Chapter 6s

Chapter 6S Statistical Process Control (SPC) Statistical Quality Control (SQC) Management Management Science Science

CMJ SPKAL UMS-KAL

Lecture Outline  Define Quality/SQC Concepts  Control Charts   

Control Charts for Attributes Control Charts for Variables Control Chart Patterns

 Develop Control Charts  Process Capability- Process is in control 12-2

Introduction  Quality is a major issue in today’s organizations.  …………………………….., or quality management, tactics are used throughout the organization to assure deliverance of quality products or services.  …………………………………………… uses statistical and probability tools to help control processes and produce consistent goods and services. 12-3

Basics of Statistical Process Control  Statistical Process Control (SPC) 

…………………………… …………………………… …………………………….

UCL

 Sample 

…………………………… ……………………………..

LCL

 Control Charts 

…………………………… …………………………… …………………………… 12-4

Variability  Random

 Non-Random



……………. causes



……………… causes



………….. …… in a process



due to ……………… factors



can be ……………….. only through improvements in the ……………………..



can be ……………… through …………….. or …………………….

12-5

SPC in TQM  SPC 





…………… for identifying problems and make improvements contributes to the ………….. goal of continuous improvements Statistical technique used to ensure process is making product to ………………. It can also monitor, measure, and correct quality problems. 12-6

Quality Measures  …………………. 



a product characteristic that can be …………… with a ……………… response good – bad; yes - no

 ……………………… 



a product characteristic that is ……………… and can be ………………………. weight - length

12-7

Applying SPC to Service  Nature of defect is different in services  Service defect is a failure to meet customer requirements  Monitor times, customer satisfaction

12-8

Applying SPC to Service  Hospitals  timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts  Grocery stores  waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors  Airlines  flight delays, lost luggage and luggage handling, waiting time at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenance 12-9

Control Charts  A graph that establishes control limits of a process

 Types of charts 

Attributes

Thus, SPC involves taking



…………………

samples of the process



………………………..

output and plotting the averages on a control chart.  Control limits 



Variables 

…………………………



…………………………..

……………. and …………….. bands of a control chart 12-10

Process Control Chart Out of control Upper control limit Process average Lower control limit

1

2

3

4

5

6

7

8

9

10

Sample number 12-11

Normal Distribution

95% 99.74% -3σ

-2σ

-1σ

µ =0

1σ

2σ

3σ

12-12

A Process Is in Control If …

1. … no sample points outside limits 2. … most points near process average 3. … about equal number of points above and below centerline 4. … points appear randomly distributed

12-13

Control Chart Patterns Upper control chart limit

Target

Normal behavior. Lower control chart limit

One point out above. Investigate for cause.

One point out below. Investigate for cause. 12-14

Control Chart Patterns Upper control chart limit

Target

Two points near upper control. Investigate for cause. Lower control chart limit

Two points near lower control. Investigate for cause.

Run of 5 points above central line. Investigate for cause. 12-15

Control Chart Patterns Upper control limit

Target

Run of 5 points below central line. Investigate for cause.

Lower control limit

Trends in either Direction. Investigate for cause of progressive change.

Erratic behavior. Investigate.

12-16

Control Charts for Attributes

 p-charts  uses portion defective in a sample

 c-charts  uses number of defects in an item

12-17

p-Chart UCL = p + zσ LCL = p - zσ

p p

z = number of standard deviations from process average p = sample proportion defective; an estimate of process average σ p = standard deviation of sample proportion σ

p

=

p(1 - p) n 12-18

p-Chart Example SAMPLE

1 2 3 : : 20

NUMBER OF DEFECTIVES

PROPORTION DEFECTIVE

6 0 4 : : 18 200

.06 .00 .04 : : .18

20 samples of 100 pairs of jeans 12-19

p-Chart Example (Cont)

p=

total defectives = 200 / 20(100) = 0.10 total sample observations

UCL = p + z

p(1 - p) = 0.10 + 3 n

0.10(1 - 0.10) 100

UCL = 0.190 LCL = p - z

p(1 - p) = 0.10 - 3 n

0.10(1 - 0.10) 100

LCL = 0.010

12-20

0.20 UCL = 0.190

0.18

p-Chart Example (cont.)

Proportion defective

0.16 0.14 0.12 0.10

p = 0.10

0.08 0.06 0.04 0.02

LCL = 0.010 2

4

6

8 10 12 14 Sample number

16

18

20

12-21

c-Chart

UCL = c + zσ LCL = c - zσ

c c

σ

c

=

c

where c = number of defects per sample

12-22

c-Chart (cont.) Number of defects in 15 sample rooms SAMPLE

NUMBER OF DEFECTS

1 2 3

12 8 16

: :

: :

15

15 190

190 c= = 12.67 15 UCL = c + zσ c = 12.67 + 3 12.67 = 23.35 LCL = c + zσ c = 12.67 - 3 = 1.99

12.67 12-23

24 UCL = 23.35

c-Chart (cont.)

