Spc For Manufacturing

SPC ƒ SPC is a method to operate process efficiently using statistical methods. ƒ To identify sources of variation. ƒ Applicable when mistake proofing cannot be done . ƒ SPC uses control charts to monitor the process. ƒ SPC is a monitoring Instrument.

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VARIATION

Random ¾ Natural for the process ¾ Predictable ¾ Occurs randomly over time ¾ Also called common cause variation ¾ Generally process remains in control

Non- Random ¾ Not a part of natural process. ¾ Unexpected , Sporadic variation ¾ result of some specific assignable cause ¾ Also called special called variation ¾ Process go out of control

Control charts display the total variation in the process so it can be monitored and kept in control (within its operating capability) 2

Population and Sample Statistics Population Statistics

Sample mean (X-bar)

Population mean (µ)

µ=

Xi ∑ X=

∑ xi N

n

Population variance (σ2)

σ

2

(x − µ ) ∑ =

Sample Statistics

2

i

N

Estimate for variance (s2)

s2 =

2 ( x − x ) ∑ i

n −1

Population Std Deviation(σ)

Estimate for Std Deviation(s)

σ = (σ 2 )

s = (s 2 ) 3

Introduction to Control Charts PFD

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TYPES OF CONTROL CHARTS DATA TYPE Quantitative

Qualitative

Variable’s

Attribute

Continuous

Subgroup size

N=1 IMR Chart N=2~9 XR Chart N=>9 XS Chart

Defect

Subgroup size

Fixed C Chart

Variable U Chart

Defective

Subgroup size Fixed NP Chart

Variable P Chart

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CONTROL CHARTS

9 Control charts are designed to prevent defect occurrence in advance & control process variation efficiently by detecting and addressing the occurrence of assignable cause in the process

Control chart consists of Center line CL= Sample mean (m) Upper Control limit = m+3σ ( Control limits are at a distance of 3σ from mean) Lower control limit = m-3σ

Control chart deals with analysis of process , process control & to judge if the product under study is acceptable or not

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DESIGNING CONTROL CHART

Suppose we have a process that we assume the true process mean is µ = 74 and the process standard deviation is σ = 0.01. Samples of size 5 are taken giving a standard deviation of the sample average, is

σ 0.01 σx = = = 0.0045 n 5

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DESIGNING CONTROL CHART

• Control limits can be set at 3 standard deviations from the mean in both directions. • “3-Sigma Control Limits” UCL = 74 + 3(0.0045) = 74.0135 CL= 74 LCL = 74 - 3(0.0045) = 73.9865

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Introduction to Control Charts Rational Subgroups Constructing Rational Subgroups • Select consecutive units of production. – Provides a “snapshot” of the process. – Good at detecting process shifts. • Select a random sample over the entire sampling interval. – Good at detecting if a mean has shifted – out-of-control and then back in-control. 9

WHAT DO WE CHECK IN THE CHARTS

The Automotive Industry Action Group (AIAG) suggests using the following guidelines to test for special causes: ■ Test 1: 1 point > 3 standard deviations from center line ■ Test 2: 9 points in a row on the same side of center line ■ Test 3: 6 points in a row, all increasing or all decreasing Also additional to these tests we can also check ¾ Test 4: 14 points in a row ,alternating up & down ¾ Test 5: 2 out of 3 points > 2 standard deviation from center line (same side). Too much Variations ¾ Test 6: 4 out of 5 points > 1 standard deviation from center line (same side).Too much Variations ¾ Test 7 : 15 points in a row within 1 standard deviation of center line (either side).Measurement error ¾ Test 8 : 8 points in a row > 1 standard deviations from center line (either side). Mixture of data

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IMR CHART (SUB GROUP SIZE=1) I-MR Chart 1) IMR charts is used when data is slow , that is time range & Collection is pretty large. 2) There is one value per subgroup. 3) There is one between variation and no within variation. 4) Range between adjacent data points (moving range) is used to control process standard deviation.

