Statistical Process Control

(SPC)

What is Quality?

Fitness for use Conformance to the standard

Quality ImprovementQuality improvement processes that involve statistical method;

1. Incoming Quality Control

2. Statistical Process Control

3. Outgoing Quality Control

Incoming & Outgoing QCAcceptance Sampling

Lot by lot sampling plan for attributes Acceptance sampling by variables

Lot by Lot Sampling Plan For Attributes

Types Of Sampling Plan Single Sampling Plan Double Sampling Plan Multiple Sampling Plan Sequential Sampling Plan

MIL STD 105E (ISO 2859)

Acceptance Sampling By VariablesTypes Of Sampling Plan Plan that control the lot/process fraction

defective/nonconforming. Plan that control the lot/process parameter

MIL STD 414 Tables

Statistical Pocess ControlChance and Assingable Cause Of Quality

Statistical basis for control chart Basic Principles Choice Of Control Limit Sample Size & Sampling Frequency Subgroups Analysis Of Patterns On Control Charts

Control Charts For Variables (Univariate)

chartsRandx

xxx

chartssandx

Statistical basis of the charts Development and use of the charts Interpretation of the charts The operating characteristics function Average Run Length (ARL) for the mean chart

chartsRandx

Constuction & Operation of the charts

Control charts with variable sample size

chartssandx

Control Charts For The AttributesControl Charts for the fraction non-conforming Development & Operation Variable sample size OC and ARLControl Charts for non-conformities Procedure with constant sample size Procedure with variable sample size OC and ARL

Process Capability Analysis

Using histogram Using probality plots Process Capability Ratio (PCR)

Cp

PCR for an of center process Normality and PCR Confidence Interval & Test on PCR PCR using control charts

Chance and Assingable Cause Of Quality 2 types of variation

1. Natural variability (chance)

2. Assignable causes

Process with assignable causes is said to be out of control.

Basic Principles Control charts consist of

Center line Upper control limit Lower control limit

These limits is chosen so that when the process is in control, almost all the sample points will fall within the control limits.

Choice Of Control Limit2 types of control limits Three-sigma limits.

The distance between CL and the UCL/LCL is 3 sigma.

The 0.001 probability limits chart (use 3.09 sigma). The distance between CL and the UCL/LCL is 3.09 sigma.

Note:-

3-sigma limits popular in US.

0.001 prob. limits popular in UK & Western Europe.

Sample Size & Sampling Frequency Larger samples easier to detect.

Use large sample if the shift of interest is small and small sample if the shift of interest is large.

Frequent sampling is better.

Current practice favour small but more frequent samples.

Analysis Of Patterns On Control Charts

Process out of control if

1. One or more points fall outside the control limits.

2. Points exhibit some non-random pattern.

3. Exhibit a cyclic behaviour.

Pattern recognitionProcess is out of control if One point plots outside the control limit. Two out of three consecutive points plot beyond the

two sigma warning limits. Four out of five consecutive points plot at a distance

of the one sigma or beyond from the center line. Eight consecutive points plot on one side of the

center line.

Control Charts For Variables (Univariate)

chartsRandx

xxx

chartssandx

Control Charts For Attributes

•Control Chart For Fraction Nonconforming

•Control Chart For Nonconformities

chartsx

RAxLCL

xCL

RAxUCL

2

2

chartsR

RDLCL

RCL

RDUCL

3

4

chartsS

24

4

24

4

c1c

S3SLCL

SCL

c1c

S3SUCL

givenstd)chartsp(

ChartgminNonconforFraction

n

)p1(p3pLCL

pCLn

)p1(p3pUCL

)givenstdno()chartsp(

ChartgminNonconforFraction

n

)p1(p3pLCL

pCLn

)p1(p3pUCL

)givenstd()chartsc(

ChartControlitiesNonconform

c3cLCL

cCL

c3cUCL

)givenstdno()chartsc(

ChartControlitiesNonconform

c3cLCL

cCL

c3cUCL

Process CapabilityCalculated using

1. Process capability ratio (PCR), Cp.

2. Probability ;

*need to know process std deviation

)ˆ

xUSLz(P)

ˆxLSL

z(P

)USLx(P)LSLx(P

Process standard deviation

Process standard deviation is calculated by

*use to estimate process capability

2d

Rˆ

Process Capability Ratio (PCR), Cp

6

LSLUSLCp

And is estimated by

ˆ6

LSLUSLCp

Interpretation

What does it mean if Cp < 1 Cp = 1 Cp > 1