Statistical Process Control - PowerPoint Presentation

Slide1

Statistical Process Control

Operations Management

Dr.

Ron

LembkeSlide2

Designed Size

10 11 12 13 14 15 16 17 18 19 20Slide3

Natural Variation

14.5 14.6 14.7 14.8 14.9 15.0 15.1 15.2 15.3

15.4Slide4

Theoretical Basis of Control Charts

95.5% of all



X fall within ± 2



Properties of normal distributionSlide5

Theoretical Basis of Control Charts

Properties of normal distribution

99.7% of all



X fall within ± 3

Slide6

Skewness

Lack of symmetry

Pearson’s coefficient of skewness:

Skewness = 0

Negative Skew < 0

Positive Skew > 0Slide7

Kurtosis

Amount of peakedness or flatness

Kurtosis < 0

Kurtosis > 0

Kurtosis = 0Slide8

Heteroskedasticity

Sub-groups with different variancesSlide9

Design Tolerances

Design tolerance:

Determined by users’ needs

USL -- Upper Specification Limit

LSL -- Lower Specification LimitEg: specified size +/- 0.005 inchesNo connection between tolerance and 

completely unrelated to natural variation.Slide10

Process Capability

LSL

USL

LSL

USL

Capable

LSL

USL

LSL

USL

Not Capable

Slide11

Process Capability

Specs: 1.5 +/- 0.01

Mean: 1.505 Std. Dev. = 0.002

Are we in trouble?Slide12

Process Capability

Specs: 1.5 +/- 0.01

LSL

= 1.5 – 0.01 = 1.49

USL = 1.5 + 0.01 = 1.51Mean: 1.505 Std. Dev. = 0.002LCL = 1.505 - 3*0.002 = 1.499UCL = 1.505 + 0.006 = 1.511

1.499

1.51

1.49

1.511

Process

SpecsSlide13

Capability Index

Capability Index (

C

p) will tell the position of the control limits relative to the design specifications.C

p>= 1.0, process is capableCp< 1.0, process is not capableSlide14

Process Capability, Cp

Tells how well parts produced fit into specs

Process

Specs

3



3



LSL

USLSlide15

Process Capability

Tells how well parts produced fit into specs

For our example:

C

p

=0.02/0.012 = 1.667 1.667>1.0 Process not capableSlide16

Packaged Goods

What are the Tolerance Levels?

What we have to do to measure capability?

What are the sources of variability?Slide17

Production Process

Make Candy

Package

Put in big bags

Make Candy

Make Candy

Make Candy

Make Candy

Make Candy

Mix

Mix %

Candy irregularity

Wrong wt.

Wrong wt.Slide18

Processes Involved

Candy Manufacturing:

Are M&Ms uniform size & weight?

Should be easier with plain than peanut

Percentage of broken items (probably from printing)Mixing: Is proper color mix in each bag?Individual packages:Are same # put in each package?

Is same weight put in each package?Large bags:Are same number of packages put in each bag?Is same weight put in each bag?Slide19

Weighing Package and all candies

Before placing candy on scale, press “ON/TARE” button

Wait for 0.00 to appear

If it doesn’t say “g”, press Cal/Mode button a few times

Write weight down on formSlide20

Candy colors

Write Name on form

Write weight on form

Write Package # on form

Count # of each color and write on formCount total # of candies and write on form

(Advanced only): Eat candiesTurn in forms and complete wrappersSlide21
Slide22

Peanut Candy Weights

Avg. 2.18, stdv 0.242, c.v. = 0.111Slide23

Plain Candy Weights

Avg 0.858, StDev 0.035, C.V. 0.0413 Slide24

Peanut Color Mix

website

Brown 17.7% 20%

Yellow 8.2% 20%Red 9.5% 20%

Blue 15.4% 20%Orange 26.4% 10%Green 22.7% 10%Slide25

Class website

Brown 12.1% 30%

Yellow 14.7% 20%

Red 11.4% 20%

Blue 19.5% 10%Orange 21.2% 10%Green 21.2% 10%

Plain Color MixSlide26

So who cares?

Dept. of Commerce

National Institutes of Standards & Technology

NIST Handbook 133Fair Packaging and Labeling ActSlide27

Acceptable?Slide28
Slide29

Package Weight

“Not Labeled for Individual Retail Sale”

If individual is 18g

MAV is 10% = 1.8gNothing can be below 18g – 1.8g = 16.2g Slide30

Goal of Control Charts

See if process is “in control”

Process should show random values

No trends or unlikely patterns

Visual representation much easier to interpretTables of data – any patterns?Spot trends, unlikely patterns easilySlide31

NFL Control Chart?Slide32

Control Charts

UCL

LCL

avg

Values

Sample NumberSlide33

Definitions of Out of Control

No points outside control limits

Same number above & below center line

Points seem to fall randomly above and below center line

Most are near the center line, only a few are close to control limits8 Consecutive pts on one side of centerline

2 of 3 points in outer third4 of 5 in outer two-thirds regionSlide34

Control Charts

Normal

Too Low

Too high

5 above, or below

Run of 5

Extreme variabilitySlide35

Control

Charts

UCL

LCL

avg

1

σ

2

σ

2

σ

1

σSlide36

Control Charts

2 out of 3 in the outer thirdSlide37

Out of Control Point?

Is there an “assignable cause?”

