control charts for variables - faculty of …fkm.utm.my/~shari/download/qc05 controlchart1.pdf ·...
Post on 27-May-2018
214 Views
Preview:
TRANSCRIPT
Control charts for variables
CONTROL CHARTS FOR VARIABLES
• Concept of variation - No 2 things are alike
∴ Variation exists
- Even if variation small and appears same; precision instruments show differences
- Ability to measure variation necessary
– before can control. Basically 3 categories of variation in piece – part production (e.g. Light bulbs, washer, nuts, etc.) 1. Within piece - e.g. surface roughness
2. Piece to piece - eg. dimensions
3. Time to time - different outcomes e.g.
morning & afternoon, tool
wear, workers tired
control chartsvariable©smy.fkm.utm 1
Control charts for variables
Many factors contribute to variation
Source of variation - combination of equipments, materials, environment, operator, etc. Equipment - tool wear, electrical fluctuations
for welding Material - tensile strength, moisture content
(e.g. raw material) Environment - temperature, light, humidity etc. Operator - method, SOP followed, motivation
level, training Inspection - inspector, inspection equipment,
environment
control chartsvariable©smy.fkm.utm 2
Control charts for variables
CONCEPT OF CHANCE & ASSIGNABLE CAUSE
• Chance causes are inevitable (unavoidable)
• As long as fluctuate in natural/expected manner stable pattern of chance causes of variation which are small - OK ✓
• If causes of variation large in magnitude; can be identified, classified as assignable causes of variation. If present, process variation is excessive (beyond expected natural variation)
• State of statistical control – chance
• State of out of control – assignable cause
• Body temperature - 36.5oC ~ 37.5oC
control chartsvariable©smy.fkm.utm 3
Control charts for variables
CONTROL CHART METHOD - c.c. means of visualizing variations that
occur in the central tendency and dispersion of a set of observations
- graphical record of a particular quality
characteristic
control chartsvariable©smy.fkm.utm 4
Control charts for variables
• Control limits are not specification limits
• CL are permissible limits of a quality characteristic
• Evaluate variations in quality subgroup to subgroup
• Limits established at ±3 standard dev. from central line; Normal Dist. – 99.73% of items lie within the limits
control chartsvariable©smy.fkm.utm 5
Control charts for variables
OBJECTIVES OF VARIABLE CONTROL CHART
• For quality improvement • To determine process capability • For decisions in product specifications • Provide info. on production processes for
current decisions – SOSC – leave alone SOOC – investigate, solve, rectify, improve
• Make decisions on recently produced items -
release next process, customer or other disposition method, sorting, rework, reject
control chartsvariable©smy.fkm.utm 6
Control charts for variables
VARIABLE CHART How to establish x (average) R (Range) chart? Steps. 1. Select quality characteristics
2. Choose rational subgroup 3. Collect data
4. Determine trial limits and central
line
5. Establish revised central line and control limits
6. Achieve the objective
control chartsvariable©smy.fkm.utm 7
Control charts for variables
1. Choosing quality charac. - measurable data i.e. numbers - 7 basic units, length, mass, time, etc. - affecting performance, function of prdt. - Pareto analysis – highest % rejects,
high prod. costs
- Impossible to put X - R on all charac. selective OR treat as attributes chart
2. Choose rational subgroup
- rational subgroup which have variation within the group due only to chance causes
- two ways selecting subgroup samples 1. Select subgroup samples at one
instant of time or as close as possible
2. Select period of time product produced
control chartsvariable©smy.fkm.utm 8
Control charts for variables
- lots must be homogeneous : same machine, same operator
- decisions on size of sample empirical
judgement & relates to costs
choose n = 4 or 5 → use R-chart
when n ≥ 10 → use s-chart - frequency of taking subgroups often
enough to detect process changes - Guideline of sample sizes/frequency using
Say, 4000 parts/day ∴ 75 samples
if n = 4 ∴ 19 subgroups or n = 5 15 subgroups
control chartsvariable©smy.fkm.utm 9
Control charts for variables
3. Collect data - Use form or standard check sheet - Collect a minimum of 25 subgroups
• Does not matter Vertical or Horizontal
Subgroup Number Measure 1 2 3 4 5 …… ….. …. 25
x1
x2
x3
x4
x5
35
40
32
37
34
34 40 38 35 38
x
35.6
37.0
R 8 6
control chartsvariable©smy.fkm.utm 10
Control charts for variables
4. Determine trial control limits
Central line X and R
X = g
xg
1ii∑
= R = g
Rg
1ii∑
=
X = avg. of subgroup avg. ix = avg. of ith subgroup
g = no. of subgroups
R = avg. of subgroup ranges Ri = range of ith subgroup SIMPLIFIED
xUCL = x3X σ+ → RAX 2+
xLCL = x3σ−X → RAX 2−
UCLR = R + 3σR → D4R
LCLR = R + 3σR → D3R
Where A2, D4, D3 are factors - vary according to different n.
control chartsvariable©smy.fkm.utm 11
Control charts for variables
5. Establish Revised Control Limits
- First plot preliminary data collected using control limits & center lines established in step 4.
