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Chapter 7

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If the distribution is normal,

then mean=median=mode If R is in control and distribution

is normal, then alternatively you can plot the medians

Disadvantage: Less sensitive to changes in the average

Advantage: Simpler to use

Median & Range Charts

Randx ~

333333333

1. Select a process measurement2. Stabilize process and decrease

obvious variability3. Check the gages (10:1, GRR)4. Make a sample plan. Choose an

odd number 3, 5, 7 …5. Setup the charts and process log6. Setup the histogram7. Take the samples and chart the

points8. Calculate the control limits and

analyze for control9. Calculate the capability and

analyze for capability10. Monitor the process11. Continuous improvement

11 step procedure for control charts (median&R)

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How to calculate control limits

For the range control chart:

For the median control chart:

RDLCLRDUCL

LimitsControl

nR

RrangeAverage

R

R

3

4

RAxLCLRAxUCL

LimitsControl

nx

xx

Average

x

x

2~

2~~~

~~

~~ ~

555555555

Notes page for exercise

777777777

Exercise values

Subgroup 1 2 3 4 5 6 7 8 9 101 0.615 0.625 0.628 0.63 0.638 0.628 0.607 0.63 0.632 0.6172 0.61 0.606 0.614 0.632 0.621 0.61 0.62 0.621 0.61 0.6263 0.608 0.604 0.61 0.619 0.624 0.611 0.614 0.628 0.618 0.621

Sum 1.833 1.835 1.852 1.881 1.883 1.849 1.841 1.879 1.86 1.864Median 0.61 0.606 0.614 0.63 0.624 0.611 0.614 0.628 0.618 0.621R 0.007 0.021 0.018 0.013 0.017 0.018 0.013 0.009 0.022 0.009

Subgroup 11 12 13 14 15 16 17 18 19 201 0.63 0.604 0.605 0.625 0.621 0.634 0.618 0.63 0.639 0.6352 0.61 0.607 0.603 0.619 0.634 0.62 0.616 0.611 0.637 0.623 0.605 0.612 0.606 0.625 0.625 0.627 0.627 0.617 0.624 0.618

Sum 1.845 1.823 1.814 1.869 1.88 1.881 1.861 1.858 1.9 1.873Median 0.61 0.607 0.605 0.625 0.625 0.627 0.618 0.617 0.637 0.62R 0.025 0.008 0.003 0.006 0.013 0.014 0.011 0.019 0.015 0.017

Subgroup 21 22 23 24 251 0.619 0.624 0.611 0.625 0.6072 0.63 0.61 0.618 0.614 0.6343 0.628 0.62 0.615 0.622 0.623

Sum 1.877 1.854 1.844 1.861 1.864Median 0.628 0.62 0.615 0.622 0.623R 0.011 0.014 0.007 0.011 0.027

888888888

Same type of chart as the

average and range chart Uses sample standard deviation

instead of range Used for large sample sizes Need the use of a computer or

calculator to make this practical

Average & Standard Deviation Charts

sandx

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1. Select a process measurement2. Stabilize process and decrease

obvious variability3. Check the gages (10:1, GRR)4. Make a sample plan 5. Setup the charts and process log6. Setup the histogram7. Take the samples and chart the

points8. Calculate the control limits and

analyze for control9. Calculate the capability and

analyze for capability10. Monitor the process11. Continuous improvement

11 step procedure for control charts

101010101010101010

How to calculate control limits

For the standard deviation control chart:

For the mean control chart:

sBLCLsBUCL

LimitsControl

ns

ss

s

3

4

DeviationStandardAverage

sAxLCLsAxUCL

LimitsControl

nx

xx

Average

x

x

3

3

443 ˆ 3

cs

ncA

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Notes page for exercise

Class exercise (pg 597)

s

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In industry, there are many different types of processes. The main types, along with a brief description of each are listed below:

Short run/small run - Could be very slow or very fast manufacturing cycles. Some short run processes produce a few intricate products over long time periods while other short runs produce large numbers of parts, but in short time periods.

Mass production - Repetitive, long-running assembly line type processes that produce large numbers of individual products.

Batch - Producing quantities of similar materials in a single lot or batch. Examples include vats of materials produced for the food industry, drums of paint all mixed at one time, or other quantities of raw materials mixed together to produce a finished product.

Continuous - A non-stop process that is continually fed raw materials on one end, producing a steady stream of finished product on the other end. Examples include petroleum, paper, powders, and pellets.

Industrial processes

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Short run processes include both very slow and very fast manufacturing cycles.◦ Short run processes include operations that

create: A small number of complex products in a long

period of time A large number of products in a very short

period of time One product per run

Mass production may produce hundreds, thousands or millions of parts per year. ◦ It becomes economically impossible to

measure each and every part as it is finished on the machine.

◦ Requires dedicated measuring equipment, tooling and checking fixtures to be used and a much different quality measurement system than other processes.

Short run vs. mass production

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We have seen how to deal with large quantities of data – usually associated with mass production (sampling for control and acceptance)

Part of this topic is in Chapter 7 (short run) and part is in Chapter 8 (small run)

We also have to think statistical “process” control – not statistical “part” control

How to handle short run

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Limited data Spread out over long periods of

time Less chance to detect variation Part runs finish before trends

can be seen Risk of control limits too tight

(over sensitive)

Problems with short/small run

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Statistical “process” control or statistical “part” control?

Your book mentions a way to deal with small data sets using inflated D4 and A2 values.

We will skip that part because it promotes “part” control and calculating control limits based on limited data

Instead we will concentrate on the part that promotes “process” control – nominal or target charts

Note:Your book uses a term called the “T test” – don’t confuse this with the student-t test, commonly referred to as the “t-test”

S”P”C?

