case study 2 six sigma?

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Lecture 5

Six Sigma Metrics

What is Six Sigma Metrics?

It is a unit of measurement that provides a way to objectively quantify a process.
It is a measurement that helps management understand its operations, for example, number of products completed per unit of time, percent of defects, time required to deliver a certain number of outputs or provide a service etc...
Six Sigma metrics provide data which managers can use to better understand their processes and identify areas of improvement.

Traditional versus Six Sigma approach

In a Traditional approach the management often operates by the “seat of the pants”, by tradition, by impression, by reaction to events or by gut instincts.

In a Six sigma approach the management uses objective data to make decisions.

Why do you need to implement metrics?

You need to implement metrics to quantify the effect of variation in your processes.
If you can measure your processes, then you can understand them.
If you can understand them, then you can analyze and reduce process variation.
If you can reduce process variation, then you can reduce costs and improve quality of the outputs.

What is process variation?

It is a quantifiable difference between individual measurements of a process.
Any process improvement must reduce variation in order to consistently meet customer expectations.
In order to reduce process variation, we must be able to measure it.
It is therefore very important to understand how to measure process variation

Method to measure process variation

To understand the method, let us take the following example:

There are two assembly lines with the different assembly times (minutes).

Assembly process “A”: 3.7, 6.5, 3.2, 3.2, 5.7, 7.4, 5.7, 7.7, 4.2, 2.9

Assembly process “B”: 4.7, 5.3, 4.7, 5.4, 4.7, 4.4, 4.7, 5.8, 4.2, 5.7

Understanding of process variation

Assembly process A:

Mean (Xbar) = 5.02 minutes,

Range (R) = 4.8 (7.7-2.9)

Standard deviation (s) = 1.81

Assembly process B:

Mean (Xbar) = 4.96 minutes,

Range (R) = 1.6 (5.8-4.2)

Standard deviation (s) = 0.55

To understand process variation, we must do statistical analysis.

Standard deviation (s) =

Statistical analysis shows that the variation in process A is greater than the variation in process B

Distribution of process values

Generally the distribution of process values form a bell-shaped curve called normal distribution curve.
68.2% of the values are within one standard deviation (1s) of the mean.
95.5% of the values are within two standard deviations (2s) of the mean
99.7% of the values are within three standard deviations (3s) of the mean.

How much variation is acceptable?

What is LSL and USL?

LSL = Lower specification limit
USL = Upper specification limit
These are upper and lower boundaries of the process variation, which is acceptable values for a process to satisfy customer needs.
In the current example of assembly processes A and B, let us assume that USL = 6 min. and LSL = 4 min.
This is + 1 minute of ideal 5 minutes

Acceptable variations of processes A & B

Comparison of process A vs. B

For Process A

The standard deviation is 1.81.
It is greater than the interval between the LSL and the mean or 1.02 (5.02-4.00).
It is greater than the interval between the USL and the mean or 0.98 (6.00-5.02).

For Process B

The standard deviation is 0.55.
It is less than the interval between the LSL and the mean or 0.96 (4.96-4.00).
It is less than the interval between the USL and the mean or 1.04 (6.00-4.96).

Conclusion: Process B is meeting customer expectations

What is the goal of Six Sigma?

The goal of Six Sigma is to reduce the standard deviation of your process variation to the point that six standard deviation (6s) can fit within your specification limits.

Benefits of Six Sigma metrics

Measurement is crucial to the success of a Six Sigma initiative.
Six Sigma metrics shows you the ways to achieve dramatic improvements in your process.
It applies statistical tools to any process to evaluate and quantify its performance.
It analyzes the effect on dependent variable by independent variable and identifies the information that can improve the process.
By improving the process, it can improve customer satisfaction and reduce costs.

Six Sigma philosophy at GE

By instituting key Six Sigma metrics across functions and groups and at every level, you directly link individual performance to measurable outcomes. This sends a clear message that not only do you care about customers and revenues, but so should everyone else, since they are accountable for the results measured by their particular metrics.

How do you actually select appropriate metrics?

1) Determine the expectations of your customers, in other words what aspects of the product or service are key to customer satisfaction.

2) For each aspect, list what are your customers’ expectations for example, size, weight, durability, price, ease of use, versatility, colors, styles, availability, maintenance, service, warranty and so on.

3) Find out ways to measure how well your product or service is meeting those expectations.

4) Establish metrics for activities that are critical to meeting those expectations.

Pitfalls of measurement

When setting metrics, keep the numbers of measurements small.
It is natural to want to measure everything- DON’T (the key is quality over quantity).
Select only a true set of indicators that will give you the needed information on process factors that affect customer satisfaction and revenue.
When establishing a metric, find out why you are measuring it, why is it important and what’s causing the results.

Avoid bad metrics

When developing metrics, beware of the following:

Metrics for which you cannot collect accurate or complete data.
Metrics that are complex and difficult to explain to others.
Metrics that complicate operations and create excessive overhead.
Metrics that cause employees to act not in the best interests of the business, just to “make their numbers”.

What is DPMO?

