06control Chart 1

7/29/2019 06control Chart 1

1/37

Process Capability


2/37

Process Capability

Process Capabilityis an important conceptin SPC. Process capability examines

-- the variability in process characteristics

-- whether the process is capable ofproducing products which conforms to

specifications


3/37

Process Capability

Process capability studies distinguish betweenconformance to control limits and conformanceto specification limits (also calledtolerancelimits)

-- if the process is in control, then virtually all

points will remain within control limits

-- staying within control limits does not necessarily

mean that specification limits are satisfied-- specification limits are usually dictated by

customers


4/37

Process Capability: Concepts

The following distributions show differentprocess scenarios. Note the relative positions

of the control limits and specification limits.


5/37


In control and productmeets specifications.

Control limits are within

specification limits

UCL: Upper Control Limits

LCL: Lower Control Limits

USL: Upper Specification Limits

LSL: Lower Specification Limits


6/37


In control but someproducts do not meet

specifications.

Specification limits arewithin control limits


7/37

Data from process with low capability

Data from process with

mediumcapability

Data from process with highcapability

relative capability


8/37

Process capability: capability index

The capability index is defined as: Cp = (allowablerange)/6 =T (Tolerance)/ 6= (USL - LSL)/6s

The distribution of process quality

is often assumed to be

approximated

with a normal distribution.

Px3=99.73%,


9/37

Normal Distribution

x

f(x)

0

=0.5

=1

=2

0

f(x)

x1 2

The normal distribution N(,2) has several

distinct properties:

--The normal distribution is bell-shaped and is

symmetric

--The mean, , is located at the centre

-- is the standard deviation of the data

The smallerthe steeper the curve

For same changing the value of

is to move the curve without anychange in its shape


10/37

3 Principle

XN(,2) P{-


11/37

Process capability: capability index

The capability index (T/6) show how well a processis able to meet specifications. The higher the value

of the index, the more capable is the process:

-- Cp < 1 (process is unsatisfactory)

-- 1 < Cp < 1.6 ( process is of medium relativecapability)

-- Cp > 1.6 (process shows high relative capability):

better to analyze the actual specifications

(Tolerance) and process technics to save resources

in enhancing the process capability, such as the

increased accuracy of equipment.


12/37

Process capability:process performance index

The capability index-- considers only the spread of the

characteristic in relation to specification limits

-- assumes two-sided specification limits

The product can be bad if the mean is not setappropriately. The process performanceindex takes account of the mean () and is

defined as:Cpk = min[ (USL - )/3, ( - LSL)/3]


13/37

Process capability:process performance index

The process performance index can alsoaccommodate one sided specification limits

-- for upper specification limit:

Cpk = (USL - )/3

-- for lower specification limit:

Cpk = ( - LSL)/ 3


14/37

Process capability: the message

The message from process capability studiesis:

-- first reduce the variation in the process

-- then shift the mean of the process towardsthe target

This procedure is illustrated in the diagram

below:


15/37


16/37

Basic Forms of Statistical Sampling for

Quality Control

Sampling to determine if the process is within

acceptable limits (Statistical Process

Control).

Sampling to accept or reject the immediate

lot ofproductat hand (Acceptance

Sampling).


17/37

Process Control

Process Control is concerned withmonitoring quality while the production orservice is being conducted.


18/37

UCL

LCL

Samples

over time

1 2 3 4 5 6

UCL

LCL

Samples

over time

1 2 3 4 5 6

UCL

LCL

Samples

over time

1 2 3 4 5 6

Normal Behavior

Possible problem, investigate

Possible problem, investigate

Statistical Process Control

-- Control Charts


19/37

Control charts

Processes that are notin a state ofstatistical control-- show excessive variations

-- exhibit variations that change with time

A process in a state of statistical control is said to be

statistically stable. Control charts are used to detectwhether a process is statistically stable. Controlcharts differentiates between variations

-- that is normally expected of the process due chance

orcommon causes-- that change over time due to assignable orspecial

causes


20/37

Control charts: common cause variations

Variations due to common causes-- have small effect on the process

-- are inherent in the process because of:

the nature of the system

the way the system is managed

the way the process is organized and operated

-- can only be removed by

making modifications to the process changing the process

-- are the responsibility of higher management


21/37

Control charts: special cause variations

Variations due to special causes are-- localized in nature

-- exceptions to the system

-- considered abnormalities

-- often specific to a certain operator

certain machine

certain batch of material, etc.

