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 = + z * s = + * • LCL = - z * s = - *

Where s = with d2 given in table for small n

or with d2 or given in table for small n & assuming z=3

• Range Chart• UCL(R) = * with D4 given in table for n• LCL(R) = * with D3 given in table for n

X

XX

X

Process Capability• 2 common measures used to determine if a process is

capable:• Process Capability Ratio =

where USL is the Upper Specification Limit and LSL is the Lower Specification Limit as defined by the design requirements or customer needs

If > 1, then the process is capable.

• Process Capability Index = minimum( , )

If > 1, then the process is capable.

When the process mean is not centered between LSL and USL, must be used to test capability.