1. IE 355: Quality and Applied Statistics I Short Run SPC
IENG Lecture 21
Short Run SPC
4/19/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen

2. IENG 486 Statistical Quality & Process Control
Assignment
Reading:
Chapter 6
Section 6.4: pp
Chapter 9
Sections 9.1 – 9.1.5: pp
Sections 9.2 – 9.2.4: pp
Sections 9.3: pp
Homework:
CH 9 Textbook Problems:
1a, 17, 26 Hint: Use Excel charts!
4/19/2017
IENG 486 Statistical Quality & Process Control

3. TM 720: Statistical Process Control
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
4/19/2017
TM 720: Statistical Process Control

4. TM 720: Statistical Process Control
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
4/19/2017
TM 720: Statistical Process Control

5. TM 720: Statistical Process Control
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
4/19/2017
TM 720: Statistical Process Control

6. TM 720: Statistical Process Control
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:
4/19/2017
TM 720: Statistical Process Control

7. TM 720: Statistical Process Control
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
4/19/2017
TM 720: Statistical Process Control

8. 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
4/19/2017
TM 720: Statistical Process Control

9. 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
4/19/2017
TM 720: Statistical Process Control

10. 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
4/19/2017
TM 720: Statistical Process Control

11. 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
4/19/2017
TM 720: Statistical Process Control

12. Standardized Charts – Attributes
Standardized zi for Proportion Defective:
Plotted variable is
Control Limits:
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TM 720: Statistical Process Control

13. Standardized Charts – Attributes
Standardized zi for Number Defective:
Plotted variable is
Control Limits:
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TM 720: Statistical Process Control

14. Standardized Charts – Attributes
Standardized zi for Count of Defects:
Plotted variable is
Control Limits:
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TM 720: Statistical Process Control

15. Standardized Charts – Attributes
Standardized zi for Defects per Inspection Unit:
Plotted variable is
Control Limits:
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TM 720: Statistical Process Control

16. Guidelines for Implementing Control Charts
IE 355: Quality and Applied Statistics I
Guidelines for Implementing Control Charts
Determine which process or product characteristic(s) to control
Determine where the charts should be implemented in process
Choose proper type of control charts
Decide what actions should be taken to improve processes
Select data-collection systems and computer software
4/19/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen

17. Determine Which Characteristic to Control and Where to Put Charts
IE 355: Quality and Applied Statistics I
Determine Which Characteristic to Control and Where to Put Charts
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
4/19/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen

18. Determine Which Characteristic to Control and Where to Put Charts
IE 355: Quality and Applied Statistics I
Determine Which Characteristic to Control and Where to Put Charts
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
4/19/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen

19. Choosing Proper Type of Control Chart: Variables Charts
IE 355: Quality and Applied Statistics I
Choosing Proper Type of Control Chart: Variables Charts
Use (x & R) or (x & S) charts when:
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
4/19/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen

20. Choosing Proper Type of Control Chart: Attributes Charts
IE 355: Quality and Applied Statistics I
Choosing Proper Type of Control Chart: Attributes Charts
Use p, np, c or u charts when:
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
4/19/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen

21. Choosing Proper Type of Control Chart: Individuals Charts
IE 355: Quality and Applied Statistics I
Choosing Proper Type of Control Chart: Individuals Charts
Use (x & MR), MA, EWMA, or CUSUM charts when:
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.
4/19/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen