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UNIT 4 :UNIT 4 :CONTROL CHART FOR ATTRIBUTES

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Introduction

Attribute vs Variable Control Chart

Advantages & Disadvantages

Defectives vs Defect

P, np, C and U Charts

LOGOINTRODUCTIONINTRODUCTIONATTRIBUTE

The term attribute, as used in quality, refers to those quality characteristics that conform to specifications or do not conform to specifications.

Where measurements are not possible - - for example, visually inspected items such as color, missing parts, scratches, and damage.

Where measurements can be made but are not made because of time, cost, or need.

Attributes are used:

LOGOINTRODUCTIONINTRODUCTIONTwo basic types of attribute control charts:

1. Classification Charts2. Count Charts

Classification Charts deal with either the fraction of items or the number of

items in a series of subgroups that have a particular characteristics

p Chart used to control the fraction of items with the

characteristics.

np Chart serves the same function as the p chart except that it

is used to control the number rather than the fraction of items with the characteristics and is used only with constant subgroup sizes.

LOGOINTRODUCTIONINTRODUCTION

Count Charts deal with the number of times a particular characteristic

appears in so me given area of opportunity.

c Chart used to control the number of times a particular

characteristic appears in a constant area of opportunity.

µ Chart serves the same basic function as a c chart, but is used

when the area of opportunity changes from subgroup to subgroup.

LOGOATTRIBUTE VS VARIABLE

Attribute Variable

Used for product characteristics that can be evaluated with a discrete response (pass/fail, yes/no, good/bad, number defective)

Used when the quality characteristic can be measured and expressed in numbers

less costly when it comes to collecting data

must be able to measure the quality characteristics in numbers

can plot multiple characteristics on one chart

may be impractical and uneconomical

loss of information vs variable chart

LOGOADVANTAGES & DISADVANTAGES

Advantages DisadvantagesSome quality characteristics can only be viewed as a attribute

Attributes don’t measure the degree to which specifications are met or not met

Quality characteristic may be measurable as a variable but an attribute is used for time, cost or convenience

Doesn’t provide much information on cause

Combination of variables can be measured as an attribute rather than use a multivariate chart

Variable chart can indicate potential changes which allow preventive actions

loss of information vs variable chart

Larger sample size required

LOGODEFECT VS DEFECTIVES

‘Defect’ – a single nonconforming quality characteristic.

‘Defective’ – items having one or more defects.

LOGO

p, np - Chart

p and np charts deal with nonconforming P is fraction nonconforming np is total nonconforming

Charts based on Binomial distribution.Sample size must be large enough (example p=2%)Definition of a nonconformity.Probability the same from item to item.

DEFECT VS DEFECTIVES

LOGO

c, u - Charts

c and u charts deal with nonconformities. c Chart – total number of nonconformities u Chart – nonconformities per unit

Charts based on Poisson distribution.Sample size, constant probabilities.

DEFECT VS DEFECTIVES

LOGOCONSTRUCTION PROCEDUREThe following procedure is used to construct all type of attribute charts

Step 1Preliminary samples are taken and inspected

Step 2When the process achieves the control state, the required quality characteristics is measured and recorded in the prescribed data sheet

Step 3Trial control limits are calculated using appropriate formulae. Each chart is suitable for different applications

LOGOCONSTRUCTION PROCEDUREStep 4Draw the control chart

Step 5Draw the control limits for computed values

Let X – axis Be the sample number

Let Y – axis Be the fraction defectives for the p–chartsBe the number of defectives for the np–chartsBe the number of non-conformities for the c–chart Be the number of non-conformities per unit for the u – chart

UCL (Dotted line)

Centre Line, CL (Continuous line)

LCL (Dotted line)

LOGOCONSTRUCTION PROCEDUREStep 6Plot all the measured points (i.e.,past data) on the appropriate charts. Connect successive points by straight line segments.

Step 7If all the points fall within the trial control limits, accept the trial control limits for present and future references.

Step 8If there is no systematic behaviour (i.e.,it implies random pattern), it shown that the process was in control in the past, therefore, the trial control limits are suitable for controlling current and future production.

