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Statistical Process Contol (SPC)

- Lec-1

Quality and SPC

- The concept of quality has been with us since the

beginning of time. - Typically the quality of products was described

by some attribute such as strength, beauty or

finish. - However, the mass production of products that the

reproducibility of the size or shape of a product

became a quality issue.

Quality and SPC

- Quality was obtained by inspecting each part and

passing only those that met specifications. - With SPC, the process is monitored through

sampling. - Considering the results of the sample,

adjustments are made to the process before the

process is able to produce defective parts.

Process Variability

- The concept of process variability forms the

heart of SPC. - For example, if a basketball player shot free

throws in practice, and the player shot 100 free

throws every day, the player would not get

exactly the same number of baskets each day. - Some days the player would get 84 of 100, some

days 67 of 100, and so on. - All processes have this kind of variation or

variability.

Process Variability

- The variation can be partitioned into 2

components. - Natural process variation (common cause) or

system variation. - In the case of the basketball player, this

variation would fluctuate around the player's

long-run percentage of free throws made. - Special cause variation is typically caused by

some problem or extraordinary occurrence in the

system. - In the case of the player, a hand injury might

cause the player to miss a larger than usual

number of free throws on a particular day.

Statistical Process Control (SPC)

- SPC is a methodology for charting the process and

quickly determining when a process is "out of

control. - (e.g., a special cause variation is present

because something unusual is occurring in the

process). - The process is then investigated to determine the

root cause of the "out of control" condition. - When the root cause of the problem is determined,

a strategy is identified to correct it.

Statistical Process Control (SPC)

- The management responsible to reduce common cause

or system variation as well as special cause

variation. - This is done through process improvement

techniques, investing in new technology, or

reengineering the process to have fewer steps and

therefore less variation. - Reduced variation makes the process more

predictable with process output closer to the

desired or nominal value.

Statistical Process Control (SPC)

- The process above is in apparent statistical

control. - Notice that all points lie within the upper

control limits (UCL) and the lower control limits

(LCL). CL-centerline - This process exhibits only common cause variation.

- The process above is out of statistical control.
- Notice that a single point can be found outside

the control limits (above them). - This means that a source of special cause

variation is present. - Having a point outside the control limits is the

most easily detectable out-of-control condition.

- The graphic above illustrates the typical cycle

in SPC. - First, the process is highly variable and out of

statistical control. - Second, as special causes of variation are found,

the process comes into statistical control. - Finally, through process improvement, variation

is reduced. - This is seen from the narrowing of the control

limits. - Eliminating special cause variation keeps the

process in control process improvement reduces

the process variation and moves the control

limits in toward the centerline of the process.

Out-of-Control Conditions

- Several types of conditions exist that indicate

that a process is out of control - Extreme Point Condition
- This process is out of control because a point is

either above the UCL or below the LCL.

Out-of-Control Conditions

- Control Chart Zones
- Control charts can be broken into 3 zones, a, b,

c on each side of the process center line. - A series of rules exist that are used to detect

conditions in which the process is behaving

abnormally to the extent that an out of control

condition is declared.

Out-of-Control Conditions

- The probability of having 2 out of 3 consecutive

points either in or beyond zone A is an extremely

unlikely occurrence when the process mean follows

the normal distribution. - This criteria applies only to X-bar charts for

examining the process mean.

X, Y, and Z are all examples of this phenomena.

Out-of-Control Conditions

- The probability of 4 out of 5 consecutive points

either in or beyond zone B is also an extremely

unlikely occurrence when the process mean follows

the normal distribution. - Applied to X-bar chart when analyzing a process

mean.

X, Y, and Z are all examples of this phenomena.

Out-of-Control Conditions

- Runs Above or Below the Centerline
- The probability of having long runs (8 or more

consecutive points) either above or below the

centerline is also an extremely unlikely

occurrence when the process follows the normal

distribution. - Applied to both X-bar and r charts.

Out-of-Control Conditions

- Linear Trends
- The probability of 6 or more consecutive points

showing a continuous increase or decrease is also

an extremely unlikely occurrence when the process

follows the normal distribution. - Applied to both X-bar and r charts.

Out-of-Control Conditions

- Oscillatory Trend
- The probability of having 14 or more consecutive

points oscillating back and forth is also an

extremely unlikely occurrence when the process

follows the normal distribution. - Applied to both X-bar and r charts.

Out-of-Control Conditions

- Avoidance of Zone C
- The probability of having 8 or more consecutive

points occurring on either side of the center

line and do not enter Zone C. - This phenomena occurs when more than one process

is being charted on the same chart, the use of

improper sampling techniques, or perhaps the

process is over controlled.

Out-of-Control Conditions

- Run in Zone C
- The probability of having 15 or more consecutive

points occurring the Zone C. - This condition can arise from improper sampling,

falsification of data, or a decrease in process

variability that has not been accounted for when

calculating control chart limits, UCL and LCL.

The basics

- Dont inspect the product, inspect the process.
- You cant inspect it in, youve got to build it

in. - If you cant measure it, you cant manage it.

