Quality Assurance - Lecture - SPC , Lecture notes of Material Engineering

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Statistical Process

Control

Learning Objectives

To learn and understand the fundamentals

of Statistical Process Control, industry wide

known as SPC, to detect, monitor, and

control process variation.

SPC is the discipline of using statistical tools,

such as control charts, to monitor process

output overtime.

Control charts are used to help identify sources

of process variation.

Definition of Statistical Process Control

Process Variation

Variation is the amount of change in data,

characteristics, or output in a process caused by

“common” or “special” causes.

It is very important to detect process variation

trends to predict process output.

Also, it is very important to understand what is

the natural variation of a process.

Control Charts

Line graph of measurements of a process overtime

that has control limits placed on it

Control limits are bounds for the expected natural

variation of the process

Located at a distance of +/- 3 standard deviations

from the centerline of the control chart.

The purpose of a control chart is to expose variation

and separate it into:

Common or random fluctuation

• Special fluctuation

Type of Control Charts

Variable Control charts

• Uses quantitative data: - Quality characteristics that can be measured - Length, - Diameter, etc

Attribute control charts:

Uses discrete data that needs to be counted

Examples are:

Number of scratches,

Pass/fail data

Control charts characteristics

Plot points are displayed in chronological order

providing time oriented visibility.

The centerline is the average of the plotted points

Control limits are based on short term variability of

the sampled data

Control limits are not based on specifications

Control limits are spaced 3 standard deviations (

above and below the centerline

Control charts characteristics (continuatio

Once established, the control limits are extended

into the future, creating the basis to judge the

stability of the process.

The control limits should not be revised unless

there is a significant process change.

Some rules for determining significant process

changes are defined by the Western Electric rules

D1-9000, “Advanced Quality System”, requires at

least 20 plot points before setting the initial control

limits

UCL established

LCL established

UCL extended

LCL extended

Out-of-control condition

indicate a significant

change in the process

(special cause variation)

• Out-of-control points should be investigated and corrective action taken
• Control limits distinguish between common cause and special cause variation

Control limits

Limits are based on inherent process variation

Limits distinguish between common and special

cause variation

Help focus investigation and actions only on causes

of process changes and out-of-control conditions

Minimizes reaction to variation which should have

been expected (false alarms)

Prevent reaction to random variation

It is a common mistake to assume that by setting

the specification limits as control limits, the process

will be monitored properly.

Process capability analysis sets the basis for

adjusting process performance to meet specification

limits.

Specification tolerance and control limits

(continuation)

X and R charts

X and R charts are control charts for variable data

They are used to monitor the behavior of the

process average X and range R of a single

measurable characteristic

X is subgroup average = Sum (X 1 + X 2 …..Xn)/n

• n = quantity of elements in a subgroup
• R is subgroup range = Xmax – Xmin

They are mostly used in situations where parts are

produced frequently or in high volume

Variation of the process at any point in time

represent the natural variability of the process

The range of each subgroup is a good measure of

short-term process variability

The average of the ranges, R, is a measure of the

short term variability of the process over time

The subgroup average, X, measures process output

at a point in time and between subgroup variability

The average of the subgroup averages, X, estimates

the long term center of the process

General characteristics of X – R charts

Chart Control

limits

Centerline Plot

points

Subgroup

size

UCL = X + A 2 R

LCL = X - A 2 R

UCLR = D 4 R

LCLR = D 3 R

x

R

K= number of

subgroups

X=

Sum X

K

R=

Sum R

K

X=

Sum X

n

R= range of

subgroup

measurements

= Xmax - Xmin

N = 2 to 9

3 to 5 preferred

Subgroup sizes

can vary, but

constant is

preferred

Calculations for X – R charts