BA 302 - Process Variability

BA 302 - Process Variability

Process Capability - Six Sigma - Statistical Process Control (SPC)

Learning outcomes:

Understand the role of averages (means) vs. variation. Why the mean tells only half the story.

Appreciate why in quality, variation is not our friend ==> in quality improvement, variability reduction comes first.

Know the sources of variation (common & special causes) in quality.

Know how to 'hunt down' these causes.

Relate quality targets (specification limits) to quality variation (control limits).

Understand the capability of processes (C_p, C_pk).

Relate the 'cost of quality' diagrams (ECM vs. 'Quality is free') to the capability of processes.

Understand the meaning of Six Sigma.

Understand Six Sigma as a program.

Understand Six Sigma relative to the normal distribution.

Comment on the Six Sigma critiques in BusinessWeek.

Appreciate the difficulties of measurement.

Understand and be able to formulate the ideas of SPC.

Know what we mean by in-control and out-of-control processes.

Variability in processes is not our friend:

Kirkpatrick, Bank of America quote (from Metters et al., p. 213): "Managers are trained to manage based on the average, but our customers feel variation and they hate it."

Problem: What does this mean?

Averages only tell part of the story:

"Corvallis averages about 34 inches of rain and 34 inches of ET (evapotranspiration) each year. Theoretically, nobody should ever have to water their lawn at all!" (City of Corvallis, 2007 Water Quality Report, p.15)

Annual estimated profit vs. monthly cash flows.

Average(10, 10, 10, 10, 10) = 10; Average(0 , 20, 5, 15, 10) = 10.

Single queue, multiple clerks vs. multiple queues, multiple clerks.

Unpredictability of process variables indicates lack of process control.

As our process outcomes vary less, they are more predictable.

As variance gets reduced, more things happen as specified. If we have no variance, the process behaves as specified; i.e., as designed!!

Remember the cost of quality?

As our process outcomes vary less, we have to inspect/appraise less ==> lowers quality appraisal cost.

As our process outcomes vary less, sudden variations are easier to spot and track down ==> lowers quality prevention cost.

TQM/'Quality is Free': as variability goes down, so does our cost of quality!

Our goal: variability reduction!!

What causes variability?

Example: Archery
- Notice how the arrows are 'spread' over the target (variability).
- Problem: what causes this spread?
- Problem: What could be some natural causes of the arrows' spread?
- Problem: What could be some assignable causes of the arrows' spread?
- Problem: So, in archery, how do we go after these assignable and natural causes?

Capability of a process:

When aiming for a specific level of quality, two 'windows' of variability apply:

Specification limits: upper and lower value within which your product or service must stay; e.g.,

Piece of chalk must be between 2.9 and 3.1 inches.

Pizza will be delivered between 0 and 20 minutes from ordering.

Jam must contain between 75% and 80% fruit by volume.

Wine must contain between 12.5% and 12.8% alcohol by volume.

Etc.

Control limits: variability of the process caused by common causes.

Process capability:

A process is 'capable' if its control limits are within its specification limits:

e.g., dustless chalk spec. limits:

2.9" <= actual length <= 3.1" (target = 3.0").

.370" <= actual diameter <= .380" (target = .375").

Sample: two boxes of Sparco brand, dustless chalk, ivory, 3/8" diameter.

Complies to American Society for Testing and Materials (ASTM) D4236.
- n = 24.
- length: mean=79.56 mm; σ=0.67mm.
- width: mean= 9.10 mm;σ=0.11mm.

Excursion: How do we measure variability?
- Notice that standard deviation = σ = √variance.
- Notice the "n - 1" in the formula for the standard deviation (σ).

Process Capability Index: C_p = [ USL - LSL ] / 6σ

Assume processes A, B and C:
Problem: Which of the following is true for the σ's of these three processes?

a. A’s σ and B’s σ are identical.

b. A’s σ and C’s σ are identical.

c. B’s σ and C’s σ are identical.

d. All three σ’s are very different.

Problem: If, for all three processes A, B and C above, the lower specification limit is set at 25.0 and the upper specification limit is set at 75.0, which of the following is true?

a. A’s C_p and B’s C_p are identical.

b. A’s C_p and C’s C_p are identical.

c. B’s C_p and C’s C_p are identical.

d. All three C_p’s are very different.

Problem: What are acceptable C_p values for a process?

Problem: Given the above specification limits, which process would you prefer?