DPMO = Defects per million opportunities.
This will establish metrics in terms of million of defects.
It can be used to calculate quality levels according to the complexity of the product, service, or process.
Six Sigma allows for metrics that make it easier and more realistic to compare performance for products, services or processes that differ.

Defects per million opportunities (DPMO)

DPO is defined as “defects-per-opportunity, which includes the number of opportunities for failure

If there are 100 circuit boards and each circuit board has 100 opportunities for failure. Assume that 21 defects were found after inspecting 100 boards.

% defect = 0.21%

DPO rate = 0.0021 (21 defects per 10,000 opportunities)

DPMO rate = 2,100 (21 defects per million opportunities)

Following chart can be used to convert DPMO into sigma quality level:

DPMO 697700 = + 1s

DPMO 308700 = + 2s

DPMO 66800 = + 3s

DPMO 6210 = + 4s

DPMO 233 = + 5s

DPMO 3.4 = + 6s

What questions do you need to ask as you establish metrics?

What are our business (customer satisfaction) metrics?
What are the measurement criteria?
Do the metrics link to the criteria?
Do they correlate to competitive advantage?
If they don’t correlate, what must we change?

What is COPQ?

COPQ = Cost of poor quality
It is a key indicator that can be used for any services, products, or processes, regardless of business focus.
It is a financial iceberg, you only see the tip of the iceberg however its full impact is enormous.
Measurement reveals the sources of COPQ so you can take steps to eliminate them.
As you target and resolve the root causes of poor quality, you improve productivity and quality, which in turn will have positive impact throughout customer service and delivery cycle.

What are the elements of COPQ?

Internal failure: These are costs which result from defects found before the customer receives the product or service, for example, scrap, rework, reinspection, retesting etc.

External failure: These are costs resulting from defects found after the customer receives the product or service, for example, warranty charges, customer complaints, returned material, compensation, damage to reputation etc.

Appraisal: These are costs of determining the degree of conformance to quality requirements, for example, inspection, testing, quality audits, process control etc.

Prevention: These are costs of minimizing failure and appraisal costs for example quality planning, , policies and procedures, in-process inspections and testing, education and training etc.

Examples of how can Six Sigma metrics
align with business goals

1) Business goal: Improve product quality.

6s metric: conformance of raw materials with specification.

2) Business goal: Products are guaranteed unconditionally.

6s metric: Measure reasons for returns.

3) Business goal: Promising next day shipping.

6s metric: Measure turnaround time to customer.

4) Business goal: To take care of the customers.

6s metric: Measure type of customer problems discussed.

5) Business goal: Reduce prices through improving efficiency.

6s metric: Measure factors throughout its operation

Process yield & throughput yield

Yield is referred to as “final yield” which is the percentage of units that pass final test compared to total number of units that entered the process.
This includes the units which were passed after rework.
RTY is defined as “Rolled Throughput Yield” Which is the percentage of units that passed the first time. It does not include the units which are reworked.
RTY is a measure of how good is the “process quality”. RTY of 50% indicates that only one out of two units completed the entire production process without being reworked or scrapped.

Example of process yield versus RTY

PROCESS CAPABILITY ANALYSIS

What is the capability index Cp?

Capability index (Cp) is statistical measure of the variation of a given process.
It is expressed as process width (the difference between USL and LSL) divided by six times the standard deviation of the process:

Cp = (USL-LSL) / 6s

The higher the value of Cp the better the process with less variation.
A process is said to be equal to six sigma quality level if Cp > 2.0

What is Cpk?

It is a capability index which splits the process capability of Cp into two values:

1) (USL - mean) / 3s 2) (mean - LSL) / 3s

These are used to develop upper control limits (UCL) and lower control limits (LCL) of the process based on the data collected from the sample.
If the “control limits” are the same or within the “specification limits”, then the process is considered to be capable of meeting customer specification.
If the “control limits” are outside the “specification limits”, then the process is considered to be not capable of meeting customer specifications.

Process control design for Six Sigma

Cp and Cpk are the process capability indices.
USL and LSL are the upper and lower specification limits.
“s” is standard deviation and “m” is the process mean.
A process is said to be equal to at “six sigma quality level” if Cp = 2.0 and Cpk = 1.5. This equates to 3.4 PPM using 1.5s standard shift.

Process capability distribution for Cp

Cp = 2.00 equates to 3.4 PPM using 1.5 standard shift. This is also defined as “Six Sigma quality level”.

Process capability distribution for Cpk

Cpk = 1.50 equates to 3.4 PPM using 1.5 standard shift. This is also defined as “Six Sigma quality level”.

Process Capability Analysis is necessary to:

determine the area of focus which will ensure successful resolution of the project.
benchmark a process to enable demonstrated levels of improvement after successful resolution of the project.
demonstrate improvement after successful resolution of the project.

IMPROVEMENT ROADMAP
Uses of Process Capability Analysis

Breakthrough

Strategy

Phase 4:

Control

Characterization

Phase 1:

Measurement

Phase 2:

Analysis

Optimization

Phase 3:

Improvement

Baselining a process primary metric (Y) prior to starting a project.