Investigation and removal of variations due to specialcauses are key to process improvement

Note: Sometimes the delineation between common andspecial causes may not be very clear.


22/37

Control charts: how they work

The principles behind the application of control charts

are very simple and are based on the combined use of-- run charts

-- hypothesis testing

The control limits most commonly used in

organizations are plus and minus three standarddeviations. We know from statistics that the chancethat a sample mean will exceed three standaddeviations, in either direction, due simply to chance

variation, is less than 0.3 percent (i.e., 3 times per1000 samples). Thus, the chance that a sample willfall above the UCL, or below the LCL because ofnatural random causes is so small that this occurrenceis strong evidence of assignable variation.


23/37

Control charts: how they work

The procedure is to-- sample the process at regular intervals

-- plot the statistic(or some measure ofperformance), e.g.

mean range

variable

number of defects, etc.

-- check (graphically) if the process is understatistical control

-- if the process is not under statistical control, dosomething about it


24/37

Control charts: types of charts

Different charts are used depending on the nature of the charteddata. Commonly used charts are:

-- forcontinuous (variables) data

Shewhart sample mean ( -chart)

Shewhart sample range (R-chart)

Shewhart sample (X-chart) Cumulative sum (CUSUM)

Exponentially Weighted Moving Average (EWMA) chart

Moving-average and range charts

-- fordiscrete (attributes and countable) data

sample proportion defective (p-chart) sample number of defectives (np-chart)

sample number of defects (c-chart)

sample number of defects per unit (u-chart)

x


25/37

Control charts: assumptions

Control charts make assumptions about theplotted statistic, namely

-- it is independent, i.e. a value is not influenced

by its past value and will not affect futurevalues

-- it is normallydistributed, i.e. the data has a

normal probability density function


26/37

Normal Probability Density Function

The assumptions of normality and independence enable

predictions to be made about the data.


27/37

Control charts: interpretation

Control charts are normal distributions with anadded time dimension.


28/37

Control charts: interpretation

Control charts are run charts with superimposednormal distributions.


29/37

Control charts: run rules

Run rules are rules that are used to indicate out-of-statistical control situations. Typical run rules forShewhart X-charts with control and warning limits are:

-- a point lying beyond the control limits

-- 2 consecutive points lying beyond the warning limits,namely within the area of 2 ~3 or even beyond thecontrol limits

-- 7 or more consecutive points lying on one side of themean

-- 5 or 6 or more consecutive points going in the samedirection (indicates a trend)

-- Other run rules can be formulated using similar principles


30/37


31/37

UCL

CL

LCL

X

LCL

CL

UCL

X

attention investigate Prompt action

Trend


32/37

Control charts: run rules

If only chance variation is present in theprocess, the points plotted on a control

chart will not typically exhibit any pattern.

If the points exhibit some systematicpattern, this is an indication that

assignable variation may be present and

corrective action should be taken.


33/37

Attribute Measurements (p-Chart)

p =T o ta l N u m b e r o f D e fe c tiv e s

T o ta l N u m b e r o f O b s e rv a tio n s

n

s

)p-(1p

=p

p

p

3-p=LCL3+p=UCLs

s

Given:

Compute control limits:


34/37

Example of Constructing a p-chart:

Sample n Defectives p1 100 4 0.042 100 2 0.023 100 5 0.054 100 3 0.035 100 6 0.066 100 4 0.047 100 3 0.038 100 7 0.079 100 1 0.01

10 100 2 0.02

11 100 3 0.0312 100 2 0.0213 100 2 0.0214 100 8 0.0815 100 3 0.03

1. Calculate thesample proportions, p

(these are what can

be plotted on thep-

chart) for eachsample.


35/37


2. Calculate the average of the sample proportions.

0.036=1500

55=p

3. Calculate the standard deviation of the sample

proportion

.0188=100

.036)-.036(1=)p-(1p=pn

s


36/37


4. Calculate the control limits.

3(.0188).036

UCL = 0.0924LCL = -0.0204(or 0)

p

p

3-p=LCL

3+p=UCL

s

s


37/37

Example of Constructing a p-chart:5. Plot the individual sample proportions and the controllimits

UCL

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample number

p

UCL

CL

06control Chart 1

Documents

Transcript of 06control Chart 1