives
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Count ChartsA defective item is a nonconforming unit. It must be discarded, reworked, returned, sold, scrapped, or downgraded. It is unusable for its intended purpose in its present form. A defect, on the other hand, is an imperfection of some type that is undesirable, although it does not necessarily render the entire good or service unusable. One or more defects may not make an entire good or service defective. For example, we would not scrap or discard a computer, a washing machine, or an air conditioner because of a small scratch in the paint.
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Type of Attribute Chartsp chartsThis chart shows the fraction of nonconforming or defective product produced by a manufacturing process. It is also called the control chart for fraction nonconforming. np chartsThis chart shows the number of nonconforming. Almost the same as the p chart.c chartsThis shows the number of defects or nonconformities produced by a manufacturing process.u chartsThis chart shows the nonconformities per unit produced by a manufacturing process.
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p chartsIn this chart, we plot the percent of defectives (per batch, per day, per machine, etc.). However, the control limits in this chart are not based on the distribution of rate events but rather on the binomial distribution (of proportions).
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FormulaFraction nonconforming:p = (np)/nwhere p = proportion or fraction nc in the sample or subgroup, n = number in the sample or subgroup, np = number nc in the sample or subgroup.
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ExampleDuring the first shift, 450 inspection are made of book-of the month shipments and 5 nc units are found. Production during the shift was 15,000 units. What is the fraction nc?
p = (np)/n = 5/450 = 0.011
The p, is usually small, say 0.10 or less.If p > 0.10, indicate that the organization is in serious difficulty.
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p-Chart contruction for constant subgroup sizeSelect the quality characteristics.Determine the subgroup size and methodCollect the data.Calculate the trial central line and control limits.Establish the revised central line and control limits.Achieve the objective.
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Select the quality characteristicsThe quality characteristic?A single quality characteristicA group of quality characteristicsA partAn entire product, orA number of products.
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Determine the subgroup size and methodThe size of subgroup is a function of the proportion nonconforming.If p = 0.001, and n = 1000, then the average number nc, np = 1. Not good, since a large number of values would be zero. If p = 0.15, and n = 50, then np = 7.5, would make a good chart.
Therefore, the selection subgroup size requires some preliminary observations to obtain a rough idea of the proportion nonconforming.
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Collect the dataThe quality technician will need to collect sufficient data for at least 25 subgroups.The data can be plotted as a run chart.Since the run chart does not have limits, its is not a control chart.
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Calculate the trial central line and control limitsThe formula:
= average of p for many subgroups
n = number inspected in a subgroup
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Negative value of LCL is possible in a theoritical result, but not in practical (proportion of nc never negative).
Sub-group NumberNumber Inspectednnpp1300120.040230030.010330090.030430040.013530000.0630060.020730060.020830010.00319300160.053
2530020.007Total7500138
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p Chartp-barLCLUCLSubgroupp5 10 15 20 2500.010.020.030.040.053
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Construction of a p-chartAn ExampleAs an illustration, consider the case of an importer of decorative ceramic tiles. Some tiles are cracked or broken before or during transit, rendering them useless scrap. The fraction of cracked or broken tiles is naturally of concern to the firm. Each day a sample of 100 tiles is drawn from the total of all tiles received from each tile vendor.
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Centerline (p) = 183/3000 = 0.061
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Using Average Subgroup Size: An ExampleConsider, for example, the case of a highway toll barrier with two types of toll collection mechanisms: automatic and manned. The automatic lanes require exact change or a transponder while the manned lanes do not. The fraction of vehicles arriving with exact change or a transponder is examined using a control chart for a series of rush hour intervals on consecutive weekdays. As the number of vehicles passing through the toll barrier varies, the control limits change day-to-day. One-hour periods (7:30 to 8:30 am) for 20 consecutive weekdays yield the data shown.
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Using Average Subgroup Size: An Example
Centerline(p) = = 2569/6421=0.400
We can also calculate the UCL, LCL, and zone boundariesfor the first data point,
Day 1 =
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Using Average Subgroup Size: An Example
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np ChartThe np chart is almost the same as the p chart.Central line = npo
If po is unknown, it must be determined by collecting data, calculating UCL, LCL.
