CorrectSPC with case studies

CorrectSPC: Non-Shewhart SPC

in Precision Machining

Presenter

BOB DOERING

DEFINITION:STATISTICAL PROCESS CONTROL

The monitoring and reactionto a process

based on statistical methodologies

DEFINITION:STATISTICAL PROCESS CONTROL

Shewhart charts are a subset

of all statistical process control methodologies

PRECISION MACHININGSTATISTICAL PROCESS CONTROL

SPC charting typically found in Precision Machining operations• X-Bar R charts or I-MR• Compressed control limits• Capability indices too high or too low, or• Bimodal distributions

PRECISION MACHININGSTATISTICAL PROCESS CONTROL

IT SIMPLY CANNOT BE THAT BAD!

STATISTICAL PROCESS CONTROL

AIAG PPAP 4th Edition2.2.11.3 Acceptance Criteria for Initial StudyThe organization shall use the following as acceptance criteria

for evaluating initial process study results for processes that appear stable.

Results

Index > 1.67

1.33≤ Index ≤ 1.67

Index ≤ 1.33

Interpretation

Meets acceptance criteria

May be acceptable

Does not meet acceptance criteria


AIAG PPAP 4th Edition2.2.11.5 Processes with One-Sided Specifications or

Non-Normal Distributions

The organization shall determine with the authorized customer representative alternative acceptance criteria for processes with one sided specifications or non-normal distributions.


When this is not true, using this analysis may result in unreliable information.



NOTE: The above mentioned acceptance criteria (2.2.11.3) assume normality and a two-sided specification (target in the center).




NOTE (cont.): These alternate acceptance criteria could require a different type of index

or some method of transformation of the data. The focus should be on understanding reasons for the

non-normality (e.g. is it stable over time?) and managing variation.

CONTROL CHARTING

HOW DO MOST PEOPLE CHOOSE THEIR CONTROL CHART?

CONTROL CHARTINGTHEY BELIEVE THE

URBAN LEGEND THAT X-BAR/R CHARTS WORK FOR

ANY DISTRIBUTION!

CONTROL CHART BASICSNORMAL PROCESS:

IN CONTROL WITH CHANCE VARIATION

IN ORDER FOR A PROCESS TO BE NORMAL, IT SHOULD BE ABLE TO BE SET AT THE MEAN, AND WILL CONTINUE TO RANDOMLY VARY

ABOUT THE MEANWITHOUT ANY OPERATOR INTERVENTION!

CONTROL CHART BASICSEXAMPLES OF PROCESSES WITH

NORMAL VARIATION

CUTTING GRASS

WHAT IS CONTROL?

A process in control is in the ideal state 100% conforming and predictablemust remain stable over timemust operate in a stable and consistent

mannermust be set at the proper level

(centered)the natural process spread must not

exceed the product’s specified tolerance (capable)

WHAT ARE THE TYPES OF VARIATION CAUSES?

COMMON CAUSE• Inherent in the process• Affects every part• Examples: gravity, air pressure, tool wear SPECIAL CAUSE• “Assignable”• Does not affect every part• Examples: tool breakage, start up, change of

operators

TRADITIONAL SPC• Expects all “special causes” have been

eliminated• Expects the remaining variation is

random, with most variation close to a central value

• Seeks to find trends from within an otherwise random output to act upon when they occur

TRADITIONAL SPC

Traditional SPC is like looking out into space seeking signs of life

Search for Extraterrestrial

Intelligence(SETI)

TRADITIONAL SPC

Typically, you listen to random radio frequency noise searching for a

“pattern” – as a pattern shows intent

TRADITIONAL SPC

If you find such a trend, then you can take action to determine its origin. This is

more “monitoring” than “control”

Wow! signal was a strong narrowband radio signal

detected by Dr. Jerry R. Ehman on August 15, 1977, while

working on a SETI project at The Big Ear radio

telescope of The Ohio State University

PROCESS DEFINITIONS

DEFINITION OF PRECISION MACHININGA process where material is removed by a

cutting surface – such as grinding, honing, turning, milling, etc.

The process must be controlled in a manner that all variation (vibration, bearings, gage error) is statistically insignificant except tool wear.

CONTROL CHART DEFINITIONS

TOTAL VARIANCE EQUATION

s2T = s2

Tool Wear +s2Measurement Error +

s2Gage Error + s2

Material + s2Temperature + s2

Operator

+ s2Other

PROCESS DISTRIBUTION






“Process Control and Evaluation in the Presence of Systematic

Assignable Cause”, Ashok Sarkar and Surajit,Pal,

Quality Engineering, Volume 10(2), 1997-1998

d2

Slide 27

d2 I was sitting in a process planning meeting (APQP) when the engineers around the table proclaimed that the grinder they had would not be capable of running a part to a specific diameter tolerance. I felt they were just shooting from the hip, and I was curious if it wastrue.

I went out to the grinder and spoke to the operator. He was doing SPC on his operation, plotting the outer diameters. I looked at the chart, and it was a classic normal control chart with points randomly jumping about the mean.

