SPC presentation.ppt

STATISTICAL PROCESS STATISTICAL PROCESS CONTROLCONTROL

STATISTICAL PROCESS STATISTICAL PROCESS CONTROLCONTROL

OUTLINEOUTLINE

Introduction. Summarising Data. Variation. Some Fundamentals. Control Charts. Stability ,Capability & Continuous

improvement. Deming’s 14 points.

IntroductionIntroduction

Management is responsible for 95% of Quality problems.

E.Deming What is Quality? How to improve Quality? What is value?

Summarizing DataSummarizing Data Types of data: Variables & Attributes.

Purpose of Data gathering: “Decision making”– Can we make it right?– Are we making it right?– Have we made it right?– Can we make it better?

Reasons for collection of Data– To understand an actual situation– For analysis– Data for process control and acceptance and

rejection.

Summarizing DataSummarizing Data

Measures of Location– Average– E.g. 3,10,16,1,5,14,11,6– Median

Measures of Dispersions– Range– RMSP– Standard Deviation

Histograms Run Chart.

VariationVariation

“If I had to reduce my message for management to just a few words, I’d say it all had to do with reducing variation.”

E. Deming.

VariationVariation

There is variation among the products from any manufacturing process.

We would like to completely get rid of variation but we know that can’t be done.

The goal is to be able to measure/identify variation and than work to minimize it.

VariationVariation

Sources of Variation Equipment

Direct Materials

Indirect Materials

People

Methods

Orders

Facilities

Product Quality

Direct MaterialHardnessMachiniabilityPick up points

Indirect MaterialToolsCoolantBushingsLubricantsChemicals

EquipmentMachinesFixturesGauges/MastersSpindles/Collects

PeopleTrainingSkillMotivationCommunicationAttitudeTrust

FacilitiesTemperatureCleanlinessHumidityNoiseCentral coolant system

OrdersClarityTimelinessAdequacyProduct mixQuantity

MethodsSpecificationSpeedsFeedsProcess Documentation

VariationVariation

VariationVariation

Types of variation Controlled variation (Common causes):

Is stable and consistent pattern of variation over time.

Uncontrolled variation (Assignable cause): Is a pattern of variation that changes over time.

Time

Fre

qu

en

cy f

or

each

siz

e

Product size

Uncontrolled Variation

Time

Fre

qu

en

cy f

or

each

siz

e

Product size

Controlled Variation

VariationVariation

VariationVariation

Common Cause1) A large number are in effect

at any time.2) Each has an individual effect

that is too small to mention.3) Only a change in the system

will reduce that part of the variability.

4) Only management has the ability to make changes.

5) Remain constant over time.

Assignable Cause1) Very few in effect at any

time.2) The effect is measurable.3) They can be found and

eliminated.4) The machine operator is

best able to discover and make changes.

5)They occur infrequently in an unpredictable manner.

Difference between Common and Assignable cause

VariationVariation

Fabricate Inspect Pack Ship

ScrapRework

Inspect Quality Audit

Report to Management

Detection based system

Approaches to Variation

VariationVariation

“t” Test demonstrating 100% inspection.

Instructions: When the instructor says “go”, please count the number of “t’s” in the paragraph. You will have one minute. At the end of that time, be able to state how many “t’s” are in the paragraph.

‘T’ test - Exercise

VariationVariation

Suppliers of raw materials

Test of raw material

Production, assembly, inspection, test

Final inspection

Distribution

Consumers and service to customer

Prevention based system

Approaches to Variation

Some FundamentalsSome Fundamentals

50% 50%

“Balanced”Normal DistributionNormal Distribution

68%

95%

99.73%

1s1s 1s 1s 1s 1s

Normal Distribution.Normal Distribution.



Threshold State•Process in control•Some non confirming Product•Must Either…Change process, orChange specifications•Sorting is temporary fix•Control Charts Maintain process in control Evaluate efforts at improvement

Ideal State•Process in Control•100% conforming products•Control ChartsMaintain process in controlEvaluate efforts at improvement

State of Chaos•Process out of control•Some non conforming product•Assignable causes still dominate•Random fluctuations due to assignable causes will eventually frustrate efforts at process improvement.•The only way out of chaos is to first eliminate the assignable caused

Brink of Chaos•Process out of control•100% conforming product•All may seem okay, but…•Assignable causes determine what is produced by the process!•Quality and conformance can change in a moment.

