04/19/23 IENG 486 Statistical Quality & Process Control 1

IENG 486 - Lecture 21

Short Run SPC

04/19/23 IENG 486 Statistical Quality & Process Control 2

Assignment

Reading: Chapter 6

Section 6.4: pp. 259 - 265 Chapter 9

Sections 9.1 – 9.1.5: pp. 399 - 410 Sections 9.2 – 9.2.4: pp. 419 - 425 Sections 9.3: pp. 428 - 430

Homework: CH 9 Textbook Problems:

1a, 17, 26 Hint: Use Excel charts!

04/19/23 TM 720: Statistical Process Control 3

Review

Shewhart Control charts Are for sample data from an approximate Normal distribution

Three lines appear on all Shewhart Control Charts UCL, CL, LCL

Two charts are used: X-bar for testing for change in location R or s-chart for testing for change in spread

We check the charts using 4 Western Electric rules Attributes Control charts

Are for Discrete distribution data Use p- and np-charts for tracking defective units Use c- and u-charts for tracking defects on units Use p- and u-charts for variable sample sizes Use np- and c-charts with constant sample sizes

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Short Run SPC

Many products are made in smaller quantities than are practical to control with traditional SPC

In order to have enough observations for statistical control to work, batches of parts may be grouped together onto a control chart

This usually requires a transformation of the variable on the control chart, and a logical grouping of the part numbers (different parts) to be plotted.

A single chart or set of charts may cover several different part types

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DNOM Charts

Deviation from Nominal Variable computed is the difference between the

measured part and the target dimension

where: Mi is the measured value of the ith part

Tp is the target dimension for all of part number p

pii TMx

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DNOM Charts

The computed variable (xi) is part of a sub-sample of size n

xi is normally distributed n is held constant for all part

numbers in the chart group.

Charted variables are x and R, just as in a traditional Shewhart control chart, and control limits are computed as such, too:

RARAxLCL

xCL

RARAxUCL

22

22

0

RDLCL

RCL

RDUCL

3

4

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DNOM Charts

Usage: A vertical dashed line is used to mark the charts at the point at

which the part numbers change from one part type to the next in the group

The variation among each of the part types in the group should be similar (hypothesis test!)

Often times, the Tp is the nominal target value for the process for that part type

Allows the use of the chart when only a single-sided specification is given

If no target value is specified, the historical average (x) may be used in its’ place

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Standardized Control Charts

If the variation among the part types within a logical group are not similar, the variable may be standardized

This is similar to the way that we converted from any normally distributed variable to a standard normal distribution:

Express the measured variable in terms of how many units of spread it is away from the central location of the distribution

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Standardized Charts – x and R

Standardized Range: Plotted variable is

where: Ri is the range of measured values for the ith sub-sample of this part type j

Rj is the average range for this jth part type

j

isi

R

RR

3

4

DLCL

RCL

DUCL

j

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Standardized Charts – x and R

Standardized x: Plotted variable for the sample is

where: Mi is the mean of the original measured values for this sub-sample of the current part type (j)

Tj is the target or nominal value for this jth part type

j

jisi

R

TMx

2

2

0

ALCL

CL

AUCL

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Standardized Charts – x and R

Usage: Two options for finding Rj:

Prior History Estimate from target σ:

Examples: Parts from same machine

with similar dimensions Part families – similar part

tolerances from similar setups and equipment

4

2

c

dσR j

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Standardized Charts – Attributes

Standardized zi for Proportion Defective: Plotted variable is

Control Limits:

npp

ppz ii

)1(

3

0

3

LCL

CL

UCL

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Standardized Charts – Attributes

Standardized zi for Number Defective: Plotted variable is

Control Limits:

)1( ppn

pnnpz ii

3

0

3

LCL

CL

UCL

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Standardized Charts – Attributes

Standardized zi for Count of Defects: Plotted variable is

Control Limits:

c

ccz ii

3

0

3

LCL

CL

UCL

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Standardized Charts – Attributes

Standardized zi for Defects per Inspection Unit:

Plotted variable is

Control Limits:

nu

uuz ii

3

0

3

LCL

CL

UCL

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Guidelines for Implementing Control Charts

1. Determine which process or product characteristic(s) to control

2. Determine where the charts should be implemented in process

3. Choose proper type of control charts

4. Decide what actions should be taken to improve processes

5. Select data-collection systems and computer software

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Determine Which Characteristic to Control and Where to Put Charts

1. To start, apply charts to any process or product characteristics believed important.

2. Charts found unnecessary are removed; others that may be required are added. (Usually more charts to start than after process has stabilized)

3. Keep current records of all charts in use, i.e., types and parameters of each.

4. If charts used effectively number of charts for variables increases and number of attributes charts decreases

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5. At beginning, use more attributes charts applied to finished units, i.e., near end of process. As more is learned about the process, these are replaced with variables charts earlier in process on critical process characteristics that affect nonconformities.Rule of thumb: the earlier in the process that control can be established, the better.

6. Control charts are an on-line process monitoring procedure; Maintain charts as close to work center as possible.Operators and process engineers should be directly responsible for using, maintaining and interpreting charts

Determine Which Characteristic to Control and Where to Put Charts

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Choosing Proper Type of Control Chart: Variables Charts

Use (x & R) or (x & S) charts when:1. New process or product coming online2. Chronically troubled process3. Wish to reduce downstream acceptance sampling4. Using attributes charts but yield still unacceptable5. Very tight specifications6. Operator decides whether or not to adjust process7. Change in product specs desired8. Process capability (stability) must be continually

demonstrated

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Choosing Proper Type of Control Chart: Attributes Charts

Use p, np, c or u charts when:1. Operators control assignable causes and it is necessary to

reduce fallout2. Process is complex assembly operation and product quality

measured in terms of occurrence of nonconformities: e.g. computers, automobiles

3. Measurement data cannot be obtained4. Historical summary of process performance is necessary.

Attributes charts are effective for summarizing a process for management

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Choosing Proper Type of Control Chart: Individuals Charts

Use (x & MR), MA, EWMA, or CUSUM charts when:1. Repeated measures do not make sense

2. Inconvenient / impossible to obtain more than one measurement per sample

3. Automated testing allows you to measure every unit

(EWMA chart may be best)

4. Data becomes available very slowly and waiting for a larger sample is impractical.