Or day-to-day variability?

If not usual variability, GET IT OUT

Remove data point from data set, and recalculate control limitsIf it is regular, day-to-day variability, LEAVE IT IN

Include it when calculating control limitsSlide38

Attributes vs. Variables

Attributes:

Good / bad, works / doesn’t

count % bad (P chart)

count # defects / item (C chart)Variables:measure length, weight, temperature (x-bar chart)measure variability in length (R chart)Slide39

NormalitySlide40

R Chart

Type of variables control chart

Interval or ratio scaled numerical data

Shows sample ranges over time

Difference between smallest & largest values in inspection sampleMonitors variability in processExample: Weigh samples of coffee & compute ranges of samples; PlotSlide41

You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on

5

deliveries per day. Is the

process in control

?Hotel ExampleSlide42

Hotel Data

Day

Delivery Time

1 7.30 4.20 6.10 3.45 5.55 2 4.60 8.70 7.60 4.43 7.62 3 5.98 2.92 6.20 4.20 5.10

4 7.20 5.10 5.19 6.80 4.21 5 4.00 4.50 5.50 1.89 4.46 6 10.10 8.10 6.50 5.06 6.94 7 6.77 5.08 5.90 6.90 9.30Slide43

Mean and Range - Hotel

Data

Sample

Day

Delivery Time Mean Range

1 7.30 4.20 6.10 3.45 5.55 5.32

7.30 + 4.20 + 6.10 + 3.45 + 5.55

5

Sample Mean = Slide44

R &



X

Chart Hotel Data

Sample

Day Delivery Time

Mean Range 1 7.30 4.20 6.10 3.45 5.55 5.32 3.85

7.30 - 3.45

Sample Range =

Largest

SmallestSlide45

Hotel Data – Mean and Range

Sample

Day

Delivery Time Mean Range

1 7.30 4.20 6.10 3.45 5.55 5.32 3.85 2 4.60 8.70 7.60 4.43 7.62 6.59 4.27 3 5.98 2.92 6.20 4.20 5.10 4.88 3.28

4 7.20 5.10 5.19 6.80 4.21 5.70 2.99 5 4.00 4.50 5.50 1.89 4.46 4.07 3.61 6 10.10 8.10 6.50 5.06 6.94 7.34 5.04 7 6.77 5.08 5.90 6.90 9.30 6.79 4.22Slide46



X

Chart Control Limits

Sample Range at Time

i

# Samples

Sample Mean at Time

iSlide47



X

Chart Control Limits

A

2 from

Figure 13.10Slide48

Figure 13.10 Limits

Sample

Size (n)

A2

D4

D52

1.8803.273

1.0202.57

40.7302.28

50.580

2.1160.48

02.0070.42

0.081.928

0.37

0.14

1.86

9

0.34

0.18

1.82

10

0.31

0.22

1.78

11

0.29

0.26

1.74Slide49

R &



X

Chart Hotel Data

Sample

Day Delivery Time Mean Range

1 7.30 4.20 6.10 3.45 5.55 5.32 3.85 2 4.60 8.70 7.60 4.43 7.62 6.59 4.27

3 5.98 2.92 6.20 4.20 5.10 4.88 3.28 4 7.20 5.10 5.19 6.80 4.21 5.70 2.99 5 4.00 4.50 5.50 1.89 4.46 4.07 3.61 6 10.10 8.10 6.50 5.06 6.94 7.34 5.04 7 6.77 5.08 5.90 6.90 9.30 6.79 4.22Slide50



X

Chart Control LimitsSlide51



X

Chart Solution*

0

2

4

6

8

1

2

3

4

5

6

7

`

X, Minutes

Day

UCL

LCLSlide52

R Chart Control Limits

Sample Range at Time

i

# Samples

Figure 13.10,

p.402Slide53

Figure 13.10 Limits

Sample

Size (n)

A2

D4

D521.88

03.2731.02

02.574

0.7302.285

0.5802.11

60.480

2.0070.420.08

1.9280.37

0.14

1.86

9

0.34

0.18

1.82

10

0.31

0.22

1.78

11

0.29

0.26

1.74Slide54

R

Chart Control LimitsSlide55

R

Chart Solution

UCLSlide56

Attribute Control Charts

Tell us whether points in tolerance or not

p chart: percentage with given characteristic (usually whether defective or not)

np chart: number of units with characteristicc chart: count # of occurrences in a fixed area of opportunity (defects per car)

u chart: # of events in a changeable area of opportunity (sq. yards of paper drawn from a machine)Slide57

p Chart Control Limits

# Defective Items in Sample i

Sample i

Size

# Samples

z

= 2 for 95.5% limits;

z

= 3 for 99.7% limitsSlide58

p Chart Example

You’re manager of a

1,700 room

hotel.

For 7 days, you collect data on the readiness of all of the rooms that someone checked out of. Is the process in control

(use z = 3)?

© 1995 Corel Corp.Slide59

p Chart Hotel Data

# Rooms

No.

Not Proportion

Day n

Ready p 1

1,300 130 130/1,300 =.100 2 800 90

.113 3 400 21 .053 4

350 25 .071 5 300 18

.06 6 400 12 .03

7 600 30 .05Slide60

p Chart Control LimitsSlide61

p Chart SolutionSlide62

Hotel Room Readiness P-Bar