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Used when a process produces several different parts

This type of process is assumed to produce the same variation on all parts produced

This allows all parts to be tracked on one control chart

Commonly known as the

Nominal or target charts

chart & Nominal Rx

191919191919191919

All processes are considered the same

Variation is the same for all parts produced

Sample size is the same Recommended for use with

specific types of gaging that resolves in delta values (i.e. indicators)

Criteria for use

202020202020202020

Used to simplify arithmetic with the chart

Used with certain types of gaging

Used on target charts

Coding data

Measurement Coded Value Coded Valuebased on .1 based on target Base=1.5

1.5 0 01.6 1 0.11.3 -2 -0.21.1 -4 -0.41.7 2 0.2

212121212121212121

1. Code each measurement by subtracting the target value

2. Chart the coded values on the

and specify different parts with vertical lines

3. Calculate average, range, and control limits - analyze for control in the usual manner

4. Calculate and analyze process capability

How we do it

chart & Nominal Rx

222222222222222222

Used to track several measurements from several processes on one chart.

Only restriction is they must have the same sample size and they are expected to perform the same.

This is a very advanced control chart used to normalize the data.

We will do one similar to these when we do the Gage R&R analysis, except we will not code the data.

Transformation chart

232323232323232323

Notes page for exercise

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Nominal chart exercise data

Subgroup 1 Subgroup 2 Subgroup 3 Subgroup 4 Subgroup 5 Subgroup 6 Subgroup 7 Subgroup 8 Subgroup 9 Subgroup 101.95 3.93 1.91 3.51 2.83 2.03 1.76 2.52 2.67 2.042.91 3.33 2.91 2.34 2.40 5.01 3.93 4.52 5.04 2.142.95 3.33 1.84 3.42 3.49 1.54 2.10 3.11 3.99 2.542.20 2.71 2.87 3.85 2.88 1.21 2.72 2.42 2.66 4.54

xbar 2.4996 3.3267 2.3843 3.2798 2.8997 2.4467 2.6287 3.1414 3.5888 2.8186R 1.0014 1.2206 1.0715 1.5082 1.0904 3.7933 2.1676 2.0972 2.3750 2.4997

-1.05 0.93 -1.09 0.51 -0.17 -0.97 -1.24 -0.48 -0.33 -0.96-0.09 0.33 -0.09 -0.66 -0.60 2.01 0.93 1.52 2.04 -0.86-0.05 0.33 -1.16 0.42 0.49 -1.46 -0.90 0.11 0.99 -0.46-0.80 -0.29 -0.13 0.85 -0.12 -1.79 -0.28 -0.58 -0.34 1.54

xbar -0.5004 0.3267 -0.6157 0.2798 -0.1003 -0.5533 -0.3713 0.1414 0.5888 -0.1814R 1.0014 1.2206 1.0715 1.5082 1.0904 3.7933 2.1676 2.0972 2.3750 2.4997

Xbar-bar -0.09856 2.9014Rbar 1.88249

Subgroup 11 Subgroup 12 Subgroup 13 Subgroup 14 Subgroup 15 Subgroup 16 Subgroup 17 Subgroup 18 Subgroup 19 Subgroup 205.08 5.33 6.20 4.86 5.64 7.99 5.06 5.61 4.62 4.396.50 4.97 4.83 6.02 6.09 6.33 6.13 5.64 5.02 7.104.99 6.85 5.92 4.09 6.79 6.73 6.02 3.82 4.11 6.655.58 6.13 6.20 5.14 5.74 6.48 4.69 5.46 7.40 5.36

xbar 5.5377 5.8199 5.7866 5.0265 6.0667 6.8820 5.4743 5.1322 5.2864 5.8759R 1.5146 1.8814 1.3653 1.9310 1.1571 1.6559 1.4380 1.8194 3.2922 2.7060

-0.92 -0.67 0.20 -1.14 -0.36 1.99 -0.94 -0.39 -1.38 -1.610.50 -1.03 -1.17 0.02 0.09 0.33 0.13 -0.36 -0.98 1.10

-1.01 0.85 -0.08 -1.91 0.79 0.73 0.02 -2.18 -1.89 0.65-0.42 0.13 0.20 -0.86 -0.26 0.48 -1.31 -0.54 1.40 -0.64

xbar -0.4623 -0.1801 -0.2134 -0.9735 0.0667 0.8820 -0.5257 -0.8678 -0.7136 -0.1241R 1.5146 1.8814 1.3653 1.9310 1.1571 1.6559 1.4380 1.8194 3.2922 2.7060

Xbar-bar -0.31118 5.6888Rbar 1.87609

Subgroup 21 Subgroup 22 Subgroup 23 Subgroup 24 Subgroup 253.46 5.58 2.07 4.12 3.944.60 4.28 4.52 3.89 3.873.69 3.06 1.14 2.39 4.194.29 3.54 3.45 3.86 3.05

xbar 4.0132 4.1156 2.7968 3.5621 3.7606R 1.1395 2.5271 3.3789 1.7302 1.1410

-0.54 1.58 -1.93 0.12 -0.060.60 0.28 0.52 -0.11 -0.13

-0.31 -0.94 -2.86 -1.61 0.190.29 -0.46 -0.55 -0.14 -0.95

xbar 0.0132 0.1156 -1.2032 -0.4379 -0.2394R 1.1395 2.5271 3.3789 1.7302 1.1410

Xbar-bar -0.35033 3.6497 Xbar-bar -0.23396Rbar 1.98334 Rbar 1.90010

Overall

Actual Values

Coded Values

Actual Values

Tolerance 3+/- 2

Actual Values

Coded Values

Coded Values

Tolerance 6+/-3

Tolerance 4+3/-1