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Example
Instructions
Instructions:
1. The next sheet is an example problem. It was created from the sheet called template. Select the cells at the top of the columns to see the
formulas.
2a. The following sheet, called template, should be copied before using the program. This activity is accomplished by selecting EDIT,
selecting MOVE OR COPY SHEET, selecting CREATE A COPY, and locating the new sheet called, template (2), in the dialog box.
2b. The template is designed for the recommended minimum of 25 subgroups; however 35 are possible without changing the formulas. The
procedure is to copy the formulas to the additional subgroups. Then click on the template chart to get the chart icon. Select CHART
WIZARD and obtain step 1. Change the range to include additional rows for the appropriate columns. This activity is accomplished by
either changing the range in the dialog box or dragging the mouse and using the control key.
2c. The control limits and central line are automatically calculated and displayed with the plotted points as data are entered.
2d. The chart is designed for a maximum of 35 points. If more are desired, add additional ones with the appropriate formulas.
2e. It is sometimes necessary to adjust the scales to have a pleasing chart appearance.
2f. It is usually necessary to change the decimal point for different data.
2g. When space is available and it is desired, the chart can be located on the sheet with the data and then printed full size.
&Cnp-Chart Instructions
Page &P of &N
Example Problem
ID NumberSubgroupnnpUCLnp-barLCL
1300312.05.240.0
2300612.05.240.0
3300412.05.240.0
4300612.05.240.0
53002012.05.240.0
6300212.05.240.0
7300612.05.240.0
8300712.05.240.0
9300312.05.240.0
10300012.05.240.0
11300612.05.240.0
12300912.05.240.0
13300512.05.240.0
14300612.05.240.0
15300712.05.240.0
16300412.05.240.0
17300512.05.240.0
18300712.05.240.0
19300512.05.240.0
20300012.05.240.0
21300212.05.240.0
22300312.05.240.0
23300612.05.240.0
24300112.05.240.0
25300812.05.240.0
26
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30
31
32
33
34
35
Sum/np-bar1315.24
&Cnp-Chart Example ProblemCh. 7, Ex. 2
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Example Problem
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&A
Page &P
np
UCL
np-bar
LCL
Subgroup Number
Number Nonconforming
np-Chart
Template
ID NumberSubgroupnnpUCLnp-barLCL
10.000.0
20.000.0
30.000.0
40.000.0
50.000.0
60.000.0
70.000.0
80.000.0
90.000.0
100.000.0
110.000.0
120.000.0
130.000.0
140.000.0
150.000.0
160.000.0
170.000.0
180.000.0
190.000.0
200.000.0
210.000.0
220.000.0
230.000.0
240.000.0
250.000.0
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Sum/np-bar00
&Cnp-Chart Template
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Template
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&A
Page &P
np
UCL
np-bar
LCL
Subgroup Number
Number Nonconforming
np-Chart
Instructions
Instructions:
1. The next sheet is an example problem. It was created from the sheet called template. Select the cells at the top of the columns to see the
formulas.
2a. The following sheet, called template, should be copied before using the program. This activity is accomplished by selecting EDIT,
selecting MOVE OR COPY SHEET, selecting CREATE A COPY, and locating the new sheet called, template (2), in the dialog box.
2b. The template is designed for the recommended minimum of 25 subgroups; however 35 are possible without changing the formulas. The
procedure is to copy the formulas to the additional subgroups. Then click on the template chart to get the chart icon. Select CHART
WIZARD and obtain step 1. Change the range to include additional rows for the appropriate columns. This activity is accomplished by
either changing the range in the dialog box or dragging the mouse and using the control key.
2c. The control limits and central line are automatically calculated and displayed with the plotted points as data are entered.
2d. The chart is designed for a maximum of 35 points. If more are desired, add additional ones with the appropriate formulas.
2e. It is sometimes necessary to adjust the scales to have a pleasing chart appearance.
