Statistical Process Control (SPC)

Quality Control (QC) Control – the activity of ensuring conformance to requirements and taking corrective action when necessary to correct problems „ Importance „

Daily management of processes „ Prerequisite to longer-term improvements „

Designing the QC System „

Quality Policy and Quality Manual „ „ „ „

„

Contract management, design control and purchasing Process control, inspection and testing Corrective action and continual improvement Controlling inspection, measuring and test equipment (metrology, measurement system analysis and calibration) Records, documentation and audits

Example of QC: HACCP System 1. 2. 3. 4. 5. 6. 7.

Hazard analysis Critical control points Preventive measures with critical limits for each control point Procedures to monitor the critical control points Corrective actions when critical limits are not met Verification procedures Effective record keeping and documentation

Inspection/Testing Points „ Receiving

inspection „ In-process inspection „ Final inspection

5

Receiving Inspection „ Spot

check procedures „ 100 percent inspection „ Acceptance sampling

6

Acceptance Sampling Lot received for inspection Sample selected and analyzed Results compared with acceptance criteria

Accept the lot Send to production or to customer

Reject the lot Decide on disposition 7

Pros and Cons of Acceptance Sampling „

Arguments for: „ Provides an assessment of risk „ Inexpensive and suited for destructive testing „ Requires less time than other approaches „ Requires less handling „ Reduces inspector fatigue

„

Arguments against: „ Does not make sense for stable processes „ Only detects poor quality; does not help to prevent it „ Is non-value-added „ Does not help suppliers improve

In-Process Inspection „

What to inspect? „

„

Where to inspect? „

„

Key quality characteristics that are related to cost or quality (customer requirements) Key processes, especially high-cost and value-added

How much to inspect? „

All, nothing, or a sample 9

Economic Model C1 = cost of inspection and removal of nonconforming item C2 = cost of repair p = true fraction nonconforming Breakeven Analysis: p*C2 = C1 If p > C1 / C2 , use 100% inspection If p < C1 / C2 , do nothing 10

Human Factors in Inspection complexity defect rate repeated inspections inspection rate

Inspection should never be a means of assuring quality. The purpose of inspection should be to gather information to understand and improve the processes that produce products and services.

Gauges and Measuring Instruments „ Variable

gauges „ Fixed gauges „ Coordinate measuring machine „ Vision systems

12

Examples of Gauges

Metrology - Science of Measurement Accuracy - closeness of agreement between an observed value and a standard Precision - closeness of agreement between randomly selected individual measurements

Repeatability and Reproducibility Repeatability (equipment variation) – variation in multiple measurements by an individual using the same instrument. „ Reproducibility (operator variation) variation in the same measuring instrument used by different individuals „

Repeatability and Reproducibility Studies „

Quantify and evaluate the capability of a measurement system Select m operators and n parts „ Calibrate the measuring instrument „ Randomly measure each part by each operator for r trials „ Compute key statistics to quantify repeatability and reproducibility „

Reliability and Reproducibility Studies(2) Measurement (M) made by Operators (i from 1 to m) on Parts (j from 1 to n) in Trials (k from 1 to r) ⎞ ⎛ ⎜ ∑∑ M ijk ⎟ ⎟ ⎜ j k ⎠ average for each operator ⎝ xi = n⋅r xD = max( xi ) − min ( xi ) difference (range) of operator averages i

i

R ij = max( M ijk ) − min ( M ijk ) range for each part for each operator k

k

⎞ ⎛ ⎜ ∑ Rij ⎟ ⎟ ⎜ j ⎠ average range for each operator ⎝ Ri = n ⎞ ⎛ ⎜ ∑ Ri ⎟ ⎠ average range of all R =⎝ i m

Reliability and Reproducibility Studies(3) Control limit of ranges Rij = D4 ⋅ R Use number trials (r) for n in table. Check for randomness of errors. Repeatability or Equipment Variation EV = K1 ⋅ R

K1 is a constant tied to # of trials

Reproducibility or operator (appraisal) variation ⎛ EV 2 ⎞ ⎟⎟ K 2 is a constant tied to # of operators AV = (K 2 ⋅ xD ) − ⎜⎜ n r ⋅ ⎠ ⎝ Repeatability and Reproducibility 2

