Short Run Statistical Process Control.ppt

IENG 486 - Lecture 21

Short Run SPC

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IENG 486 Statistical Quality & Process Control

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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: 

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1a, 17, 26

Hint: Use Excel charts!

IENG 486 Statistical Quality & Process Control

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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    

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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 TM 720: Statistical Process Control

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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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TM 720: Statistical Process Control

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DNOM Charts  Deviation from Nominal 

Variable computed is the difference between the measured part and the target dimension

xi  M i  Tp where:

Mi is the measured value of the ith part Tp is the target dimension for all of part number p

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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:

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UCL  x  A2 R  A2 R CL  x  0 LCL  x  A2 R   A2 R

UCL  D4 R CL  R LCL  D3 R

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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  

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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 TM 720: Statistical Process Control

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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: 

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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

Ri R  Rj s i

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

UCL  D4 CL  R j LCL  D3

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Standardized Charts – x and R  Standardized x: 

Plotted variable for the sample is s i

x  where:

M i  Tj Rj

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

UCL   A2 CL  0 LCL   A2 09/22/16

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Standardized Charts – x and R  Usage: 

Two options for finding Rj: Prior History  Estimate from target σ: 



Examples:

 d2   R j  σ   c4 

Parts from same machine with similar dimensions  Part families – similar part tolerances from similar setups and equipment 

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Standardized Charts – Attributes  Standardized zi for Proportion Defective: 



Plotted variable is

Control Limits:

zi 

pi  p p (1  p ) n

UCL  3 CL  0 LCL  3

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Standardized Charts – Attributes  Standardized zi for Number Defective: 

Plotted variable is

zi 



Control Limits:

npi  n p n p (1  p)

UCL  3 CL  0 LCL  3

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Standardized Charts – Attributes  Standardized zi for Count of Defects: 

Plotted variable is

zi 



Control Limits:

ci  c c

UCL  3 CL  0 LCL  3

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Standardized Charts – Attributes  Standardized zi for Defects per Inspection Unit: ui  u  Plotted variable is zi  u n UCL  3 

Control Limits:

CL  0 LCL  3

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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. 2.

3. 4.

To start, apply charts to any process or product characteristics believed important. Charts found unnecessary are removed; others that may be required are added. (Usually more charts to start than after process has stabilized) Keep current records of all charts in use, i.e., types and parameters of each. If charts used effectively  number of charts for variables increases and number of attributes charts decreases

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Determine Which Characteristic to Control and Where to Put Charts 5.

6.

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. 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

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Choosing Proper Type of Control Chart: Variables Charts 

Use (x & R) or (x & S) charts when: 1. 2. 3. 4. 5. 6. 7. 8.

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New process or product coming online Chronically troubled process Wish to reduce downstream acceptance sampling Using attributes charts but yield still unacceptable Very tight specifications Operator decides whether or not to adjust process Change in product specs desired 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. 2.

3. 4.

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Operators control assignable causes and it is necessary to reduce fallout Process is complex assembly operation and product quality measured in terms of occurrence of nonconformities: e.g. computers, automobiles Measurement data cannot be obtained 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. 2. 3. 4.

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Repeated measures do not make sense Inconvenient / impossible to obtain more than one measurement per sample Automated testing allows you to measure every unit (EWMA chart may be best) Data becomes available very slowly and waiting for a larger sample is impractical.

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