Quality Control
• All activities undertaken to control materials,
processes and products in order to ensure quality
of conformance
• Detects defects before further failure costs are incurred
• Determines if processes are under control and deliver
consistent results
• Determines if processes deliver the quality customers
expect
• Identifies how quality of conformance can be improved
Quality Control Tools
• Acceptance Sampling
• Inspection of goods before, during or after production
• What/where to inspect?
• How many to sample and how often to sample (rigor)?
• Tradeoff between appraisal costs and failure costs
• Statistical Process Control
• Cause-and-effect (fishbone) diagram
• Pareto chart
Statistical Process Control (SPC)
• Variability in the inputs (labor, material, equipment) will
cause variability in the output
• SPC detects variability in outputs by
• Measuring and controlling it
• Establishing systems to flag situations where quality exceeds
defined bounds
• SPC reduces variability in outputs by improving product
and/or process design (including inputs and process
execution)
SPC Focus
• For a chosen variable (a product or a process attribute),
SPC is concerned with the variable’s mean and variability.
• The process mean and standard deviation is estimated by
calculating sample means and measures of sample
variation for different samples taken over time.
• SPC measures, manages and
• Reduces the dispersion (variability) as needed
• Ensures that the mean does not shift
Four Key Concepts for SPC
• All processes have an inherent variation (sometimes
referred to as common, natural or noise variation)
• Variability that is not inherent in a process is called
assignable or special variation. It arises when something
has changed in the process itself and can be assigned to
a specific cause.
• A process is in control (stable) when it exhibits only
inherent variation. A process is out of control when it
exhibits assignable variation.
• A process is capable if it consistently meets design and/or
customer specifications (tolerances). A process that is in
control is not necessarily capable.
Control Limits
• Mean Chart
• UCL X= X + z * s = 𝑋 + 𝐴2 * 𝑅
• LCL X = X - z * s = 𝑋 - 𝐴2 * 𝑅
Where s = 𝑅
or 𝐴2 =
(𝑑2 ∗√𝑛)
3
(𝑑2 ∗√𝑛)
with d2 given in table for small n
with d2 or 𝐴2 given in table for small n
& assuming z=3
• Range Chart
• UCL(R) = 𝑅 * 𝐷4
• LCL(R) = 𝑅 * 𝐷3
with D4 given in table for n
with D3 given in table for n
Process Capability
• 2 common measures used to determine if a process is
capable:
𝑈𝑆𝐿−𝐿𝑆𝐿
• Process Capability Ratio 𝐶𝑝 =
2∗𝑧∗𝜎
where USL is the Upper Specification Limit and LSL is the Lower
Specification Limit as defined by the design requirements or customer
needs
If 𝐶𝑝 > 1, then the process is capable.
𝑈𝑆𝐿−𝑋
• Process Capability Index 𝐶𝑝𝑘 = minimum(
3∗𝜎
,
𝑋−𝐿𝑆𝐿
3∗𝜎
)
If 𝐶𝑝𝑘 > 1, then the process is capable.
When the process mean is not centered between LSL and USL,
𝐶𝑝𝑘 must be used to test capability.