I asked how often he was plotting his data, he said every two hours, just like the control plan said. I asked him how often he was adjusting his process, he said every 15 minutes.

My head dropped in dismay...

I asked him to try something different. I asked him to adjust his grinder to the lower control limit. I told him to ignore the mean. Run the grinder, and do not adjust it until the diameter reached the upper control limit. Then, adjust it back to the lower control limit.

He did that. Do you know how long it took to reach the upper control limit?

A week.

So, clearly his adjusting every 15 minutes to try to keep the machine at the mean was overadjustment. In fact, the operator had become the process. That made the process "normal", and most operator processes are normal distributions. But the machine processwas not. It was a uniform distribution. It was masked by the unnecessary adjustments to the mean by the operator. CNC operators are notorious for overadjustment, because it is easy to push the buttons for an offset. I tell them if they want to push buttons, push the buttons on their calculator, not the machine.

Many quality professionals are fooled by seeing these supposedly 'normal' processes and their accompanying charts, and believe theyreally are. They use these charts to justify their claim that the process is indeed normal, in control and capable. Fools gold, my friends. It is usually garbage data.

X-bar-R charts encourage adjusting to the mean - and therefore encourage overadjustment in precision machining. That is one reasonwhy they are the absolute worst chart for precision machining. For the uniform distribution, the mean has no meaning!

If I walk up to a precision machining process and see an X-bar-R chart exhibiting random variation about the mean, my first assumption is the process is out of control! doeringr, 10/13/2008


d3

Slide 28







A week.






d4

Slide 29







A week.






AIAG SPC 2nd EditionRepeating Patterns

“There are times when repetitive patterns are

present in control charts due to known assignable causes – causes that can

not be economically eliminated.” (p. 175)

d5

Slide 30







A week.







“When these types of repetitive patterns exist, the average chart will exhibit conditions associated with an out-of-control process since there is

(economically influenced) special cause acting on the process .”

d6

Slide 31







A week.







“If the influence of this special cause can be shown to be predictable over time and the additional variation is

acceptable to the customer (?), then the process controls can be modified

to allow it.” (p. 176)

d7

Slide 32







A week.





CENTRAL LIMIT THEOREM

The central limit theorem (CLT)sufficiently large number of

independent,each with finite mean and variance,will be approximately normally distributed (Rice 1995).

random variables

CENTRAL LIMIT THEOREM

Precision machining hassufficiently large number ofdependenteach with finite mean and variance,will be not be normally distributed

The central limit theorem does not apply!

non-random variablesof

independent random variables

CHEBYSHEV INEQUALITY

Chebyshev Inequality gives an upper and lower bound for the probability that a value of a random independent variable with finite variance lies within a certain distance from the variable's mean

CONTROL CHART FEATURES

Interesting points:The MEAN has no real value in

controlling a process with the uniform distribution

CONTROL CHART FEATURES

Interesting points:“Running to the mean” is not how to control a process with the uniform

distribution – it causes overcontrol!

TYPES OF VARIABLE CONTROL CHARTS

There are many types, but the most common on the precision machining shop floor is:

X Bar-R (or X Mean - R)X-Moving Range

and then there is a new option:X Hi/Low – R

But, which is best?

X-BAR R CHARTS

X-BAR R CHARTS

X-BAR R CHARTS

Control Chart Data CollectionKey Question For Machining Round Parts:How many diameters are there in a circle?

d

X-BAR R CHARTS

Control Chart Data CollectionHow many diameters are there in a circle?

There are an infinite number of diameters in a circle!

X-BAR R CHARTS

X-BAR R CHARTS

X-BAR R CHARTS

Control Chart Data CollectionThere are also an infinite number of lengths

in a linear feature!

X-BAR R CHARTSWhy are X-bar – R chart control limits

ridiculously tight for precision machining?

• Because they are based on the range of your sample.

• The variation of the range of your sample is nearly zero, except for your measurement error!

• It has nothing to do with your process variation over time!

X-BAR R CHARTS

The X bar chart from the X bar – R charts represent the average of an insignificant sample of measurements for a of a circular featureMeasuring multiple samples is a waste of time in precision machining R charts from the X bar – R charts represent the range of measurement errorControl limits are calculated using statistics for the wrong distribution – the normal distribution

PRECONTROL CHARTS

X-MR CHART

Rule No.1Original data should be presented in a way

that will preserve the evidence of the original data for all the predictions assumed to be

useful.

-Dr. Walter A. ShewhartStatistical Method from the Viewpoint of Quality Control

CONTROL CHART DATA

Rule of life:If you measure one diameter, you will

measure a good one…and the customer will measure a bad

one!

CONTROL CHART DATA

How do you control diameters?

Measure the part and record the largest and smallest diameters

– then, by definition, you are controlling all possible diameters!

CONTROL CHART DATA

CONTROL CHART DATA

What else can you learn from the largest and smallest

diameter?