Common Uses

Characterizing the capability of causitive factors (x).

Characterizing a process primary metric after changes have been implemented to demonstrate the level of improvement.

KEYS TO SUCCESS

Must have specification limits - Use process targets if no specs available

Don’t get lost in the math

Relate to Z for comparisons (Cpk x 3 = Z)

For Attribute data use PPM conversion to Cpk and Z

WHAT IS PROCESS CAPABILITY?

Process capability is simply a measure of how good a metric is performing against and established standard(s). Assuming we have a stable process generating the metric, it also allows us to predict the probability of the metric value being outside of the established standard(s).

Spec

Out of Spec

In Spec

Probability

Spec (Lower)

Spec (Upper)

In Spec

Out of Spec

Probability

Upper and Lower Standards (Specifications)

Single Standard (Specification)

WHAT IS PROCESS CAPABILITY?

Process capability (Cpk) is a function of how the population is centered (|m-spec|) and the population spread (s).

Spec (Lower)

Spec (Upper)

In Spec

Out of Spec

High Cpk

Spec (Lower)

Spec (Upper)

In Spec

Out of Spec

Poor Cpk

Process Center (|m-spec|)

Spec (Lower)

Spec (Upper)

In Spec

Out of Spec

Spec (Lower)

Spec (Upper)

In Spec

Out of Spec

Process Spread (s)

HOW IS PROCESS CAPABILITY CALCULATED

Spec (LSL)

Spec (USL)

Note:

LSL = Lower Spec Limit

USL = Upper Spec Limit

Distance between the population mean and the nearest spec limit (|m-USL |). This distance divided by 3s is Cpk.

Expressed mathematically, this looks like:

PROCESS CAPABILITY EXAMPLE

Calculation Values:
Upper Spec value = $200,000 maximum
No Lower Spec
m = historical average = $250,000
s = $20,000
Calculation:

Answer: Cpk= -.83

We want to calculate the process capability for our inventory. The historical average monthly inventory is $250,000 with a standard deviation of $20,000. Our inventory target is $200,000 maximum.

(

)

(

)

MIN

LSL

USL

$200

$250

$20

-.83

000

ATTRIBUTE PROCESS CAPABILITY TRANSFORM

PPM

(+1.5

)

0.0

500,000

0.0

933,193

0.1

460,172

0.0

919,243

0.2

420,740

0.1

903,199

0.3

382,089

0.1

884,930

0.4

344,578

0.1

864,334

0.5

308,538

0.2

841,345

0.6

274,253

0.2

815,940

0.7

241,964

0.2

788,145

0.8

211,855

0.3

758,036

0.9

184,060

0.3

725,747

1.0

158,655

0.3

691,462

1.1

135,666

0.4

655,422

1.2

115,070

0.4

617,911

1.3

96,801

0.4

579,260

1.4

80,757

0.5

539,828

1.5

66,807

0.5

500,000

1.6

54,799

0.5

460,172

1.7

44,565

0.6

420,740

1.8

35,930

0.6

382,089

1.9

28,716

0.6

344,578

2.0

22,750

0.7

308,538

2.1

17,864

0.7

274,253

2.2

13,903

0.7

241,964

2.3

10,724

0.8

211,855

2.4

8,198

0.8

184,060

2.5

6,210

0.8

158,655

2.6

4,661

0.9

135,666

2.7

3,467

0.9

115,070

2.8

2,555

0.9

96,801

2.9

1,866

1.0

80,757

3.0

1,350

1.0

66,807

3.1

968

1.0

54,799

3.2

687

1.1

44,565

3.3

483

1.1

35,930

3.4

337

1.1

28,716

3.5

233

1.2

22,750

3.6

159

1.2

17,864

3.7

108

1.2

13,903

3.8

72.4

1.3

10,724

3.9

48.1

1.3

8,198

4.0

31.7

1.3

6,210

(

)

MIN

LSL

USL

CALC

MIN

LSL

USL

MIN

LSL

USL

(

)

(

)

If we take the Cpk formula below

We find that it bears a striking resemblance to the equation for Z which is:

with the value m-m0 substituted for MIN(m-LSL,USL-m).

Making this substitution, we get :

We can now use a table similar to the one on the left to transform either Z or the associated PPM to an equivalent Cpk value.

So, if we have a process which has a short term PPM=136,666 we find that the equivalent Z=1.1 and Cpk=0.4 from the table.

Summary of guidelines for metrics

1) Get leaders involved who set company strategy to ensure that the metrics are linked to the business goals.

2) Visually display metrics through charts, graphs & diagrams.

3) Metrics must provide prompt feedback, so that you can identify problems and correct them quickly.

4) Metrics must be simple and must clearly communicate its results so that direct actions can be taken.

5) Metrics should drive only important activities such as waste and defects and correct the processes to reduce costs.

6) Limit the number of metrics, generally implementing no more than 10 metrics at a given time.

7) Take corrective action as soon as possible once you have the feedback.

(

)

MIN

LSL

USL

(

)