Introduction to Quality Assurance 255323

2 2 .....

( Quality Characteristics)

variables (continuous)

Variable control charts ()

attributes (discrete) attributes (discrete)

Attribute control charts ( Attribute control charts ()

Variable control charts

Variable control charts ()

(continuous)

- Quality characteristic Quality characteristic

- Central tendency () (e.g. mean)

- measure of variability () (e.g. R or SD)

- X R Chart, X S Chart

Control Charts for and Rx

Control Charts for and R xX chart ()R Chart ()R Chart ()

Choice of control limitsChoice of control limits control limits (k-sigma limits) 3 control limits

+3

- 3

The use of 3 control limits is a widespread practice.

0 997 (99 73%)

xx 3 0.997 (99.73%)

xx 2 0.9545 (95.45%)

x

1 0.6826 (68.26%)

xx 1( )

- The # of items between 3 = 99.73%- It is expected that over 997 times out of 1000 the subgroup- It is expected that over 997 times out of 1000, the subgroup values will fall between the upper and lower limits, and when this occurs, the process is considered to be in control.

Subgroup Data with Unknown and

Center lineCenter line

Average range

Phase I Application of and R Chartsxase pp cat o o a d C a ts m subgroups

20-25 subgroups

xg p

subgroup (sample size, n) 3 5 T i l t l li it Trial control limits

out-of-control assignable causes assignable causes

trial control limits out of control control

charts control charts

11

control charts out of control

(N t i t l (Note in control out of control

assignable causes trial control limits )

in control control limits

assignable causes , 2 g ,1.

2. control limits

-25 samples, each of size 5 -time between subgroup = 1hr

13

R chart control limits on the X chart process

variability process variability in control X chart control, X chart

Revision of Control Limits and Center LinesRevision of Control Limits and Center Lines

control charts control limits and center lines control limits and center lines 25,50 or 100 samples

Phase II Operation of ChartsPhase II Operation of Charts

control limits control chart (monitoring) control chart (monitoring)

Out of control

(Douglas C. Montgomery, 2005) ( g g y, )- R chart

- R chart out of control assignable cause R

- R control limits X R chart

- out of control assignable cause assignable cause

Control vs. Specification Limitsp Control limits

(natural process variability) ( p y) subgroupsubgroup

Specification limits quality ycharacteristic

22

control limits specification limits

R Charts x R chart

R Charts x R chart in control

( assignable causes R chart )( g )

Cyclic patterns

h t x chart

x

(operator fatigue)

( regular rotation of operators/mc)

R chart

(maintenance schedules), (operator fatigue)

Mixture

control limits , center line center line

2

overcontrol overcontrol ( dj t t) (process adjustment) ,

Shift in process level ,

Trend

(operator fatigue)

(Seasonal influences) (Seasonal influences)

Stratification

control charts

1 5

X h d MR h X-chart and MR-chart

Sample size, n = 1 -

- continuous process - continuous process

C t l h t f i di id l Control chart for individual

Moving range of 2 successive observations

31

Control chart for individual observations (X-chart)

Moving Range Chart (MR-chart)Moving Range Chart (MR-chart)

(X-chart)

(MR-chart)

(Process standard deviation)

MR=2

d

n = 2, d2 = 1.128

Process Capability Analysis

( ifi ti ) ( specification)

C , C k Cp, Cpk

In control

(Lower Natural Tolerance Limit)

(Upper Natural Tolerance Limit)

Process Capability The uniformity of the process The true process capability cannot be determined until the

process is in control.p Process capability = 6 can be obtained from control charts

Capability Index or Process Capability Ratio Capability Index or Process Capability Ratio (PCR)

The larger, the betterthe better

From Example 5 1From Example 5.1

Spec 1.50 0.50 microns From X bar R chartFrom X bar R chart

Cp 1.33 Assume that processed is centered at the midpoint of the pspecification band.

43

If Cp = 1.00 2 process capability is If Cp 1.00 2 process capability is equal to tolerance

Cp > 1.00 1 process capability is less than tolerance (Most wanted!)

Cp < 1.00 3 process capability is t th t lgreater than tolerance

- Cp process is centered. ( process mean

ifi ti ( i l))specification (nominal))

spread of specification 6- spread of specification 6spread in the process

-Cp doesnt measure process performance in terms of the nominal or target value.

C does not take process centering Cp does not take process centering into account

It is a measure of potentialcapability, not actual capability

(Process potential (Process potential capability)

Process Capability Ratio for an Off-Center Process

Use Cpk if the process mean differs from the spec medium valuemedium value.

GuidelineCpk 1.0: Insufficient process capabilityCpk 1.33: No major problem with the

process capabilityprocess capability

Cp = Cpk Process is centered at the midpoint of specificationCp Cpk Process is centered at the midpoint of specificationCpk < Cp Process is off-center.

Cp measures potential capabilityCpk measures actual capability

Potential improvement that would bePotential improvement that would be possible by centering the process

Since LSL = 200 Since LSL = 200

7-5 strength PCR (one sided) PCR (one- sided) 1.45

Attribute control chartsAttribute control charts

quality characteristic Variable control charts ()

(Continuous Value)

Attribute control charts ()

(Discrete Value) quality characteristic quality characteristic /

(C f i / f i ) (Conforming/nonconforming)

(# of nonconforming on a unit of product)

Go no go gage

spec

59Go no go gage is on left, finishedpart to be checked is on right

Attribute control charts Attribute control charts

np Chart, p Chart (control charts for fraction nonconforming)

Ch Ch ( l h f c Chart, u Chart (control charts for nonconformities (defects))nonconformities (defects))

np Chart, p Chart

p Chart (proportion) p (p p )

(sample or subgroup) np Chart (# nonconforming) np Chart (# nonconforming) p Chart np Chart

p Chart () ,

Binomial distribution (success/failure, pass/fail, heads/tails)Binomial distribution (success/failure, pass/fail, heads/tails)

1. (Variables)

R (or S) Chart ( ) x Chart ()

2. (Attributes)

np Chart ()(Attributes)

p Chart ()

c Chart ()

u Chart ()

p Chart

p Chart (proportion) p Chart (proportion) (sample or subgroup)

n (sample size) m (subgroups) n (

20, 50, 100 ) (D)

(The average proportion nonconforming)

p-chart p-chart quality characteristics

Trial central line and control limits (3 control limits)

LCL 0

c Chart, u Chart (Defects)

1 c Chart

(count of nonconformities (defects)) u Chart

(count of nonconformities per unit) c Chart u Chart u Chart Poisson distribution

c-chart Subgroup size = 1 inspected unit Subgroup size 1 inspected unit, subgroup 25 1 inspected unit =

1000 f 2 1000 feet2

1

Trial control limits

LCL 0

Inspection unitInspection unit

subgroup

n =1 Inspection unit = 100 boards n =1 Inspection unit = 100 boards 1 Inspection unit = 250 boards 2.5

(n =2.5 Inspection units ) Control limits Control limits

cncn 3 CL = (2 5)(19 67) = 49 18

cncn 3CL (2.5)(19.67) 49.18

Control limits = 18.49318.49 LCL = 28.14, UCL = 70.22