The difference between the largest and smallest radii – by

definition– is the roundness!

CONTROL CHART DATA

Although technically the difference between the largest and smallest radii is the roundness,

charting the difference between the largest and smallest diameters is less math,

less opportunity for math errors and will still exhibit the same signals.

It also keeps the charts consistent in terms of diameters .

CONTROL CHART DATA

CONTROL CHART DATA• You are going to have to “untrain” your

operators from adjusting to the mean to properly control a precision machining process

CONTROL CHART DATA

• They will have to “stop pushing the buttons”

CONTROL CHART DATA• They will have to be trained to adjust

the process to the control limit, stand back and let the tool wear

CONTROL CHART DATA• They will have to be trained to adjust

the process to the control limit, stand back and let the tool wear

CONTROL CHART DATA

Variation observed is actually from measurement error, not process variation

CONTROL CHART DATA

Measurement error does not provide process information

TREND CHARTPopular chart for tool wear applications

Trend chart uses control limits calculated from measurement error, not process variationTHAT IS WHY IT IS A USELESS CHART!


TOTAL VARIANCE

s2T = s2


s2Gage Error + s2


Operator

+ s2Other


TOTAL VARIANCE

s2T = s2


s2Gage Error + s2


Operator

+ s2Other

CONTROL CHART DEFINITIONSTREND CHART

• Difficult to prepare and maintain• Difficult to train and use• Has invalid statistical basis for its control• Provides little useful information to control the

process

X HI/LO – R CHART

X HI/LO – R CHART

X HI/LO – R CHARTSAMPLING FEQUENCY

• Sane sampling frequency• Number of parts it takes to go from one control

limit ot the other - divide by five

X HI/LO – R CHART CONTROL LIMITS


TOTAL VARIANCE

s2T = s2


s2Gage Error + s2


Operator

+ s2Other

OBSERVE THE COLOR CODE!


99.73%

75%


99.73%

75%

Guard banding to protect from remaining sources of variances

EVALUATING CAPABILITY

Capability = USL - LSLUCL - LCL

1.33 = USL – LSL .75 (USL – LSL)

EVALUATING CAPABILITYEFFECT OF

INCREASING CAPABILITY

X HI/LO CHARTEVALUATION RULES

• Look for trends in the “wrong” direction• Can occur with roughing/finishing

operations• Roughing tool wears at a different rate

that finishing tool• Change in tool pressure can affect

finished dimension• As long as you know the cause – continue• If not, stop and assess the problem

R CHARTEVALUATION RULES

• If the Range starts to increase, this means the roundness is getting worse

• Increased roundness is a leading indicator of tool wear, and by changing the tool at the control limit for the range, you will maintain more consistent results and may catch the tool before it breaks

CASE STUDIES

CASE STUDY• Three groups were sent to the shop floor to collect

data from CNC machining processes• Each group had one person charting X-bar/R,

another person charting I-MR and a third charting X hi/lo-R. A fourth person was charged with observing any changes – tool change, offsets, etc.

• At the end of the study, the charts and their signals were compared

GROUP 1 – CNC OD

GROUP 1 – CNC ODX hi/lo-R Chart

GROUP 2 – CNC OD

GROUP 2 – CNC ODX hi/lo-R Chart

CONCLUSION• Precision diameters and lengths should

be primarily affected by tool wear• Tool wear and associated adjustment for

tool wear generates the “sawtooth curve”• The sawtooth curve’s distribution is the

continuous uniform or rectangular distribution

• The uniform distribution is non-normal, and does not follow the rules of normality, such as Cpk calculations or the ‘Western Electric Rules” for control chart evaluation

CONCLUSION• In order to properly control precision

machining the process must be set to the control limit, then do not touch the process until the tool wears to the opposite limit

• This generates the proper “sawtoothcurve”

• Operators will have to be trained notto run to the mean

CONCLUSION• The X bar chart from the X bar – R charts

represent the average of a statistically insignificant sample of measurements for a of a circular feature

• R charts from the X bar – R charts represent the range of measurement error

• Control limits are calculated using statistics for the wrong distribution – the normal distribution

CONCLUSION• X hi/lo – R charts represent the GD&T

characteristics of a circular feature: diameter and the zone represented by roundness (or length and parallelism for a linear dimension)

• X hi/lo – R charts provide more valuable data, such as tool wear rate

• X hi/lo – R charts use the correct uniform distribution for precision machining

CONCLUSION• X hi/lo – R charting techniques can be

expanded to control taper• Automated tool wear compensation is not

statistical process control• The algorithm for compensation

becomes the process, not tool wear• Lose some benefits of SPC because

the constant adjustment masks the information

• Would help if the compensation was tracked

CONCLUSION

"The total information is given by the observed

distribution.”

-Dr. Walter A. ShewhartEconomic Control of Quality of Manufactured Product

CorrectSPC

PROCESS CONTROL FOR PRECISION MACHINING

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CorrectSPC with case studies