2f. It is usually necessary to change the decimal point for different data.
2g. When space is available and it is desired, the chart can be located on the sheet with the data and then printed full size.
&Cnp-Chart Instructions
Page &P of &N
Example Problem
ID NumberSubgroupnnpUCLnp-barLCL
1300312.05.240.0
2300612.05.240.0
3300412.05.240.0
4300612.05.240.0
53002012.05.240.0
6300212.05.240.0
7300612.05.240.0
8300712.05.240.0
9300312.05.240.0
10300012.05.240.0
11300612.05.240.0
12300912.05.240.0
13300512.05.240.0
14300612.05.240.0
15300712.05.240.0
16300412.05.240.0
17300512.05.240.0
18300712.05.240.0
19300512.05.240.0
20300012.05.240.0
21300212.05.240.0
22300312.05.240.0
23300612.05.240.0
24300112.05.240.0
25300812.05.240.0
26
27
28
29
30
31
32
33
34
35
Sum/np-bar1315.24
&Cnp-Chart Example ProblemCh. 7, Ex. 2
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Example Problem
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&A
Page &P
np
UCL
np-bar
LCL
Subgroup Number
Number Nonconforming
np-Chart
Template
ID NumberSubgroupnnpUCLnp-barLCL
10.000.0
20.000.0
30.000.0
40.000.0
50.000.0
60.000.0
70.000.0
80.000.0
90.000.0
100.000.0
110.000.0
120.000.0
130.000.0
140.000.0
150.000.0
160.000.0
170.000.0
180.000.0
190.000.0
200.000.0
210.000.0
220.000.0
230.000.0
240.000.0
250.000.0
26
27
28
29
30
31
32
33
34
35
Sum/np-bar00
&Cnp-Chart Template
Page &P of &N
Template
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&A
Page &P
np
UCL
np-bar
LCL
Subgroup Number
Number Nonconforming
np-Chart
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c ChartThe procedures for c chart are the same a s those for the p chart. If count of nonconformities, co, is unknown, it must be found by collecting data, calculating UCL & LCL.
= average count of nonconformities
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Example
Instructions
Instructions:
1. The next sheet is an example problem. It was created from the sheet called template. Select the cells at the top of the columns to see the
formulas.
2a. The following sheet, called template, should be copied before using the program. This activity is accomplished selecting on EDIT,
selecting MOVE OR COPY SHEET, selecting CREATE A COPY, and locating the new sheet called, template (2), in the dialog box.
2b. The template is designed for the recommended minimum of 25 subgroups; however 35 are possible without changing the formulas. The
procedure is to copy the formulas to the additional subgroups. Then click on the template chart to get the chart icon. Select CHART
WIZARD and obtain step 1. Change the range to include additional rows for the appropriate columns. This activity is accomplished by
either changing the range in the dialog box or dragging the mouse and using the control key.
2c. The control limits and central line are automatically calculated and displayed with the plotted points as data are entered.
2d. The chart is designed for a maximum of 35 points. If more are desired, add additional ones with the appropriate formulas.
2e. It is sometimes necessary to adjust the scales to have a pleasing chart appearance.
2f. It is usually necessary to change the decimal point for different data.
2g. When space is available and it is desired, the chart can be located on the sheet with the data and then printed full size.
&Cc-Chart Instructions
Page &P of &N
Example Problem
ID NumberSubgroupcUCLc-barLCL
MY1021712.765.640
MY1132612.765.640
MY1213612.765.640
MY1254312.765.640
MY13252012.765.640
MY1436812.765.640
MY1507612.765.640
MY1528112.765.640
MY1649012.765.640
MY16610512.765.640
MY172111412.765.640
MY18312312.765.640
MY18513112.765.640
MY19814312.765.640
MY20815212.765.640
MY22216712.765.640
MY23517512.765.640
MY24118712.765.640
MY25819212.765.640
MY25920812.765.640
MY26421012.765.640
MY26722412.765.640
MY278231412.765.640
MY28124412.765.640
MY28825512.765.640
26
27
28
29
30
31
32
33
34
35
Sum141
&Cc-Chart Example Problem
Page &P of &N
Example Problem
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&A
Page &P
c
UCL
c-bar
LCL
Subgroup Number
Count of Nonconformities
c-Chart
Template
ID NumberSubgroupcUCLc-barLCL
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
19000
20000
21000
22000
23000
24000
25000
26
27
28
29
30
31
32
33
34
35
Sum0
&Cc-Chart Template
Page &P of &N
Template
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
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0000
0000
0000
0000
0000
&Cc-Chart Template
Page &P of &N
c
UCL
c-bar
LCL
Subgroup Number
Number of Nonconformities
c-Chart
Sheet6
&A
Page &P
Sheet7
&A
Page &P
Sheet8
&A
Page &P
Sheet9
&A
Page &P
Sheet10
&A
Page &P
Sheet11
&A
Page &P
Sheet12
&A
Page &P
Sheet13
&A
Page &P
Sheet14
&A
Page &P
Sheet15
&A
Page &P
Sheet16
&A
Page &P
Instructions
Instructions:
1. The next sheet is an example problem. It was created from the sheet called template. Select the cells at the top of the columns to see the
formulas.
2a. The following sheet, called template, should be copied before using the program. This activity is accomplished selecting on EDIT,
selecting MOVE OR COPY SHEET, selecting CREATE A COPY, and locating the new sheet called, template (2), in the dialog box.
2b. The template is designed for the recommended minimum of 25 subgroups; however 35 are possible without changing the formulas. The
procedure is to copy the formulas to the additional subgroups. Then click on the template chart to get the chart icon. Select CHART
WIZARD and obtain step 1. Change the range to include additional rows for the appropriate columns. This activity is accomplished by
either changing the range in the dialog box or dragging the mouse and using the control key.
2c. The control limits and central line are automatically calculated and displayed with the plotted points as data are entered.
2d. The chart is designed for a maximum of 35 points. If more are desired, add additional ones with the appropriate formulas.
2e. It is sometimes necessary to adjust the scales to have a pleasing chart appearance.
2f. It is usually necessary to change the decimal point for different data.
2g. When space is available and it is desired, the chart can be located on the sheet with the data and then printed full size.
&Cc-Chart Instructions
Page &P of &N
Example Problem
ID NumberSubgroupcUCLc-barLCL
MY1021712.765.640
MY1132612.765.640
MY1213612.765.640
MY1254312.765.640
MY13252012.765.640
MY1436812.765.640
MY1507612.765.640
MY1528112.765.640
MY1649012.765.640
MY16610512.765.640
MY172111412.765.640
MY18312312.765.640
MY18513112.765.640
MY19814312.765.640
MY20815212.765.640
MY22216712.765.640
MY23517512.765.640
MY24118712.765.640
MY25819212.765.640
MY25920812.765.640
MY26421012.765.640
MY26722412.765.640
MY278231412.765.640
MY28124412.765.640
MY28825512.765.640
26
27
28
29
30
31
32
33
34
35
Sum141
&Cc-Chart Example Problem
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Example Problem
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&A
Page &P
c
UCL
c-bar
LCL
Subgroup Number
Count of Nonconformities
c-Chart
Template
ID NumberSubgroupcUCLc-barLCL
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
19000
20000
21000
22000
23000
24000
25000
26
27
28
29
30
31
32
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35
Sum0
&Cc-Chart Template
Page &P of &N
Template
0000
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0000
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&Cc-Chart Template
Page &P of &N
c
UCL
c-bar
LCL
Subgroup Number
Number of Nonconformities
c-Chart
Sheet6
&A
Page &P
Sheet7
&A
Page &P
Sheet8
&A
Page &P
Sheet9
&A
Page &P
Sheet10
&A
Page &P
Sheet11
&A
Page &P
Sheet12
&A
Page &P
Sheet13
&A
Page &P
Sheet14
&A
Page &P
Sheet15
&A
Page &P
Sheet16
&A
Page &P
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Chart1
712.76460525225.640
612.76460525225.640
612.76460525225.640
312.76460525225.640
2012.76460525225.640
812.76460525225.640
612.76460525225.640
112.76460525225.640
012.76460525225.640
512.76460525225.640
1412.76460525225.640
312.76460525225.640
112.76460525225.640
312.76460525225.640
212.76460525225.640
712.76460525225.640
512.76460525225.640
712.76460525225.640
212.76460525225.640
812.76460525225.640
012.76460525225.640
412.76460525225.640
1412.76460525225.640
412.76460525225.640
512.76460525225.640
c
UCL
c-bar
LCL
Subgroup Number
Count of Nonconformities
c-Chart
Instructions
Instructions:
1. The next sheet is an example problem. It was created from the sheet called template. Select the cells at the top of the columns to see the
formulas.