LOGOCONSTRUCTION PROCEDURE

Revised control limits:

Step 9If one or more points fall outside the control limits, try to find the causes and eliminate these points to the calculation of the revised control limits.

Step 10Draw the revised control limits on the previously draw chart itself.

LOGOCONSTRUCTION PROCEDUREStep 11If the points other than the eliminated points fall within the revised control limits, accept the revised control limits for present and future use.

Step 12If one or more points other than the removed points fall outside the revised control limits, repeat the process as before.

LOGOCONSTRUCTION PROCEDURE

TYPES OF ATTRIBUTE CHARTS ARE :

TYPE

p – chart chart for fraction rejected

np – chart chart for number of defective

c – chart chart for non-conformities

u - chart chart for non-conformities per unit

LOGOP CHART FORMULA

n

pppUCLp

)1(3

n

pppLCLp

)1(3

inspectednumberTotal

defectivesofnumberTotalpCLLineCentre p ,

The centre line and upper and lower control limits for the P charts are :

LOGOP CHART EXAMPLEProblem : (constant sample size)The following table gives the result of inspection of 50 items per day for 20 days. Construct the fraction defectives or percent defectives chart and give inference about the process.

Day No. of defectives

1 4

2 0

3 3

4 2

5 3

6 5

7 1

8 2

9 2

10 0

Day No. of defectives

11 3

12 4

13 2

14 5

15 1

16 0

17 4

18 4

19 5

20 2

LOGOP CHART EXAMPLESolution : (constant sample size)

052.01000

52,

inspectednumberTotal

defectivesofnumberTotalppCLLineCentre

50)052.01(052.0

3052.0)1(

3

n

ppp

pUCL

1462.00942.0052.0

50)052.01(052.0

3052.0)1(

3

n

ppp

pLCL

00422.00942.0052.0

LOGOP CHART EXAMPLE

Inference :•All the sample points fall within the control limit and pattern of variation shows the random pattern.•The process is in control.•This limits can be used for future references.

LOGOP CHART EXAMPLEProblem : (variable sample size)Construct the fraction defectives or percent defectives chart and give inference about the process.

Day Sample size

No. of defectives

1 200 4

2 200 2

3 300 4

4 300 5

5 300 3

6 300 3

7 250 1

8 250 2

9 250 2

10 250 4

Day Sample size

No. of defectives

11 250 2

12 250 5

13 250 4

14 250 5

15 250 2

16 200 0

17 200 1

18 200 3

19 200 1

20 200 3

LOGOP CHART EXAMPLE

Samples n number of defective p UCL CL LCL

1 200 4 0.020 0.080 0.0115 -0.05644

2 200 2 0.010 0.080 0.0115 -0.05644

3 300 4 0.013 0.067 0.0115 -0.04397

4 300 5 0.017 0.067 0.0115 -0.04397

5 300 3 0.010 0.067 0.0115 -0.04397

6 300 3 0.010 0.067 0.0115 -0.04397

7 250 1 0.004 0.072 0.0115 -0.04926

8 250 2 0.008 0.072 0.0115 -0.04926

9 250 2 0.008 0.072 0.0115 -0.04926

10 250 4 0.016 0.072 0.0115 -0.04926

11 250 2 0.008 0.072 0.0115 -0.04926

12 250 5 0.020 0.072 0.0115 -0.04926

13 250 4 0.016 0.072 0.0115 -0.04926

14 250 5 0.020 0.072 0.0115 -0.04926

15 250 2 0.008 0.072 0.0115 -0.04926

16 200 0 0.000 0.080 0.0115 -0.05644

17 200 1 0.005 0.080 0.0115 -0.05644

18 200 3 0.015 0.080 0.0115 -0.05644

19 200 1 0.005 0.080 0.0115 -0.05644

20 200 3 0.015 0.080 0.0115 -0.05644

Total 4850 56 0.228

Solution : (variable sample size)

LOGOP CHART EXAMPLE

Inference :•All the sample points fall within the control limit and pattern of variation shows the random pattern.•The process is in control.•This limits can be used for future references.

