spc

Statistical process control Key Quality characteristic :Forecast Error for demand

BENEFITS of SPC

  

Monitors and provides feedback for keeping processes in control.

Triggers when a problem occurs

Differentiates between problems that are correctable and those

that are due to chance.

Gives you better control of your process.

Reduces need for inspection

Provides valuable knowledge in the working of the process

Have you ever…

Shot a rifle? Played darts? Played basketball? Shot a round of golf?

What is the point of these sports?

What makes them hard?

Have you ever…

Shot a rifle? Played darts? Shot a round of golf? Played basketball?

Player A

Player B

Who is the better shot?

Discussion

What do you measure in your process? Why do those measures matter? Are those measures consistently the same? Why not?

Variability

Deviation = distance between observations and the mean (or average)

Player A

Player B

Observations

10

9

8

8

7

averages 8.4

Deviations

10 - 8.4 = 1.6

9 – 8.4 = 0.6

8 – 8.4 = -0.4

8 – 8.4 = -0.4

7 – 8.4 = -1.4

0.0

871089

Variability

Deviation = distance between observations and the mean (or average)

Emmett

Jake

Observations

7

7

7

6

6

averages 6.6

Deviations

7 – 6.6 = 0.4

7 – 6.6 = 0.4

7 – 6.6 = 0.4

6 – 6.6 = -0.6

6 – 6.6 = -0.6

0.0

76776

Variability

Variance = average distance between observations and the mean squared

Emmett

Jake

Observations

10

9

8

8

7

averages 8.4

Deviations

10 - 8.4 = 1.6

9 – 8.4 = 0.6

8 – 8.4 = -0.4

8 – 8.4 = -0.4

7 – 8.4 = -1.4

0.0

871089

Squared Deviations

2.56

0.36

0.16

0.16

1.96

1.0 Variance

Variability

Variance = average distance between observations and the mean squared

Emmett

Jake

Observations

7

7

7

6

6

averages

Deviations Squared Deviations 76776

Variability

Variance = average distance between observations and the mean squared

Emmett

Jake

Observations

7

7

7

6

6

averages 6.6

Deviations

7 - 6.6 = 0.4

7 - 6.6 = 0.4

7 - 6.6 = 0.4

6 – 6.6 = -0.6

6 – 6.6 = -0.6

0.0

Squared Deviations

0.16

0.16

0.16

0.36

0.36

0.24

76776

Variance

Variability

Standard deviation = square root of variance

Emmett

Jake

Variance Standard Deviation

Emmett 1.0 1.0

Jake 0.24 0.4898979

But what good is a standard deviation

Variability

The world tends to be bell-shaped

Most outcomes occur in the

middle

Fewer in the “tails”

(lower)

Fewer in the “tails” (upper)

Even very rare outcomes are

possible(probability > 0)

Even very rare outcomes are

possible(probability > 0)

Variability

Add up the dots on the dice

0

0.05

0.1

0.15

0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Sum of dots

Pro

ba

bili

ty 1 die

2 dice

3 dice

Here is why:

Even outcomes that are equally likely (like dice), when you add them up, become bell shaped

“Normal” bell shaped curve

Add up about 30 of most things and you start to be “normal”

Normal distributions are divide upinto 3 standard deviations on each side of the mean

Once your that, you know a lot about what is going on

And that is what a standard deviation is good for

Usual or unusual?

1. One observation falls outside 3 standard deviations?

2. One observation falls in zone A?

3. 2 out of 3 observations fall in one zone A?

4. 2 out of 3 observations fall in one zone B or beyond?

5. 4 out of 5 observations fall in one zone B or beyond?

6. 8 consecutive points above the mean, rising, or falling? X XXXX XX X XX1 2 3 4 5 6 7 8

Causes of Variability

Common Causes: Random variation (usual) No pattern Inherent in process adjusting the process increases its variation

Special Causes Non-random variation (unusual) May exhibit a pattern Assignable, explainable, controllable adjusting the process decreases its variation

SPC uses samples to identify that special causes have occurred

Limits

Process and Control limits: Statistical Process limits are used for individual items Control limits are used with averages Limits = μ ± 3σ Define usual (common causes) & unusual (special causes)

Specification limits: Engineered Limits = target ± tolerance Define acceptable & unacceptable

Process vs. control limits

Variance of averages < variance of individual items

Distribution of averages

Control limits

Process limits

Distribution of individuals

Specification limits

Usual v. Unusual, Acceptable v. Defective

μ Target

A B C D E

More about limits

Good quality: defects are rare (Cpk>1)

Poor quality: defects are common (Cpk<1)

Cpk measures “Process Capability”

If process limits and control limits are at the same location, Cpk = 1. Cpk ≥ 2 is exceptional.