Number of defects

21 18

c = 12.67

15 12 9 6 LCL = 1.99

3

2

4

6

8

10

12

14

16

Sample number

12-24

Control Charts for Variables

 Mean chart ( x -Chart )  uses average of a sample

 Range chart ( R-Chart )  uses amount of dispersion in a sample

12-25

x-bar Chart

x1 + x2 + ... xk = x= k = = UCL = x + A2R LCL = x - A2R where = x = average of sample means

12-26

x-bar Chart Example OBSERVATIONS (SLIP- RING DIAMETER, CM) SAMPLE k

1

2

3

4

5

x

R

1 2 3 4 5 6 7 8 9 10

5.02 5.01 4.99 5.03 4.95 4.97 5.05 5.09 5.14 5.01

5.01 5.03 5.00 4.91 4.92 5.06 5.01 5.10 5.10 4.98

4.94 5.07 4.93 5.01 5.03 5.06 5.10 5.00 4.99 5.08

4.99 4.95 4.92 4.98 5.05 4.96 4.96 4.99 5.08 5.07

4.96 4.96 4.99 4.89 5.01 5.03 4.99 5.08 5.09 4.99

4.98 5.00 4.97 4.96 4.99 5.01 5.02 5.05 5.08 5.03

0.08 0.12 0.08 0.14 0.13 0.10 0.14 0.11 0.15 0.10

50.09

1.15

Example 15.4 12-27

Setting Control Limits for the X Chart Control Limits UCL x = x +A 2 R

LCL

x

=x −A 2 R

Sample Mean at Time i i= n

x ∑

xi =

From Table

i= 1

n

Sample Range at Time i

i

Ri =

i =n

∑R i =1

i

n

number of Samples 12-28

x- bar Chart Example (cont.) 50.09 = ∑x x= = = 5.01 cm 10 k = UCL = x + A2R = 5.01 + (0.58)(0.115) = 5.08 = LCL = x - A2R = 5.01 - (0.58)(0.115) = 4.94 Retrieve Factor Value A2 12-29

5.10 – 5.08 –

UCL = 5.08

5.06 –

Mean

5.04 –

x- bar Chart Example (cont.)

x= = 5.01

5.02 – 5.00 – 4.98 – 4.96 –

LCL = 4.94

4.94 – 4.92 – | 1

| 2

| 3

| | | | 4 5 6 7 Sample number

| 8

| 9

| 10

12-30

R- Chart UCL = D4R

LCL = D3R

∑R R= k where R = range of each sample k = number of samples 12-31

Setting Control Limits for the R Chart U C L

R

=D4 R

From Table L C L

R

=D3 R

i =n

R ∑

R i = i =1 n

i

Sample Range at Time i # Samples 12-32

R-Chart Example OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k

1

2

3

4

5

x

R

1 2 3 4 5 6 7 8 9 10

5.02 5.01 4.99 5.03 4.95 4.97 5.05 5.09 5.14 5.01

5.01 5.03 5.00 4.91 4.92 5.06 5.01 5.10 5.10 4.98

4.94 5.07 4.93 5.01 5.03 5.06 5.10 5.00 4.99 5.08

4.99 4.95 4.92 4.98 5.05 4.96 4.96 4.99 5.08 5.07

4.96 4.96 4.99 4.89 5.01 5.03 4.99 5.08 5.09 4.99

4.98 5.00 4.97 4.96 4.99 5.01 5.02 5.05 5.08 5.03

0.08 0.12 0.08 0.14 0.13 0.10 0.14 0.11 0.15 0.10

50.09

1.15

Example 15.3 12-33

R-Chart Example (cont.)

∑R 1.15 R= = = 0.115 k 10

UCL = D4R = 2.11(0.115) = 0.243 LCL = D3R = 0(0.115) = 0

Retrieve Factor Values D3 and D4

Example 15.3 12-34

R-Chart Example (cont.) 0.28 – 0.24 –

UCL = 0.243

Range

0.20 – 0.16 –

R = 0.115

0.12 – 0.08 – 0.04 – 0–

LCL = 0 | | | 1 2 3

| | | | 4 5 6 7 Sample number

| 8

| 9

| 10

12-35

Using x- bar and R-Charts Together

 Process average and process variability must be in control  It is possible for samples to have very narrow ranges, but their averages is beyond control limits  It is possible for sample averages to be in control, but ranges might be very large

12-36

Control Chart Patterns UCL

UCL LCL Sample observations consistently below the center line

LCL Sample observations consistently above the center line 12-37

Control Chart Patterns (cont.) UCL

UCL LCL Sample observations consistently increasing

LCL Sample observations consistently decreasing 12-38

Zones for Pattern Tests = 3 sigma = x + A2R

UCL Zone A

= 2 sigma = x + 2 (A2R) 3

Zone B = 1 sigma = x + 1 (A2R) 3

Zone C = x

Process average

Zone C

= 1 sigma = x - 1 (A2R) 3

Zone B = 2 sigma = x - 2 (A2R) 3

Zone A = 3 sigma = x - A2R

LCL | 1

| 2

| 3

| 4

| 5

| 6

| 7

| 8

| 9

| 10

| 11

| 12

| 13

Sample number

12-39

Control Chart Patterns

    

8 consecutive points on one side of the center line 8 consecutive points up or down across zones 14 points alternating up or down 2 out of 3 consecutive points in zone A but still inside the control limits 4 out of 5 consecutive points in zone A or B

12-40

Performing a Pattern Test SAMPLE 1 2 3 4 5 6 7 8 9 10

x

ABOVE/BELOW

UP/DOWN

ZONE

4.98 5.00 4.95 4.96 4.99 5.01 5.02 5.05 5.08 5.03

B B B B B — A A A A

— U D D U U U U U D

B C A A C C C B A B

12-41

Sample Size  Attribute charts require larger sample sizes  50 to 100 parts in a sample  Variable charts require smaller samples  2 to 10 parts in a sample

12-42