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However, there is a variety of othersituations wherein Six Sigma problem-solving methodologies can help an organi-zation, such as the following: • Identifying and eliminating the causes

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14 Six Sigma Problem Solving

Jonathon L Andell

Many consultants and references advocate Six Sigma as a means to rectify qualityproblems in a manufacturing environment This application is indeed valid, yieldingimpressive financial results, as we shall discuss However, there is a variety of othersituations wherein Six Sigma problem-solving methodologies can help an organi-zation, such as the following:

• Identifying and eliminating the causes of nagging problems throughout abusiness — the application most commonly described in articles andbrochures

• Developing manufactured and service products with significant tive edges — the realm called Design for Six Sigma (DFSS)

competi-• Planning and implementing management initiatives, including Six Sigmaitself — setting up Six Sigma to match the requirements of each specificbusiness

As one might expect, achieving such divergent objectives depends on applyingsomewhat different tools After all, the list starts with tactical issues dealing withthings, and progresses toward strategic issues of people and organizations In order

to accommodate such diverse objectives, Six Sigma problem solving encompasses

a variety of approaches

Most organizations have individuals with excellent backgrounds in Six Sigmaproblem solving, even if they call it by another name Furthermore, many managershave seen literature and attended seminars on how it works However, it is common-place for the state of problem solving at large to lag significantly behind what anorganization’s best people contribute

The challenge, therefore, is to make excellent problem-solving teams less of anexception and more the rule As Table 14.1 shows, quite a balancing act is involved

in bringing this about

This chapter endeavors to provide managers with some guidelines for strikingsuch a balance However, there are limitations inherent in such a discussion:

• No single chapter can provide enough detail to make the reader into anexpert problem solver (For that matter, nobody can become an expertsimply by reading It’s like golf, sooner or later you have to put down thebooks and pick up the clubs.)

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296 The Manufacturing Handbook of Best Practices

• A detailed description of all problem-solving tools also is beyond thescope of a single chapter Fortunately, the chapters of this handbookaddress the more powerful tools This chapter serves partly as an overviewfor when and where each chapter’s contribution might apply within thebig picture

• Emphasis remains on tactical problem solving, the first of the three broadproblem-solving applications described above

The object of this chapter is to enable managers to support Six Sigma problemsolving within their organizations The direct implication is that somebody otherthan managers will lead the teams, specifically the practitioners, experts, and mastersdescribed in Chapter 2, “Benefiting from Six Sigma Quality.” Managers generallyprovide a combination of guidance and support, as we will discuss

Numerous anecdotes are used, some to describe traditional businesses, others toillustrate how a Six Sigma organization functions The distinction between a tradi-tional and a Six Sigma organization is not black and white In some cases, bothkinds of anecdotes emanate from within the same firm The reader might wish toreflect on how both kinds of examples apply to his or her business

The chapter starts by linking problem solving to financial performance, by ing organizational resources tied up fixing defects Next, a few established methodol-ogies are compared against the define–measure–analyze–improve–control (DMAIC)approach associated with Six Sigma problem solving, followed by a review of how theother chapters of this handbook fit into the overall picture of problem solving Thechapter ends with a return to the discussion of roles that was started in Chapter 2, thistime considering how the roles apply to successful problem solving

estimat-TABLE 14.1 The Six Sigma Balancing Act

• Allow the process to work • Attendance at meetings

• Accept realistic scope • Complete assigned action items Containment Correction

• Protect the customer • Identify the root cause

• Temporarily higher expenses • Eliminate the problem for good Executive Hands-Off Executive Hands-On

• Analytical tools • Infrastructure & reward system

• Challenge by implementation • Strategic project selection

• Resource allocations Flexibility Rigor

• Deal with team dynamics • No shortcuts

• Act on findings • Diversity on team Autonomy Accountability

• “Worker bees” on teams • Participation not optional

• Trust team’s intent & skill • Zero tolerance for obstruction

• Share information • Provide guidelines & objectives SL3003Ch14Frame Page 296 Tuesday, November 6, 2001 6:04 PM