μtarget

μtarget

Process capability

Good quality: defects are rare (Cpk>1)Poor quality: defects are common (Cpk<1)

Cpk = min

USL – x3σ

=

x - LSL3σ

=

3σ = (UPL – x, or x – LPL) = =

14 20 26 15 24

24 – 203(2)

= = .667

20 – 153(2)

= = .833

Going out of control

When an observation is unusual, what can we conclude?

μ2

The mean has changed

X

μ1

Going out of control

When an observation is unusual, what can we conclude?

The standard deviationhas changed

σ2

X

σ1

The SPC implementation process

 

•Identify what characteristics to be controlled

•Establish Control limits

•Find how to control the process

•Learn how to measure improvement of a process

•Learn how to detect shift and how to set alerts that take action.

•Learn about the two types of causes that affect your variation.

Setting up control charts:

Calculating the limits

1. Sample n items (often 4 or 5)

2. Find the mean of the sample x-bar

3. Find the range of the sample R

4. Plot x bar on the x bar chart

5. Plot the R on an R chart

6. Repeat steps 1-5 thirty times

7. Average the x bars to create (x-bar-bar)

8. Average the R’s to create (R-bar)

Setting up control charts:

Calculating the limits

9. Find A2 on table (A2 times R estimates 3σ)

10. Use formula to find limits for x-bar chart:

11. Use formulas to find limits for R chart:

RAX 2

RDLCL 3 RDUCL 4

Let’s try a small problem

smpl 1 smpl 2 smpl 3 smpl 4 smpl 5 smpl 6

observation 1 7 11 6 7 10 10

observation 2 7 8 10 8 5 5

observation 3 8 10 12 7 6 8

x-bar

R

X-bar chart R chart

UCL

Centerline

LCL

Let’s try a small problem

smpl 1 smpl 2 smpl 3 smpl 4 smpl 5 smpl 6 Avg.

observation 1 7 11 6 7 10 10

observation 2 7 8 10 8 5 5

observation 3 8 10 12 7 6 8

X-bar 7.3333 9.6667 9.3333 7.3333 7 7.6667 8.0556

R 1 3 6 1 5 5 3.5

X-bar chart R chart

UCL 11.6361 9.0125

Centerline 8.0556 3.5

LCL 4.4751 0

R chart

0123456789

10

1 2 3 4 5 6

9.0125

3.5

0

X-bar chart

11.6361

8.0556

4.4751

AP Uploads Quality control

Interpreting charts

Observations outside control limits indicate the process is probably “out-of-control”

Significant patterns in the observations indicate the process is probably “out-of-control”

Random causes will on rare occasions indicate the process is probably “out-of-control” when it actually is not

Interpreting charts

In the excel spreadsheet, look for these shifts:

A B

C D

Show real time examples of charts here

Lots of other charts exist

P chart C charts U charts Cusum & EWMA

For yes-no questions like “is it defective?” (binomial data)

For counting number defects where most items have ≥1 defects (eg. custom built houses)

Average count per unit (similar to C chart)

Advanced charts

“V” shaped or Curved control limits (calculate them by hiring a statistician)n

ppp

)1(3

cc 3

n

uu 3

SPC Station

SPC as a triggering tool

Selecting rational samples

Chosen so that variation within the sample is considered to be from common causes

Special causes should only occur between samples

Special causes to avoid in sampling passage of time workers shifts machines Locations

Chart advice

Larger samples are more accurate

Sample costs money, but so does being out-of-control

Don’t convert measurement data to “yes/no” binomial data (X’s to P’s)

Not all out-of control points are bad

Don’t combine data (or mix product)

Have out-of-control procedures (what do I do now?)

Actual production volume matters (Average Run Length)

This is a control system which uses statistical techniques for knowing, all the time, changes in the process.

It is an effective method in preventing defects and helps continuous quality improvement.

Statistical Process Control (S.P.C.)

What does S.P.C. mean?

Statistical: Statistics are tools used to make predictions on

performance.

