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Statistical Process Control

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Preventing unnecessary process adjustments. Providing diagnostic information ... In manufacturing automobile engine piston rings, the inside diameter of the ... – PowerPoint PPT presentation

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Title: Statistical Process Control


1
Statistical Process Control
  • Is a tool for
  • achieving process stability
  • improving capability by reducing variability
  • Variability can be due to
  • chance causes (relatively small)
  • assignable causes (generally large compared to
    background noise)

2
Control Charts
UCL
CL
LCL
  • UCL mW ksW
  • CL mW
  • LCL mW ksW
  • Types of Control Charts
  • Variables Control Charts
  • Attributes Control Charts

3
Purpose of Control Charts
  • Improving productivity
  • Preventing defects
  • Preventing unnecessary process adjustments
  • Providing diagnostic information
  • Providing information about process capability

4
Design of a Control Chart
  • An control chart
  • Standard deviation of the sample average.
  • Choosing the control limits.
  • Relationship to hypothesis testing.
  • Decisions
  • Sample size to use.
  • Frequency of sampling.

5
the control chart
Example of
  • In manufacturing automobile engine piston rings,
    the inside diameter of the rings is a critical
    quality characteristic. Given the process average
    diameter is 74mm, the process standard deviation
    of diameter is 0.01mm and the sample size is 5.
  • How the control limits are determined?

6
Analysis of Patterns
  • Types of patterns
  • Run (8 or more)
  • Cyclic behavior
  • Western Electric Rules (Zone Rules)
  • One point outside 3s control limits.
  • 2 / 3 consecutive points beyond a 2s CL.
  • 4 / 5 consecutive points at ?1s from CL.
  • 8 consecutive points on one side of the CL.

7
The Control Chart
  • When m and s are unknown
  • R Range of the sample
  • W Relative range R / s
  • E(W) d2 Stdev(W) d3
  • What would be an estimator for s?
  • What are the UCL and LCL?

8
Definitions
control chart
R control chart
9
The R Control Chart
  • What is a reasonable estimator for sR?
  • What are the corresponding CLs?
  • Example

10
P Chart
  • where is the observed value of the average
    fraction defective

11
U Chart
  • where is the observed value of the average
    fraction defective

12
Control Chart Performance
  • ARL Average Run Length
  • p -- probability that any point exceeds control
    limits
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