topic 4- control chart for attributes

Control Chart for Attributes

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,.

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

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.

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.

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).

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.

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.

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.

Select the quality characteristicsThe quality characteristic?A single quality characteristicA group of quality characteristicsA partAn entire product, orA number of products.

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.

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.

Calculate the trial central line and control limitsThe formula:

= average of p for many subgroups

n = number inspected in a subgroup

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

p Chartp-barLCLUCLSubgroupp5 10 15 20 2500.010.020.030.040.053

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.

Centerline (p) = 183/3000 = 0.061

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.

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 =

Using Average Subgroup Size: An Example

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.

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

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Sum/np-bar1315.24

&Cnp-Chart Example ProblemCh. 7, Ex. 2

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Example Problem

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np

UCL

np-bar

LCL

Subgroup Number

Number Nonconforming

np-Chart

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10.000.0

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&Cnp-Chart Template

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np

UCL

np-bar

LCL

Subgroup Number


np-Chart

Instructions

Instructions:


formulas.












&Cnp-Chart Instructions

Page &P of &N

Example Problem


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

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Sum/np-bar1315.24

&Cnp-Chart Example ProblemCh. 7, Ex. 2

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&Cnp-Chart Template

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Template

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np

UCL

np-bar

LCL

Subgroup Number


np-Chart

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

Example

Instructions

Instructions:


formulas.

2a. The following sheet, called template, should be copied before using the program. This activity is accomplished selecting on EDIT,











&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

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Sum141

&Cc-Chart Example Problem

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Example Problem

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c-bar

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c-Chart

Template


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&Cc-Chart Template

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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

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Sheet7

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Sheet11

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Sheet12

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Sheet13

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Sheet14

&A

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Sheet15

&A

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Sheet16

&A

Page &P

Instructions

Instructions:


formulas.













Page &P of &N

Example Problem


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

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Sum141


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Example Problem

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c

UCL

c-bar

LCL

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c-Chart

Template


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&Cc-Chart Template

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Template

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&Cc-Chart Template

Page &P of &N

c

UCL

c-bar

LCL

Subgroup Number


c-Chart

Sheet6

&A

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&A

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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


c-Chart

Instructions

Instructions:


formulas.













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

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Sum141


Page &P of &N

Example Problem

&A

Page &P

c

UCL

c-bar

LCL

Subgroup Number


c-Chart

Template

ID NumberSubgroupcUCLLCL

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&Cc-Chart Template

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Template

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&Cc-Chart Template

Page &P of &N

c

UCL

c-bar

LCL

Subgroup Number


c-Chart

Sheet6

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u ChartThe u chart is mathematically equivalent to the c chart.

Example

Instructions

Instructions:


formulas.












&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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Page &P

u

UCL

u-Bar

LCL

Subgroup Number

Count of nonconformities/Unit

u-Chart

Template


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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Sum/u-bar000.000

&Cu Chart Template

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Template

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u

UCL

u-Bar

LCL

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u-Chart

Instructions

Instructions:


formulas.












&Cu-Chart Instructions

Page &P of &N

Example Problem


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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For January 30:

Nonconformity Classification

Critical nonconformitiesIndicate hazardous or unsafe conditions.Major nonconformitiesFailureMinor nonconformities

Control Charts for Variables vs. Charts for Attributes

Sometimes, the quality control engineer has a choice between variable control charts and attribute control charts.

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.

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*

topic 4- control chart for attributes

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