Pro

cess d

isp

lays

con

trol

Pro

cess h

as L

ack o

f C

on

trol

Some nonconforming products produced

100% conforming products produced

Chaos managers

Entropy slide

Four possibilities for any Process


“We are being ruined by best efforts.”Deming

The Funnel Experiment:This experiment can be carried out with a relatively simple

apparatus:1. A funnel, such as found in kitchen.2. A holder for funnel, e.g. a desk lamp.3. A marble, small enough to pass through the stem.4. A table covered with washable table cloth.5. A felt tip pen with non permanent ink. And6. A ruler and a protractor.


Rule One :Don’t shift the funnel, irrespective of where the marble comes to rest.

“Lets do something. Don’t just sit there. Do something about it Move the Funnel.”

Funnel ExperimentFunnel Experiment


Rule two :Move the funnel in attempt to compensate for the amount by which the marble misses the target.

Suppose marble finishes six inch east of the target funnel is moved six inch west of the target.

100 marbles dropped using rule 2 of the funnel

ExampleFiring rifle bullet on the target.



Rule three :Move the funnel in attempt to compensate for the amount by which the marble misses the target.

Suppose marble finishes six inch east of the target funnel is moved six inch west of relative current position.


Example Over control



Rule four :Move the funnel directly over the position where the marble has just landed.


E.g.1. Colour matching where each batch of paint is matched with previous batch.2. Operator that tries to achieve consistency by making each piece as previous one.3. Worker training worker.


Control chartsControl charts

Purpose of control chart

“The function of a control chart is to minimize the net economic losses from over adjustment and under adjustment.”

Control chartsControl charts

Preparatory steps for Control Chart

Establish an environment suitable for action.

Define the process.

Determine characteristics to be charted.

Define the measurement system.

Minimize unnecessary variation.

Control ChartControl Chart

Uses sub groups to monitor process

R

X


VariablesBased on sample size:

x and R

x and s

x and moving range

AttributeBased on type of data:

Is the interest in non conforming unit i.e. percent defectivep chartnp chart (sample size constant)

Is the interest in non conformities i.e. discrepancies/part?c chart (sample size constant)u chart

Type of control charts

Control chartControl chart

Always use control limits which are set at 3 sigma limits on either side of central line.

In computing three sigma limit one must always use an average dispersion statistic.

Use rational sampling and rational subgrouping.

Control Chart are effective only to the extent that the organization can use, in a effective manner, the knowledge gained from the charts.

Foundations of Control Charts

Logic of control chartLogic of control chart

Assume process displays controlled variation

Predict Behaviour of Averages and ranges (Calculate Control Limit)

Compare observed or Future Average and range values with control limit

Continued operation of process within limits is the only “proof” of stability

Take action to identify and remove assignable causes

If observations are inconsistent with predictions then process is definitely unstable

If observations are consistent with predictions then process may be stable


Compute average & range for each sub group of k subgroups Compute the grand average, X, by averaging each of the k sub

group averages. Compute average range R by averaging each of k subgroup

ranges. The certral line for X- chart is X The center line for R chart is R. Find the values for A2, D3, D4, which correspond to the sub

group size n. Multiply R by A2 = A2R Add and subtract A2R from X to get UCL and LCL for X-chart. Multiply R by D4 to get UCL for R chart Multiply R by D3 to get LCL for R chart.

Control Limits


Used in several situation where the logical subgroup size is n = 1. This might happen when each measurement represents on batch or the measurement are widely spaced over time.

UNPLx = X + 2.66mR CLx = X LNPLx = X - 2.660 mR UCLr = 3.268 mR CLr = mR

Control Charts for Subgroup size one


Never subgroup unlike thing together. Minimize the variation within each subgroup. Maximize the opportunity for variation

between subgroups. Average across noise not across signal Treat the chart in accordance with the data.

Rational Subgrouping

Choice of scale for control charts: Scale should be twice as the control limit spread.

What is Reasonable Degree of statistical Control?Process is said to be in statistical control if 100 consecutive observations fail to indicate lack of control i.e 25 consecutive sub groups with size 4 or 20 consecutive with subgroup size 5.

Myths about control Chart.– Data should be normally distributed before they can be placed on

control chart.– It has been said that the data must be in control before one can

plot them on a control chart.– Only useful in shopfloor.