- Next step adopt standard values. If
good control i.e. no out-of-control points
oXX →
oRR →
- If there are points out-of-control discard
from data
Look at record - show an assignable cause – don’t use
gdgxxX dnew
−Σ−Σ
=
gdgRdRRnew −
Σ−Σ=
control chartsvariable©smy.fkm.utm 12
Control charts for variables
newo XX = newo RR =
and 2
oo d
R=σ
3σ oox AXCL σ±=
Cont.
Limits UCLR = D2σo LCLR = D1σo
control chartsvariable©smy.fkm.utm 13
Control charts for variables
- Limits for both charts become narrower
after revised - Revised limits used to report / plot future
sub-groups - For effective use – chart must be displayed
and easily seen
control chartsvariable©smy.fkm.utm 14
Control charts for variables
Final comments 1) Many analyst eliminate this revised step -
but actually more representative of process 2) Formula mathematically same
new2newoo RAXA +=σ+X
3) Initial est. of process cap. 6σo
True Cp is next 4) If use specification; nominal (target) value =
oX . Range doesn’t change
5) Adjustments made to processes while taking data – not necessarily running defectives while collecting data
6) Process determines center line and the control limits, not design or manufacturing
7) When population values known easily
obtained limits σ=σ⋅µ= ooX
control chartsvariable©smy.fkm.utm 15
Control charts for variables
6. Achieving objective Initiate control charts results in quality improvement - Less variation in sub-group averages - Reduction in variation of range Reduce frequency of inspection monitoring purpose – even once/mth.
control chartsvariable©smy.fkm.utm 16
Control charts for variables
HOW CONTROLCHART HELPS IN Q.I. • psychological effect to do better • Example: maintenance group helps shift
process center • May be purchasing changed material supplier
to ensure consistent quality • Improvements must be from investigation of
assignable causes (need technical back up)
control chartsvariable©smy.fkm.utm 17
Control charts for variables
SAMPLE STD. DEVIATION CHART
(x - s control chart )
BOTH R chart - simple, use xH & xL MEAS. S chart - more calculation needed, use
OF ALL xi’s ∴ more DISP. accurate, sub-group sample std. dev.
If n < 10 R chart ≅ s chart
n ≥ 10 s chart better R chart not accurate any more
control chartsvariable©smy.fkm.utm 18
Control charts for variables
Reminder:
( )1nxxs i
−−Σ
=
SAME STEPS, DIFF. FORMULA
sAXUCL 3x += sBUCL 4s =
sAXLCL 3x += sBLCL 3s =
DISCARD
d
dnewo ggXXXX
−−Σ
==
d
dnewo gg
ssSS−
Σ−Σ==
44
oo C
sCs
==σ
control chartsvariable©smy.fkm.utm 19
Control charts for variables
oox AXUCL σ+=
oox AXLCL σ+=
UCLs = B6σo
LCLs = B5σo
A, B5, B6 – factors for obtaining 3σ control limits
control chartsvariable©smy.fkm.utm 20
Control charts for variables
STATE OF CONTROL
• When assignable causes eliminated and points plotted are new within C.L. process state of control
• Further improvement through changing basic process, system
• What are the characteristics of process in control? (natural pattern of variation)
• 34% within 1σ from Center Line
• 13% between 1σ & 2σ
• 2.5% of plotted points - 2σ → 3σ
• Points located back & forth across center line random way
• No points out of control
• Subgroup avg’s forms freq. dist which is normal distribution.
control chartsvariable©smy.fkm.utm 21
Control charts for variables
• Control limits – established at 3σ from center line.
• Choice of 3σ is economic decision with respect to 2 types of error.
Type I - occurs when looking for assignable
cause but in reality chance cause present
FALSE ALARM
Limits set ±3σ Type I error prob = 0.27% or 3/1000
Say point our control → due to assign. Even though 3/1000 of the time can be due to chance cause Type II - assume chance cause present, but
in fact assignable cause present
A
Re
c
TRUELARM
ecords indicate 3σ limits balance between 2 rrors.
ontrol chartsvariable©smy.fkm.utm 22
Control charts for variables
control chartsvariable©smy.fkm.utm 23
Process in control 1. Individual parts will be more uniform – less
variation and fewer rejects 2. Cost of inspection will decrease 3. Process capability easily attained 4. Trouble can be anticipated before it occurs 5. Percentage of parts fall between two values can
be predicted with highest degree of accuracy, e.g. filling machines
6. X-R charts can be used as statistical evidence for process control
7. Predictable and stable process only chance causes present
top related