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Six Sigma Problem Solving 297

14.1 PRODUCT, PROCESS, AND MONEY

A manufactured product is a physical object, with tangible properties that enableyou to test its conformance to customer requirements When a product contains one

or more defects, it is called defective Presumably, defects are not deliberate Theyensue from flaws in the processes that create the product A variety of processproblems can lead to defects in manufactured products:

• Design errors

• Defects in the materials

• Defects in the manufacturing process

• Errors in the processes that support the factory floor

Problem-solving teams identify which process, and which aspect thereof, isresponsible for the defects They then identify and implement remedies, with theintent of preventing the defects from happening again Later we discuss how this isdone First, however, managers will benefit from understanding the costs of fixingdefective products once they occur

Consider a product It could be a manufactured product such as a hammer, a serviceproduct such as tax preparation, or something in between, such as automobile repair.Suppose we are able to contain every defect, meaning that the delivered productcontains zero defects (though this final supposition is most unrealistic, we beg thereader’s indulgence)

Over time, we produce an average of one defect per unit of deliverable product,

or one DPU Whether this is a good or a bad number depends on the complexity ofthe product: if a unit were one jumbo jet, one DPU would be an excellent numberindeed; 1 DPU would be horrendous if a unit was a single carpet tack Figure 14.1

shows how 100 defects might be distributed among a sample of 100 units.This typically is modeled using the Poisson distribution:

In Equation 14.1, Y TP is called throughput yield It is the probability that a givenunit is nondefective In Figure 14.1, DPU = 1.0, which corresponds to a value of Y TP

≅ 37%; thus, 37 of the units contain zero defects.*

So how does this relate to managing a business? It comes down to how much itcosts the business to fix defective product Some have called the rework process

* Over time, a process averaging 1 DPU should average approximately 37% defect-free units However, any single sample is likely to vary somewhat from the expected value.

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298 The Manufacturing Handbook of Best Practices

“the hidden factory,” because rework usually is mixed in with first-pass product.*Because the two product streams are mingled, computing the magnitude of thehidden factory is difficult, especially using traditional cost accounting

Fortunately, we can use Y TP to estimate this magnitude, based on the following:

R≅ 1 + K⋅ (1 – Y TP) (14.2)

In Equation 14.2, R represents the amount of resources required to produce andrework a product, including the 100% necessary to do everything just once FromEquation 14.1 we can tell that if DPU is low, then Y TP is nearly 1 From Equation 14.2,

we can see that if Y TP approaches 1, then R does, too In other words, low defectrates enable us to run our process very close to its “entitlement” level of R = 100%.However, as defect rates rise and Y TP falls, we must add extra resources to handlethe rework caused by the (1 – YTP) units that contain one or more defects Thecoefficient K quantifies the extra resources

To understand K, consider Figure 14.2, representing a ten-step process Twodefect scenarios are shown In one, a defect is detected at step 3 and reworked atstep 2 For this defect, the value of K is one step repeated out of a total of ten, or

K = 1/10 = 0.1

However, we also show a defect detected at step 10 and reworked at step 1.What is not shown for the rework at step 1 is whether the product can be returnedimmediately to step 10, or whether it must pass through the entire process all overagain The answer depends as much on the type of defect as on the type of product

FIGURE 14.1 How 1 DPU might appear in 100 units.

* One exception occurred on a certain automotive assembly line in Europe, where a full 1/3 of the factory floor was designated for fixing defects.

2 0 2 1 3 0 0 2 0 0

0 0 1 1 0 0 1 0 1 0

2 1 1 2 0 1 0 1 0 2

0 0 0 1 0 1 0 1 2 2

1 2 0 1 0 1 2 0 2 2

3 0 1 2 0 2 1 1 1 1

0 1 1 0 1 0 1 2 4 0

2 0 0 2 1 1 3 0 0 2

1 2 1 3 0 1 2 2 2 1

0 0 2 2 2 1 0 2 1 0 SL3003Ch14Frame Page 298 Tuesday, November 6, 2001 6:04 PM

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Six Sigma Problem Solving 299