Control ChartsControl ChartsAnalyzing Control Charts


A lack of control is indicated whenever a single point falls out

side the control limit

A lack of control is indicated whenever at least two out of

three successive values fall on the same side of and more

than two sigma units away from the central line

A lack of control is indicated whenever at least four out of

five successive values fall on the same side of, and more

than one sigma units away from the central line

A lack of control is indicated whenever at least seven

successive values fall on same side of central line

Four rules for defining Lack of Control

Stability, Capability & Continuous Improvement


“The first step in examination of data is accordingly to question the state of statistical control that produced the data”

DemingProcess Capability“Capability refers to the quantification of common cause

variation. The presence of special or assignable cause make the prediction of capability impossible and meaning of capability unclear.”

Cpk: What is it?A prediction of the level of quality (or measure of the inherent

uniformity) a process can produce.



6s

Total Tol.

LSL USL

Cp or Pp = Total Tol 6s

Note : Pp/Ppk is calculated for short run of a process & Cp/Cpk is calculated for long run of process

Cpk or Ppk = Min of zu & zl 3s

3s

Zu

LSL USL

3s

Zl

Avg.

Process capability indicesProcess capability indices



For X-R chart Find the value d2 which corresponds to the sub group

size ‘n’ Divide the Average Range by d2 to get Sigma(X) =

R/d2. Multiply this quantity by 6 to get 6 sigma(X) = 6* R/d2.

For X- mR Chart Using the grand average as the central line add and

subtract the above value to get UNPLx & LNPLx respectively.

Limits for Individual values



Short term capability study.– Will only reveal part of story as assignable causes may not have

an opportunity to arrive.– Uses anywhere between 25 - 50 values.

Steps.– Plot individual vales observe any indication of lack of statistical

control.– Plot XmR chart – Calculate control limits. Difference in UNL and LNL will give 6

sigma value. Use the same in computing Pp and Ppk.

Capability Analysis



Quality of Conformance

Cpk 1 1.33

100% good

100% defective

Total quality costs

Failure costs

Cost of Appraisal plus prevention

Cost

per

good

un

it o

f pro

du

ct

T0 T0

Cpk logic applied to Juran’s Optimal Quality Cost model



CONDUCT GR&R

GAUGE CAPABLE

CONDUCT PROCESS POTENTIAL STUDY

IMMEDIATE ACTION ON OUT OF CONTROL CONDITIONS REQUIRED

CONTINUE X AND R CHART

CONTINUE X AND R REDUCE FRQUENCY

N=2 POSSIBLE

(SPC ON GOING CONTROL)

INCAPABLE CAPABLE VERY CAPABLE

CONTROL CHARTS TO IDENTIFY SOURCE OF VARIATION

TARGETING CRITICAL - MUST REACT QUICKLY TO OUT OF CONTROL CONDITION

100% CONTROL UNTIL IMPROVEMENT MADE

CONTROL CHART FOR PROBLEM SOLVING

CONTROL CHART TO REDUCE VARIABILITY

CONTINUE CHARTING UNTIL DESIRED LONG TERM CAPABILITY IS OBTAINED

MARGINAL CAPABILITY 100% OR SPC

CAPABLE Cpk 1.33 - 2.50

EXTREMELY CAPABLE Cpk 2.5 - 4.0

Cpk> 4.0

SPC ImplementationSPC Implementation



World class quality is Quality which is on target with minimal variation.

measurement

Loss

LSL USL

Loss Function Representing the conformance to Specification Interpretation of Quality

World Class Quality



K = Targeting error

A quadratic loss function with a product distribution

measurement

Loss

Taguchi’s Loss function states that there exists a target, or ideal value, for any characteristic and a continuous loss function which indicates that the further a given product lies away from the target the higher the total economic loss to society

World Class Quality



Control Chart is effective tool to reduce process dispersion and lead to continual improvement.

“Control charts used just for monitoring is waste of valuable resources.”

Refer Handout for example on continuous improvement.

PDCA cycle

ProductionSpecification

InspectionQuality Control process shown as circle

PlanAct

Check

Quality Control process shown as circle

Do



Why Continuous Improvement? Knowledge gets the process into good shape, and

makes them so well understood, that the chance of any thing going seriously wrong with them is negligible - which itself constitutes huge saving.

Operation becomes hassle free. It contributes to innovation. Enhanced morale and pride in workmanship. Less or no warranty. Meeting specification are not good enough.

Demings Fourteen PointsDemings Fourteen Points

Constancy of Purpose. The new philosophy. Cease dependence on mass inspection. End lowest tender contract. Improve every process. Institute training. Institute Leadership of people. Drive out fear. Break down barriers. Eliminate Exhortations. Eliminate Arbitrary numerical targets. Permit pride in workmanship. Encourage education. Top management commitment and action.

Documents

SPC presentation.ppt