EXAMPLE ¾ Torque is measured daily once , in first half hour and recorded . Draw a suitable control chart to find if it is in control or not

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ANALYSIS OF IMR CHART

I-MR Chart of Torque 7.2 Individual V alue

U C L=7.072 6.9 6.6

_ X=6.431

6.3 6.0 LC L=5.790 07/03/2005

07/06/2005

07/09/2005

07/12/2005

07/15/2005

07/18/2005

07/21/2005

07/24/2005

07/27/2005

07/30/2005

Date

M oving Range

0.8

U C L=0.7875

0.6 0.4 __ M R=0.2410

0.2 0.0

LC L=0 07/03/2005

07/06/2005

07/09/2005

07/12/2005

07/15/2005

07/18/2005

07/21/2005

07/24/2005

07/27/2005

07/30/2005

Date

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X- R CONTROL CHART (1<Sub group Size<5)

¾X chart is used to control process mean ¾R chart uses the differences between the maximum & minimum of the observed values in sample , to control process variation ¾ X-R chart is useful to control both mean and variation at the same time

Example Data collected for 5 m/c for a part reading over 20 hrs find the behavior of the process for the

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ANALYSIS OF X Bar R CHART

MC process variation

Sample M ean

9.00

U C L=8.9644

8.85 _ _ X=8.636

8.70 8.55 8.40

LC L=8.3076 2

4

6

8

10 Sample

12

14

16

18

20

U C L=1.204

Sample Range

1.2 0.9

_ R=0.569

0.6 0.3 0.0

LC L=0 2

4

6

8

10 Sample

12

14

16

18

20

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X- R CONTROL CHART CONSTANTS

SAMPLE SIZE A2

D3

D4

1.880

0

3

1.023

0

4

0.729

0

5

0.577

0

6

0.483

7

0.149

0.076

1.924

8

0.373

0.136

1.864

9

0.337

0.184

10

0.308

0.223

0

2

3.267

d2

UCL (R)= R

D4

LCL (R)= R

D3

2.574 2.282 1.023

UCL(X)= X

A2

R

LCL(X)= X

A2

R

2.004

1.816 1.777

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RESULT X bar R

R Chart – Asses the process variation is in control. Consists of plotted points for subgroup ranges . Four tests are conducted for special causes to detect points beyond the control limits and specific patterns in data. A failed point(marked in RED) indicates that there is non random pattern (special cause variation).

In the given data:None of the subgroup ranges are outside the control limits The points inside the limits display a random pattern. There is no lack of control in variation . 16

RESULT X bar R

X Chart A failed point indicates that there is a Non-random pattern due to special cause variation. The R chart must be in control before X bar is interpreted. Results are shown in the session window. If the process is stable, how capable is it can be determined by capability calculation.

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COMPARISON BETWEEN X bar R & X bar S

BOTH S CHARTS & R CHARTS - Measure Subgroup variability. -Give the estimate of the process standard deviation & Control limits. S Represent Spread Calculates Accuracy Sensitivity to Variation Application

Using Standard Deviation Uses complete data

R Using Range Uses Max & Min Values

Better Greater For higher subgroup size( >5 ),high rate of production ,data collection is quick & in expensive or when increased sensitivity is desired.

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CONTROL CHART FOR DEFECTIVES P Chart’s ¾P Charts are used for defectives when SUB GROUP size is Variable. Variable. ¾ Data follows binomial distribution. P(n, N) = pn.(1 - p)N-n.NCn ¾ Can be used for supplier lot quality on the basis of delivery. ¾ The P chart consists of the following: ¾Plotted points, which represent the proportion of defectives. ¾Center line (green), which is the average proportion defective ¾Control limits (red), which are located 3 s above and below the center line and provide a visual means for when the process is out of control. The control limits are either fixed or varied, depending on your data and choices: ¾When your sample sizes are the same or when you choose to use an average sample size, then the control limits will be fixed. In this case, tests for special special causes may be conducted.

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P Chart of Number of Defectives 0.018 UCL=0.01627

0.016

Proportion

0.014

Sample size is different

0.012 _ P=0.00968

0.010 0.008 0.006 0.004

LCL=0.00310

0.002 1

2

3

4

5 6 Sample

7

8

9

10

Tests performed with unequal sample sizes 20

P Chart result analysis

¾When your sample sizes vary, then the control limits will vary. In this case, tests for special causes cannot be conducted. You should examine the P chart for points outside the control limits and trends or other nonrandom patterns. ¾ Four tests are conducted for special causes by Minitab. ¾ Plotted points representing the PROPRTION OF DEFECTIVES. ¾ Center line (green) , which is the average proportion defective. ¾ Control limit (red) either fixed or varied , depending on data. ¾ P Chart for the given data shows process in control.