2a. The following sheet, called template, should be copied before using the program. This activity is accomplished selecting on EDIT,
selecting MOVE OR COPY SHEET, selecting CREATE A COPY, and locating the new sheet called, template (2), in the dialog box.
2b. The template is designed for the recommended minimum of 25 subgroups; however 35 are possible without changing the formulas. The
procedure is to copy the formulas to the additional subgroups. Then click on the template chart to get the chart icon. Select CHART
WIZARD and obtain step 1. Change the range to include additional rows for the appropriate columns. This activity is accomplished by
either changing the range in the dialog box or dragging the mouse and using the control key.
2c. The control limits and central line are automatically calculated and displayed with the plotted points as data are entered.
2d. The chart is designed for a maximum of 35 points. If more are desired, add additional ones with the appropriate formulas.
2e. It is sometimes necessary to adjust the scales to have a pleasing chart appearance.
2f. It is usually necessary to change the decimal point for different data.
2g. When space is available and it is desired, the chart can be located on the sheet with the data and then printed full size.
&Cc-Chart Instructions
Page &P of &N
Example Problem
ID NumberSubgroupcUCLLCL
MY1021712.765.640
MY1132612.765.640
MY1213612.765.640
MY1254312.765.640
MY13252012.765.640
MY1436812.765.640
MY1507612.765.640
MY1528112.765.640
MY1649012.765.640
MY16610512.765.640
MY172111412.765.640
MY18312312.765.640
MY18513112.765.640
MY19814312.765.640
MY20815212.765.640
MY22216712.765.640
MY23517512.765.640
MY24118712.765.640
MY25819212.765.640
MY25920812.765.640
MY26421012.765.640
MY26722412.765.640
MY278231412.765.640
MY28124412.765.640
MY28825512.765.640
26
27
28
29
30
31
32
33
34
35
Sum141
&Cc-Chart Example Problem
Page &P of &N
Example Problem
&A
Page &P
c
UCL
c-bar
LCL
Subgroup Number
Count of Nonconformities
c-Chart
Template
ID NumberSubgroupcUCLLCL
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
19000
20000
21000
22000
23000
24000
25000
26
27
28
29
30
31
32
33
34
35
Sum0
&Cc-Chart Template
Page &P of &N
Template
0000
0000
0000
0000
0000
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0000
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0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
&Cc-Chart Template
Page &P of &N
c
UCL
c-bar
LCL
Subgroup Number
Number of Nonconformities
c-Chart
Sheet6
&A
Page &P
Sheet7
&A
Page &P
Sheet8
&A
Page &P
Sheet9
&A
Page &P
Sheet10
&A
Page &P
Sheet11
&A
Page &P
Sheet12
&A
Page &P
Sheet13
&A
Page &P
Sheet14
&A
Page &P
Sheet15
&A
Page &P
Sheet16
&A
Page &P
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u ChartThe u chart is mathematically equivalent to the c chart.
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Example
Instructions
Instructions:
1. The next sheet is an example problem. It was created from the sheet called template. Select the cells at the top of the columns to see the
formulas.