Here the value of K can be anything from 0.1 to 0.9 In fact, K can be any valuegreater than zero, in light of other resource requirements:

A Six Sigma problem-solving team may be able to estimate an average value

of K However, it takes a lot of work to do so Also, process changes that reducedefect rates are likely to alter the value of K

As a rule of thumb, consider using a value of K≅ 0.5 Though this tends to be

on the low side of reality, the following discussion will show its impact

Consider a process with DPU ≅ 2.3 Based on Equation 14.1, the resulting Y TP≅ 0.1,meaning that only 10% of product starts completes all steps of production defect-free Using the default value of K = 0.5, we can use Equation 14.2 to estimate that

R≅ 1 + 0.5 ⋅ (1 – 0.1) = 1 + (0.5 ⋅ 0.9) = 1.45Thus, rework consumes an estimated 45% more resources — floor space, capitalequipment, personnel, etc — than it should take to do the job right the first time.Putting it another way, approximately 31% of the process’s resources are consumedfixing defects

Suppose this team was able to reduce defects by 75% — an accomplishmentthat is fairly routine in Six Sigma problem solving Table 14.2 shows the before and

after numbers Note that the reduction in the hidden factory is 42%, which is lessthan the reduction in defects

FIGURE 14.2 Various rework scenarios.

Is rework complete after step 2 (short dotted line)?

Or must the entire process be repeated (long dotted line)?

10 3

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300 The Manufacturing Handbook of Best Practices

Consider the ramifications of DPU and hidden factory

• DPU provides ease of measurement and process information

• Hidden factory estimates the financial impact of waste due to defects

This indicates why Six Sigma seeks eventually to achieve even lower defect

levels and how such improvements relate to financial performance

Recall that we started this discussion by presuming that all defects could be detected

and contained In reality, that seldom is the case A rule of thumb is that one stage

of visual inspection detects 85 to 90% of all defects.*

Let us apply this to the process described in Table 14.2, presuming that the 2.3

DPU represent 87.5% of all defects, detected using a single visual inspection stage:

DPUActual≅ 2.30 ÷ 0.875 = 2.63DPUDelivered≅ 2.63 – 2.30 = 0.33(Y TP)Delivered≅ e–0.33 = 72%

1 – (Y TP)Delivered≅ 28%

Thus, approximately 28% of the delivered product contains at least one defect

If customer complaint data show a lower rate, the business may have to contend

TABLE 14.2 Impact of 75% Reduction in DPU

Before 6σ After 6σ

Defects Detected & Reworked

Defects per unit (DPU) 2.30 0.58 Throughput yield (Y TP) 0.10 0.56

Shipped units defective 28% 8%

* Automated inspection systems have become popular lately However, the reader is cautioned: though

their speed is indisputable, many have fared poorly in tests of accuracy.

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Six Sigma Problem Solving 301

with customers who are silently dissatisfied The second column shows how reducing

defects by 75% cuts delivered defectives to 8%

One can reduce defects by adding subsequent inspections, each of which should

detect roughly 85 to 90% of the remaining defects In this case, we include in our

estimates the cost of inspection resources A brief exercise in these numbers shows

why quality cannot be “inspected in” as anything but a temporary containment

measure

The primary mission of Six Sigma problem solving is to eliminate defects However,

the activity includes gathering defect data, which provide an estimate of the financial

impact of the team’s efforts When we compare escaping defects with customer

complaint data, we begin to understand how quality may be affecting more than just

profits

As a temporary measure, we can institute more inspections However, the object

is to eliminate defects Now that we have considered the financial ramifications of

defects, let us proceed to the means by which defects are prevented from recurring