C_pk = min. { [ USL - μ ] / 3σ } , { [ μ - LSL ] / 3σ }
- Problem: Consider again the capability situation for processes A, B and C above. Which of the following is true?
a.        A has the highest C_pk.

b.       B has the highest C_pk.

c.        C has the highest C_pk .

d.       All three C_pk ’s are identical.
- Problem: When we compare processes A and B graphed above, which can be expected to have the lowest appraisal/inspection cost?
a.        A has the lowest appraisal cost.

b.       B has the lowest appraisal cost.

c.        A and B are equally likely to have the lowest appraisal cost.

d.       A and B have equal appraisal cost.
- Problem: Suppose that you are in the situation of being both off-target and out of control, which of the following would be your preferred approach to quality improvement?

Interesting problem: measurement error!

To determine our process's capability we must measure.

Problem: Are our measurements free of error? Do they have variance?

Apparently, measurement itself introduces more variance!!! ==> must compensate for this by narrowing the spec. limits!

Six Sigma: Quality improvement framework:

""...rigorous and disciplined methodology that uses data and statistical analysis to measure and improve a company's operational performance by identifying and eliminating defects...", p. 109)

Defects Per Million Opportunities (DPMO):

cp and cpk table

Do we need 3, 4, 5 or 6 σ's?

Airlines.

Digital camera's.

Hospitals.

Amazon.com order fulfillment.

Disk drives.

Motorola moved from ±3σ (2700 DPMO) to 4σ (63 DPMO) to ±6σ (.002 DPMO).

Confusing:

Often (including Fitzsimmons (p. 109) and Hindo) Six Sigma is equated with 3.4 DPMO.

Six Sigma = C_p(k) = 1.5

However, neither 3σ nor 6σ translates to 3.4 DPMO!!
Also, why does Six Sigma equate with a C_p(k) ≈ 1.5 rather than 2.0?
Explanation: assumption that the mean can drift ± 1.5σ ==> effectively 4.5σ (3.4 DPMO = Cp(k) = 1.5).

Controlling variability:

Inspection:

inspection

Catches bad units, but does not fix the problem.

High appraisal cost.

Scrap and rework cost.

Scrap and rework overhead.

Overall: high cost of quality.

!!!Double jeopardy: what if the inspection process itself is not capable?!!!

Define, Measure, Analyze, Improve & Control (DMAIC) (Fitzsimmons, p. 109-110) with Statistical Process Control (SPC):

SPC

Process focused; not outcome focused.

Done in real time; operator oversees.

Constant feedback and analysis of data ==> strong role for information systems.

Process stops(!!!) in case of an excursion.

Indicates (new) assignable causes ==> stop process, track down cause and fix.

As in the case of archery, common cause (baseline) variation must be established first.

How do we decide that we have an excursion?

shift
Distribution (average) shifts.

spread
Variance changes

shape
Shape changes

Control charts: variability data on a timeline:

In control (common causes only):

in control

Out of control (assignable cause present):

out of control

X-chart for sample averages:

x chart

P-chart for defect counts:

p chart

Reflection: Six Sigma; friend or foe?

One hand:

Variability is not our friend.

Reduce variability and your cost of quality goes down.

Six Sigma and SPC give you a framework and tools to do this.

Other hand:

Metters et al. (p. 212). "Six Sigma was the best thing that ever killed a company."

Hindo (2007): Innovation and discipline do not go together:

In innovation, variation is your friend, not your foe.

"The very factors that make Six Sigma successful in one context make it ineffective in another."

Reducing variability is not the same as improving productivity.

Six Sigma in innovation leads to incremental rather than dramatic innovation.

"If you value sameness more than you value creativity, I think you potentially undermine the heart and soul of a company like 3M."

Test questions:

Why is quality variation at least as important as average quality?

Can you give some examples of where a mean (average) tells only half the story?

What do we mean with capable processes? How do we measure the capability of a process?

Do you see any relationship between the 'capability' of a process and the 'Capability' Maturity Model (CMM)?

Define Six Sigma; both as a program for quality improvement and as a characteristic of the normal distribution.

Why is Six Sigma often associated with 3.4 rather than 0.002 DPMO?

What's DPMO anyway?

Do all processes have to have the same DPMO? Provide some examples.

Hindo's BusinessWeek article is critical about Six Sigma. Why? Does it criticize Six Sigma as a quality improvement program?

What do we mean with the term SPC? How does it work and how is it different from inspection?

Do you see a relationship between 'hunting down' assignable causes and SPC?

Suppose that we find out that during inspection, our quality measurements have variation. How do we compensate for those errors?

When conducting SPC, what are some indications that our process may be going out of control?