R&R =

(EV )2 + ( AV )2

Results are in actual units measured. Customary to express as percentages. Under 10% - Acceptable 10 - 30% - ? based on importance and repair cost Over 30% - Unacceptable

R&R Constants Number of Trials K1 Number of Operators K2

2

3

4

5

4.56 3.05 2.50 2.21 2 3 4 5 3.65 2.70 2.30 2.08

R&R Evaluation „ Under

10% error - OK „ 10-30% error - may be OK „ over 30% error - unacceptable

R&R Example „

R&R Study is to be conducted on a gauge being used to measure the thickness of a gasket having specification of 0.50 to 1.00 mm. We have three operators, each taking measurement on 10 parts in 2 separate trials.

x 1 = 0 . 830 x

2

= 0 . 774

x

3

= 0 . 829

R

1

= 0 . 037

R

2

= 0 . 034

R

3

= 0 . 017

Calibration Calibration - comparing a measurement device or system to one having a known relationship to national standards „ Traceability to national standards maintained by NIST, National Institute of Standards and Technology „

Statistical Process Control (SPC) A methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action when appropriate „ SPC relies on control charts „

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Common Causes

Special Causes

Histograms do not take into account changes over time.

Control charts can tell us when a process changes

Control Chart Applications „ Establish

state of statistical

control „ Monitor a process and signal when it goes out of control „ Determine process capability

27

Commonly Used Control Charts „ Variables

data

„ x-bar

and R-charts „ x-bar and s-charts „ Charts for individuals (x-charts) „ Attribute

data

„ For

“defectives” (p-chart, np-chart) „ For “defects” (c-chart, u-chart) 28

Developing Control Charts 1.

Prepare „ „ „

2.

Choose measurement Determine how to collect data, sample size, and frequency of sampling Set up an initial control chart

Collect Data „ „ „

Record data Calculate appropriate statistics Plot statistics on chart

Next Steps 3.

Determine trial control limits „ „

4.

Center line (process average) Compute UCL, LCL

Analyze and interpret results „ „ „

Determine if in control Eliminate out-of-control points Recompute control limits as necessary

Typical Out-of-Control Patterns „ „ „ „ „ „ „

Point outside control limits Sudden shift in process average Cycles Trends Hugging the center line Hugging the control limits Instability

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Shift in Process Average

Identifying Potential Shifts

Cycles

Trend

Final Steps 5.

Use as a problem-solving tool „ „

6.

Continue to collect and plot data Take corrective action when necessary

Compute process capability

Process Capability „

Capability Indices

UTL − LTL 6σ if C p ≥ 1 is defined as capable (1.5 more often the minimum)

Cp =

Example : Part specification is 10.75mm ± .25mm σ = 0.0868mm

11.00−10.50 Cp = = 0.96 6• 0.0868

Process Capability (2) UTL − µ 3σ µ − LTL C pl = 3σ C pk = min (C pl , C pu ) C pu =

C pu =

Cpl =

C pk = C p (1 − K ) where K =

2⋅ µ −T

11.0 − 10.7171 = 1.086 3 • 0.0868

10.7171−10.5 = 0.834 3• 0.0868

Tolerance Example : same as above, but assume process is centered at 10.7171mm

Cp

C pm = 1+

(µ − T )

2

T is the Target

σ2 0.960

C pm =

(10.7171 − 10.75)

2

1+

0.8682

= 0.8977

Capability Versus Control Control Capability Capable

In Control

Out of Control

IDEAL

Not Capable

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Process Capability Calculations

Excel Template

Special Variables Control Charts „ x-bar

and s charts „ x-chart for individuals

Charts for Attributes „

Fraction nonconforming (p-chart) Fixed sample size „ Variable sample size „

„

np-chart for number nonconforming

„

Charts for defects c-chart „ u-chart „

Control Chart Selection Quality Characteristic variable

attribute defective

n>1?

no

x and MR

yes n>=10 or no computer? yes x and s

defect

x and R

constant sample size?

yes

no p-chart with variable sample size

constant sampling unit?

p or np

yes

no

c

u

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Control Chart Design Issues „ Basis

for sampling „ Sample size „ Frequency of sampling „ Location of control limits

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Pre-Control LTL Red Zone

UTL

Green Zone

Red Zone

nominal value

Yellow Zones

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SPC Implementation Requirements „ Top

management commitment „ Project champion „ Initial workable project „ Employee education and training „ Accurate measurement system 68

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