2a. The following sheet, called template, should be copied before using the program. This activity is accomplished by selecting EDIT,
selecting MOVE OR COPY SHEET, selecting CREATE A COPY, and locating the new sheet called, template (2), in the dialog box.
2b. The template is designed for the recommended minimum of 25 subgroups; however 35 are possible without changing the formulas. The
procedure is to copy the formulas to the additional subgroups. Then click on the template chart to get the chart icon. Select CHART
WIZARD and obtain step 1. Change the range to include additional rows for the appropriate columns. This activity is accomplished by
either changing the range in the dialog box or dragging the mouse and using the control key.
2c. The control limits and central line are automatically calculated and displayed with the plotted points as data are entered.
2d. The chart is designed for a maximum of 35 points. If more are desired, add additional ones with the appropriate formulas.
2e. It is sometimes necessary to adjust the scales to have a pleasing chart appearance.
2f. It is usually necessary to change the decimal point for different data.
2g. When space is available and it is desired, the chart can be located on the sheet with the data and then printed full size.
&Cu-Chart Instructions
Page &P of &N
Example Problem
ID NumberSubgroupncuUCLu-BarLCL
30-Jan11101201.0911.511.200.89
31-Jan282941.1461.561.200.84
1-Feb396890.9271.541.200.87
2-Feb41151621.4091.511.200.89
3-Feb51081501.3891.521.200.88
4-Feb656821.4641.641.200.76
6-Feb71201431.1921.501.200.90
7-Feb8981341.3671.531.200.87
8-Feb9102970.9511.531.200.88
9-Feb101151451.2611.511.200.89
10-Feb11881281.4551.551.200.85
11-Feb1271831.1691.591.200.81
13-Feb13951201.2631.541.200.86
14-Feb141031161.1261.521.200.88
15-Feb151131271.1241.511.200.89
16-Feb1685921.0821.561.200.84
17-Feb171011401.3861.531.200.87
18-Feb1842601.4291.711.200.69
20-Feb19971211.2471.531.200.87
21-Feb20921081.1741.541.200.86
22-Feb211001311.3101.531.200.87
23-Feb221151191.0351.511.200.89
24-Feb2399930.9391.531.200.87
25-Feb2457881.5441.641.200.77
27-Feb25891071.2021.551.200.85
28-Feb261011051.0401.531.200.87
1-Mar271221431.1721.501.200.90
2-Mar281051321.2571.521.200.88
3-Mar29981001.0201.531.200.87
4-Mar3048601.2501.671.200.73
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Sum/u-bar.282333891.200
&Cu Chart Example Problem
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Example Problem
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&A
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Template
ID NumberSubgroupncuUCLu-BarLCL
10.0000.000.000.00
20.0000.000.000.00
30.0000.000.000.00
40.0000.000.000.00
50.0000.000.000.00
60.0000.000.000.00
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80.0000.000.000.00
90.0000.000.000.00
100.0000.000.000.00
110.0000.000.000.00
120.0000.000.000.00
130.0000.000.000.00
140.0000.000.000.00
150.0000.000.000.00
160.0000.000.000.00
170.0000.000.000.00
180.0000.000.000.00
190.0000.000.000.00
200.0000.000.000.00
210.0000.000.000.00
220.0000.000.000.00
230.0000.000.000.00
240.0000.000.000.00
250.0000.000.000.00
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&Cu Chart Template
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&A
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Instructions
Instructions:
1. The next sheet is an example problem. It was created from the sheet called template. Select the cells at the top of the columns to see the
formulas.
2a. The following sheet, called template, should be copied before using the program. This activity is accomplished by selecting EDIT,
selecting MOVE OR COPY SHEET, selecting CREATE A COPY, and locating the new sheet called, template (2), in the dialog box.
2b. The template is designed for the recommended minimum of 25 subgroups; however 35 are possible without changing the formulas. The
procedure is to copy the formulas to the additional subgroups. Then click on the template chart to get the chart icon. Select CHART
WIZARD and obtain step 1. Change the range to include additional rows for the appropriate columns. This activity is accomplished by
either changing the range in the dialog box or dragging the mouse and using the control key.