There are a number of simple methods for analysing data and, if applied correctly, can lead to predictions with a high degree of accuracy.

What does S.P.C. mean?

Process: The process involves people, machines, materials, methods,

management and environment working together to produce an output, such as an end product.

What does S.P.C. mean?

Control: Controlling a process is guiding it and comparing actual

performance against a target.

Then identifying when and what corrective action is necessary to achieve the target.

S.P.C.

Statistics aid in making decisions about a process based on sample data and the results predict the process as a whole.

PeopleMachines Material

Management Methods Environment

Output

The Aim of S.P.C. - Prevention Strategy

Prevention Benefits: Improved design and process capability. Improved manufacturing quality. Improved organisation. Continuous Improvement.

The S.P.C. has to be looked at as a stage towards completely preventing defects.

With stable processes, the cost of inspection and defects are significantly reduced.

S.P.C. as a Prevention Tool

Assesses the design intent. Achieves a lower cost by providing an early warning system. Monitors performance, preventing defects. Provides a common language for discussing process performance.

The Benefits of S.P.C.

Process Element Variable Examples

Machine………………………….Speed, operating temperature, feed rate

Tools………………………………..Shape, wear rateFixtures…………………………..Dimensional accuracyMaterials…………………………Composition, dimensionsOperator…………………………Choice of set-up, fatigueMaintenance…………………Lubrication, calibrationEnvironment…………………Humidity, temperature

Process Variations

No industrial process or machine is able to produce consecutive items which are identical in appearance, length, weight, thickness etc.

The differences may be large or very small, but they are always there. The differences are known as ‘variation’. This is the reason why

‘tolerances’ are used.

Process Variations

Common causes are the many sources of variation that are always present. A process operates within ‘normal variation’ when each element varies in a random

manner, within expected limits, such that the variation cannot be blamed on one element.

When a process is operating with common causes of variation it is said to be stable.

Stability

The process can only be termed ‘under control’ if it gives predictable results.

Its variability is stable over a long period of time.

Process Control

Graphs and charts have to be chosen for their simplicity, usefulness and visibility.

They are simple and effective tools based on process stability monitoring.

They give evidence of whether a process is operating in a state of control and signal the presence of any variation.

Process Control Charts

Data InterpretationConsider these 50 measurements

Bore Diameter 36.32 ±0.05mm (36.27 - 36.37mm)

1 36.36 11 36.37 21 36.34 31 36.35 41 36.362 36.34 12 36.35 22 36.37 32 36.35 42 36.373 36.34 13 36.32 23 36.34 33 36.36 43 36.374 36.33 14 36.35 24 36.35 34 36.37 44 36.355 36.35 15 36.34 25 36.34 35 36.34 45 36.376 36.33 16 36.34 26 36.35 36 36.36 46 36.367 36.33 17 36.35 27 36.36 37 36.38 47 36.358 36.34 18 36.33 28 36.33 38 36.34 48 36.349 36.35 19 36.32 29 36.36 39 36.35 49 36.35

10 36.35 20 36.35 30 36.38 40 36.35 50 36.34

Data Interpretation As a set of numbers it is difficult to see any pattern. Within the table, numbers 30 and 37 were outside the

tolerance – but were they easy to spot? A way of obtaining a pattern is to group the measurements

according to size.

Data Interpretation – Tally Chart

The tally chart groups the measurements together by size as shown.

The two parts that were out of tolerance are now easier to detect (36.38mm).

36.39

36.38

36.37

36.36

36.35

36.34

36.33

36.32

36.31

36.30

36.29

36.28

Tally Chart - Frequency

The tally chart shows patterns and we can obtain the RANGE - 36.32mm to 36.38mm.

The most FREQUENTLY OCCURRING size is 36.35mm.

36.39

36.38

36.37

36.36

36.35

36.34

36.33

36.32

36.31

36.30

36.29

36.28

2

6

7

16

12

5

2

Tally Chart - Information

The tally chart gives us further information: The number of bores at each size; The number of bores at the most common size; The number of bores above and below the most common size (36.35mm)

- number above 36.35mm is 7+6+2=15 number below 36.35mm is 12+5+2=19

HistogramWe can redraw the frequency chart as a bar chart known as a histogram:

16

14

12

10

8

6

4

2

0 36.31 36.32 36.33 36.34 36.35 36.36 36.37 36.38 36.39