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NP CHART FOR DEFECTIVES (SUB GROUP SIZE SAME)

¾Use NP charts to examine the number of defectives in each sample and determine whether or not the process is in control. The NP chart consists of the following: ¾ Plotted points, which represent the number of defectives for each sample ¾ Center line (green), which is the average number of defectives ¾ Control limits (red), which are located 3 s above and below the center line and provide a visual means for assessing when to take action on the process. Example: For every lot of 100 Bush manufactured ,13 are randomly inspected inspected & reported for defectives .Find the data is in control.

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GRAPH NP Chart for 13 randomly slected subgroup size 9 1

8

UCL=7.709

Sample Count

7 6 5 4

__ NP=3.1

3 2 1 0

LCL=0 3

6

9

12

15 18 Sample

21

24

27

30

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Test Results for NP Chart of No. of defectives

TEST 1. One point more than 3.00 standard deviations from center line. Test Failed at points:

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NP chart should not be used for variable sample size because the control limits & center line changes when sample size changes making NP chart difficult to interpret.

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CONTROL CHART FOR DEFECT ( C CHART) SUB GROUP SIZE IS FIXED ¾Used to find defects as DPU (defects / unit) of the controlled process. ¾ Inspection unit must be fixed. ¾Inspection units can more than one if the data is not classified by the type of defect. Example: Following is the defect quantity per lot of bush manufactured , check the data is in control or not

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GRAPH C Chart of No. of defects 9 1

8

1 point outside the control limit UCL=7.204

Sample Count

7 6 5 4 3

_ C=2.48

2 1 0

LCL=0 5

10

15

20

25 30 Lot_no.

35

40

45

50

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C Chart of No. of defects

Test Results for C Chart of No. of defects TEST 1. One point more than 3.00 standard deviations from center line. Test Failed at points: 13 * WARNING * If graph is updated with new data, the results longer be correct.

above may no

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CONTROL CHART FOR DEFECT ( U CHART) SUB GROUP SIZE IS VARIABLE ¾Used to asses the number of defects per unit of measurement to determine if the process is in control. ¾ If the samples are of same size or when the average sample size is taken , Control limits will be FIXED. ¾ when the sample size vary , Control limits vary,Tests for special causes cannot be conducted.

EXAMPLE Find the given data is in control or not , sample size is not fixed.

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GRAPH

U Chart of No. of Defects 4

Sample Count Per Unit

1

UCL=3.337 3

2 _ U=1.5 1

0

LCL=0 2

4

6

8

10 12 Week_No.

14

16

18

20

Tests performed with unequal sample sizes

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Results for: U_defects

TEST 1. One point more than 3.00 standard deviations from center line. Test Failed at points:

1

* WARNING * If graph is updated with new data, the results above may no * longer be correct.

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RUN CHART (Test for randomness of Data) Run charts are plotted to find special patterns in data : 1)

Mixtures

2)

Clusters

3)

Trends

4)

Oscillations

Create a Run chart from the same data in which U charts are prepared

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GRAPH ANALYSIS Run Chart of No. of Defects 14

No. of Defects

12 10 8 6 4 2 0 2

4

Number of runs about median: Expected number of runs: Longest run about median: Approx P-Value for Clustering: Approx P-Value for Mixtures:

6 9 9.21053 5 0.45379 0.54621

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10 Sample

12

Number of runs up or down: Expected number of runs: Longest run up or down: Approx P-Value for Trends: Approx P-Value for Oscillation:

14

16

18

12 12.33333 2 0.42438 0.57562

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A normal pattern for a process in control is one of randomness. If only common causes of variation exist in your process, the data will exhibit random behavior. Run Chart provides two tests for randomness: ·Based on the number of runs about the median. ·Based on the number of runs up or down. Test for Randomness Number of runs about the

Condition More runs observed than

median

Indication Mixed data from two expected populations

Fewer runs observed than

Clustering of data

expected Number of runs up or down varies

More runs observed than Fewer runs observed than

Oscillation - data Trending of data

expected Oscillation: It suggests that process is not in a controlled state(depends upon P value). Trends:

Trends may warn that a process is about to go out of control, and may be due to such factors as worn tool, Change in operator etc.

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