LOGOnp CHART FORMULA

)1(3 ppnpnUCLnp

)1(3 ppnpnLCLnp

samplesofNumber

defectivesofnumberTotalpnCLLineCentre np ,

The centre line and upper and lower control limits for the np charts are :

LOGOnp CHART EXAMPLEProblem :The following table gives the result of inspection of 100 items per day for 25 days. Construct the fraction defectives or percent defectives chart and give inference about the process.

Sample n Number of defective1 100 22 100 03 100 34 100 05 100 06 100 07 100 18 100 19 100 1

10 100 011 100 012 100 213 100 114 100 315 100 116 100 117 100 218 100 119 100 120 100 021 100 322 100 023 100 124 100 025 100 1

LOGOnp CHART EXAMPLESolution :

0.12525

.,

samplesofNo

defectivesofnumberTotalpnnpCLLineCentre

)01.01(0.130.1)1(3 ppnpnnp

UCL

985.3985.20.1

)01.01(0.130.1)1(3 ppnpnnp

LCL

0985.1985.20.1

01.02500

25 inspectednumberTotal

defectivesofnumberTotalp

LOGOnp CHART EXAMPLE

Inference :•All the sample points fall within the control limit and pattern of variation shows the random pattern.•The process is in control.•This limits can be used for future references.

LOGOC CHART FORMULA

ccUCLc 3

ccLCLc 3

samplesofNumber

defectsofnumberTotalcCLc

The centre line and upper and lower control limits for the c charts are :

LOGOC CHART EXAMPLEProblem :In a copper foil laminations process for every 500 feet of foil laminated, one square foot of the laminated copper foil is examned for visual defect such as unever lamination, scrath, etc. The data collected are shown in the table below. Calculate the control limit and plot the c-chart.

Time Number of Defect100 5200 3300 2400 6500 6600 7700 3800 3900 6

1000 71100 71200 91300 71400 51500 31600 121700 61800 101900 72000 22100 62200 82300 02400 7100 4200 3

LOGOnp CHART EXAMPLESolution :

54.526

144.

, samplesofNo

defectsofnumberTotalccCLLineCentre

54.5354.53 ccc

UCL

60.1206.754.5

052.106.754.5

54.5354.53 ccc

LCL

LOGOC CHART EXAMPLE

Inference :•All the sample points fall within the control limit and pattern of variation shows the random pattern.•The process is in control.•This limits can be used for future references.

LOGOU CHART FORMULA

n

uuUCLu 3

n

uuLCLu 3

n

cuCLLineCentre u ,

The centre line and upper and lower control limits for the u charts are :

LOGOU CHART EXAMPLEProblem :A radio manufacturer wishes to use SQC charts for the detection of non-conformities per unit on the final assembly line. The sample size is finalised as 10 radios. The data collected are shown in the table. Calculate the control limit and plot the u-chart.

Sample number

Number of non-conformities

1 182 203 104 115 156 107 148 139 18

10 1211 1912 2013 1814 1415 1716 2017 2218 1019 1420 12

LOGOU CHART EXAMPLESolution :

35.1520

307.

samplesofNo

defectsofnumberTotalc

10

54.1354.13

n

uu

uUCL

72.218.154.1

36.018.154.1

53.110

35.15,

n

cuuCLLineCentre

10

54.1354.13

n

uu

uLCL

LOGOU CHART EXAMPLESample number

Sample size

Number of non-conformities (c)

Number of non-conformities per unit (u)

1 10 18 1.82 10 20 2.03 10 10 1.04 10 11 1.15 10 15 1.56 10 10 1.07 10 14 1.48 10 13 1.39 10 18 1.8

10 10 12 1.211 10 19 1.912 10 20 2.013 10 18 1.814 10 14 1.415 10 17 1.716 10 20 2.017 10 22 2.218 10 10 1.019 10 14 1.420 10 12 1.2

LOGOU CHART EXAMPLE

Inference :•All the sample points fall within the control limit and pattern of variation shows the random pattern.•The process is in control.•This limits can be used for future references.

LOGOCONCLUSIONControl Chart Selection

Quality Characteristic

variable attribute

n>1?

n>=10 or computer?

x and MRno

yes

x and s

x and Rno

yes

defective defect

constant sample size?

p-chart withvariable samplesize

no

p ornp

yes constantsampling unit?

c u

yes no

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