Chapter 6S Quality Control

1
Chapter 6S Quality Control

• Control process, statistical process control
  (SPC) X-bar, R, p, c, process capability

2
SPC The Control Process

• Define
• Measure
• Compare to a standard
• Evaluate
• Take corrective action (if necessary)
• Evaluate corrective action

3
Variation

• Random, chance, or common cause (natural)
• Assignable, non-random, or special cause (due to
  some specific change)
• Sampling used to detect non-random
• Sampling assumes a normal distribution
• Sample statistics calculated
• Mean
• Range

4
Control Charts

• Control limits
• When is a process out of control?
• Charts for variables
• Mean (X-bar) charts
• Range (R) charts
• Charts for attributes
• Proportion or percentage (p) charts
• Number or defects per unit (c) charts

5
Type I and Type II Errors

• Type I (Producers risk)
• Conclusion non-randomness is present and the
  process is out of control
• Reality randomness is present and the process is
  in control
• Type II (Consumers risk)
• Conclusion randomness is present and the process
  is in control
• Reality non-randomness is present and the
  process is out of control

6
Mean Range Control Charts

• Take required number of samples (often 20-25)
• Create mean (X-bar) charts
• Calculate mean (X-bar) for each sample
• Calculate grand mean (X-double-bar)
• Calculate range (R) for each sample
• Calculate mean of all sample ranges (R-bar)
• Calculate UCL and LCL for means
• Plot grand mean and control limits on X-bar chart

7
Mean (X-bar) Chart Control Limits

• UCLX-bar X-double-bar A2 (R-bar)
• LCLX-bar X-double-bar - A2 (R-bar)
• Where X-double-bar the grand mean,
• And R-bar the mean of the sample ranges
• And A2 the value in Table S6.1 for n

8
Mean Range Control Charts

• Range (R) charts
• Calculate UCL and LCL for ranges
• Plot range mean and control limits on R- chart
• Plot additional samples and determine if within
  range limits
• Note Table factors are based on the size of the
  sample, not the number of samples!

9
Range (R) Chart Control Limits

• UCLR D4 (R-bar)
• LCLR D3 (R-bar)
• Where R-bar the mean of the sample ranges, and
  D4 and D3 the values in Table S6.1 for n

10
Run tests and charts

• Counting above/below the median
• Counting ups and downs

11
Process Capability Ratios

• Non-centered process (general case)
• choose cpk the lower of
• Upper spec process mean
  cpu --------------------------
  -------- or
• 3?
• Process mean lower spec
  cpl ----------------------
  ------------
• 3?

12
Process Capability Ratios

• Centered process (special case)
• specification width
• cp ----------------------------
• process width
• Upper spec limit lower spec limit
• ----------------------------------------
  -
• 6?

13
Process Capability Requirements

• Process must be normally distributed
• Process must be in control
• Process capability result
• gt 1.33 capable and acceptable
• gt1.00 but lt 1.33 capable but not acceptable
• 1.00 barely capable but not acceptable
• Companies may seek 2.0 (Six Sigma concept)
• gt 5 or 10 is overkill, excessive resource use