The SPC steps

- Basic approach
- Awareness that a problem exists.
- Determine the specific problem to be solved.
- Diagnose the causes of the problem.
- Determine and implement remedies.
- Implement controls to hold the gains achieved by

solving the problem.

SPC requires the use of statistics

- Quality improvement efforts have their foundation

in statistics. - SPC involves the
- collection
- tabulation
- analysis
- interpretation
- presentation of numerical data.

SPC is comprised of 7 tools

- Pareto diagram
- Histogram
- Cause and Effect Diagram
- Check sheet
- Process flow diagram
- Scatter diagram
- Control chart

Pareto Principle

- Alfredo Pareto (1848-1923) Italian Economist
- Conducted studies of the distribution of wealth

in Europe. - 20 of the population has 80 of the wealth
- Joseph Juran used the term vital few trivial

many or useful many. He noted that 20 of the

quality problems caused 80 of the dollar loss.

Pareto diagram

(64)

A pareto diagram is a graph that ranks data

classifications in descending order from left to

right.

Percent from each cause

(13)

(10)

(6)

(3)

(2)

(2)

Poor Design

Defective parts

Operator errors

Machine calibrations

Defective materials

Surface abrasions

Wrong dimensions

Causes of poor quality

Pareto diagram

Complaints

Pareto diagram

- Sometimes a pareto diagram has a cumulative line.
- This line represents the sum of the data as they

are added together from left to right.

Pareto diagram

- Sometimes a pareto diagram has a cumulative line.
- This line represents the sum of the data as they

are added together from left to right.

Above the bars, using the 2nd Y-axis representing

the cumulative data, plot the cumulative

percentage values in the form of a line.

Pareto diagram

- The cumulative percentage can be computed (dotted

line). - On the right, add a vertical percent scale equal

in length to the scale on the left. - Label this from 0 to 100 .

Pareto diagram

Table 1. Example of a Tabulation of Causes of

Ball Bond Lifting for use in a Pareto Chart

Pareto diagram

Table 1. Example of a Tabulation of Causes of

Ball Bond Lifting for use in a Pareto Chart

Histogram

The histogram, graphically shows the process

capability and, if desired, the relationship to

the specifications and the nominal. It also

suggests the shape of the population and

indicates if there are any gaps in the data.

Histogram

Histogram

Cause-and-Effect Diagrams

- Show the relationships between a problem and its

possible causes. - Developed by Kaoru Ishikawa (1953)
- Also known as
- Fishbone diagrams
- Ishikawa diagrams

Cause and Effect Skeleton

Materials

Procedures

Quality Problem

Equipment

People

Fishbone Diagram

Fishbone Diagram

Cause-and-Effect Diagrams

- Advantages
- making the diagram is educational in itself
- diagram demonstrates knowledge of problem solving

team - diagram results in active searches for causes
- diagram is a guide for data collection

Cause-and-Effect Diagrams

- To construct the skeleton, remember
- For manufacturing - the 4 Ms
- man, method, machine, material
- For service applications
- equipment, policies, procedures, people

Check Sheet

Shifts

? ? ?

? ? ? ?

?

? ? ?

? ?

? ? ?

Defect Type

? ? ?

? ? ? ?

? ?

?

Check Sheet

Flowcharts

- Graphical description of how work is done.
- Used to describe processes that are to be

improved.

- "Draw a flowchart for whatever you do. Until you

do, you do not know what you are doing, you just

have a job. - Dr. W. Edwards Deming.

Flowcharts

Activity

Decision

Yes

No

Flowcharts

Flow Diagrams

Process Chart Symbols

Operations

Inspection

Transportation

Delay

Storage

Flow Diagrams

(No Transcript)

Scatter Diagram

.

(a) Positive correlation

(b) No correlation

(c) Curvilinear relationship

The patterns described in (a) and (b) are easy to

understand however, those described in (c) are

more difficult.

Run Charts

- Run Charts (time series plot)
- Examine the behavior of a variable over time.
- Basis for Control Charts

Control Chart

27

24

UCL 23.35

21

c 12.67

18

15

Number of defects

12

9

6

LCL 1.99

3

2

4

6

8

10

12

14

16

Sample number

Control Chart

7 Quality Tools

SUMMARY

- SPC using statistical techniques to
- measure and analyze the variation in processes
- to monitor product quality and
- maintain processes to fixed targets.
- Statistical quality control using statistical

techniques for - measuring and improving the quality of processes,

- sampling plans,
- experimental design,
- variation reduction,
- process capability analysis,
- process improvement plans.

SUMMARY

- A primary tool used for SPC is
- the control chart,
- a graphical representation of certain descriptive

statistics for specific quantitative measurements

of the process. - These descriptive statistics are displayed in the

control chart in comparison to their "in-control"

sampling distributions. - The comparison detects any unusual variation in

the process, which could indicate a problem with

the process.

SUMMARY - benefits

- Provides surveillance and feedback for keeping

processes in control - Signals when a problem with the process has

occurred - Detects assignable causes of variation
- Reduces need for inspection
- Monitors process quality
- Provides mechanism to make process changes and

track effects of those changes - Once a process is stable, provides process

capability analysis with comparison to the

product tolerance