2c. The control limits and central line are automatically calculated and displayed with the plotted points as data are entered.
2d. The chart is designed for a maximum of 35 points. If more are desired, add additional ones with the appropriate formulas.
2e. It is sometimes necessary to adjust the scales to have a pleasing chart appearance.
2f. It is usually necessary to change the decimal point for different data.
2g. When space is available and it is desired, the chart can be located on the sheet with the data and then printed full size.
&Cu-Chart Instructions
Page &P of &N
Example Problem
ID NumberSubgroupncuUCLu-BarLCL
30-Jan11101201.0911.511.200.89
31-Jan282941.1461.561.200.84
1-Feb396890.9271.541.200.87
2-Feb41151621.4091.511.200.89
3-Feb51081501.3891.521.200.88
4-Feb656821.4641.641.200.76
6-Feb71201431.1921.501.200.90
7-Feb8981341.3671.531.200.87
8-Feb9102970.9511.531.200.88
9-Feb101151451.2611.511.200.89
10-Feb11881281.4551.551.200.85
11-Feb1271831.1691.591.200.81
13-Feb13951201.2631.541.200.86
14-Feb141031161.1261.521.200.88
15-Feb151131271.1241.511.200.89
16-Feb1685921.0821.561.200.84
17-Feb171011401.3861.531.200.87
18-Feb1842601.4291.711.200.69
20-Feb19971211.2471.531.200.87
21-Feb20921081.1741.541.200.86
22-Feb211001311.3101.531.200.87
23-Feb221151191.0351.511.200.89
24-Feb2399930.9391.531.200.87
25-Feb2457881.5441.641.200.77
27-Feb25891071.2021.551.200.85
28-Feb261011051.0401.531.200.87
1-Mar271221431.1721.501.200.90
2-Mar281051321.2571.521.200.88
3-Mar29981001.0201.531.200.87
4-Mar3048601.2501.671.200.73
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35
Sum/u-bar.282333891.200
&Cu Chart Example Problem
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Example Problem
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&A
Page &P
u
UCL
u-Bar
LCL
Subgroup Number
Count of nonconformities/Unit
u-Chart
Template
ID NumberSubgroupncuUCLu-BarLCL
10.0000.000.000.00
20.0000.000.000.00
30.0000.000.000.00
40.0000.000.000.00
50.0000.000.000.00
60.0000.000.000.00
70.0000.000.000.00
80.0000.000.000.00
90.0000.000.000.00
100.0000.000.000.00
110.0000.000.000.00
120.0000.000.000.00
130.0000.000.000.00
140.0000.000.000.00
150.0000.000.000.00
160.0000.000.000.00
170.0000.000.000.00
180.0000.000.000.00
190.0000.000.000.00
200.0000.000.000.00
210.0000.000.000.00
220.0000.000.000.00
230.0000.000.000.00
240.0000.000.000.00
250.0000.000.000.00
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&Cu Chart Template
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Template
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&A
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u-Bar
LCL
Subgroup Number
Count of nonconformities/Unit
u-Chart
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For January 30:
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Nonconformity Classification
Critical nonconformitiesIndicate hazardous or unsafe conditions.Major nonconformitiesFailureMinor nonconformities
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Control Charts for Variables vs. Charts for Attributes
Sometimes, the quality control engineer has a choice between variable control charts and attribute control charts.
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Advantages of attribute control chartsAllowing for quick summaries, that is, the engineer may simply classify products as acceptable or unacceptable, based on various quality criteria. Thus, attribute charts sometimes bypass the need for expensive, precise devices and time-consuming measurement procedures. More easily understood by managers unfamiliar with quality control procedures.
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Advantages of variable control chartsMore sensitive than attribute control charts.Therefore, variable control charts may alert us to quality problems before any actual "unacceptables" (as detected by the attribute chart) will occur. Montgomery (1985) calls the variable control charts leading indicators of trouble that will sound an alarm before the number of rejects (scrap) increases in the production process.
*Probability**Probability*
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