14.2 BASICS OF PROBLEM SOLVING

The literature abounds with descriptions of MAIC and DMAIC as models of Six

Sigma problem solving In truth, these are variations on themes that have been

around for decades, starting with the granddaddy of them all: Shewhart’s and

Dem-ing’s plan–do–study–act (PDSA) The effectiveness Six Sigma problem solving is

based on the same principles that make many other team-based, problem-solving

approaches effective

Consider briefly the overall activities in Six Sigma problem solving, similar perhaps

to Figure 14.3 This summary does not describe any single methodology, but rather

describes common aspects of the more effective approaches Table 14.3 summarizes

the activities and why they are important Traditional problem solving is

character-ized by the tendency to omit or abbreviate steps In such environments, problems

tend to hide and reappear at inconvenient times

In Figure 14.3, each row represents a community within a business, and the

sequence of activities proceeds from left to right The white box naming each activity

encompasses the typical participants in that aspect of the problem-solving process

Finally, the crosshatched boxes represent groups that may be called upon periodically

during a given activity

Note the distinction between Upper Management and Middle Management

Middle management tends to be closer to immediate process supervision, so they

participate more than top management Also note that Team is separate from

Oper-ators, because one operator usually represents numerous peers in team activities

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302 The Manufacturing Handbook of Best Practices

Finally, note that the stages of DMAIC appear across the top of Figure 14.3, butwithout distinct boundaries Accomplished problem solvers recognize that hardboundaries simply don’t exist

FIGURE 14.3 Effective problem solving in manufacturing.

TABLE 14.3

Steps in Effective Problem Solving

Project kick-off • Common understanding • Focus on process to fix instead of “Rules

of Engagement”

 Objectives  Scope

Deliverables &

requirements

• Understand customers & needs • Objective metrics

• Fix the right problem

Describe “as is” • Qualitative process description • Quantified measures

• Objective performance data • Cost of poor quality

Root cause • Fix the right things • Consensus on “Vital Few” problem causes

Remedies • Implement the right fixes • Consensus on “Vital Few” interventions

Implement

changes

• Test drive revisions • Process improves as hoped

Implement control • Make improvements permanent • Self-sustaining at improved levels

Reap benefits • Reward contributors • Wait lists to join teams

• Spread the message • Project ideas proliferate

Success

? Remedies

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Six Sigma Problem Solving 303

Between published literature, Internet sites, and consultants’ offerings, the apparentvariety of problem-solving methodologies can be downright intimidating One way

to classify myriad materials might be to use the following categories:

• Tools: techniques and activities used to achieve specific outcomes, such

as gathering information or making decisions

• Methodologies: frameworks in which sequences of tools are selected andapplied to achieve broader objectives, such as project outcomes

• Infrastructure: organizational interventions to enhance the business’s ities to benefit from methodologies and tools

abil-The above list proceeds from the tactical to the strategic That is, individualscan understand and apply some tools rather quickly, whereas infrastructure requiresinvesting time and effort in both personal and organizational growth

The above categories can be used to create a rough classification of the chapters

of this handbook, shown in Table 14.4 As the table indicates, there is considerableoverlap among the classifications

At the methodology level, three approaches to problem solving are currently beingused extensively: DMAIC (Six Sigma), lean manufacturing (kaizen), and Ford’s eight-discipline team-oriented problem solving (also called TOPS or 8D) Ultimately, all threeadhere to the precepts of Figure 14.3, along with the PDSA philosophy

TABLE 14.4

Six Sigma Context of Handbook Chapters

Six Sigma Management (Chapt 2) Design of Experiments (DOE) (Chapt 3) Supply Chain Management (Chapts 16 and 17) Measurement System Analysis (MSA) (Chapt

9) Integrated Product & Process Development (Chapt 5) Process Analysis (Chapt 10)

Agile Enterprise

(Chapt 1)

Design for Six Sigma (DFSS) (Chapt 4)

ISO 9001 (Chapt 6) Design for Manufacture & Assembly (DFMA/DFSS) (Chapt 4)

ISO 14001 (Chapt 7) Theory of Inventive Problem Solving (TRIZ) (Chapt 19)

Theory of Constraints (TOC) (Chapt 18) Lean Manufacturing (Chapt 8) Quality Function Deployment (QFD) (Chapt

11) Six Sigma Problem Solving (Chapt 14)

Robust Design (Chapt 13)

Manufacturing Controls Integration (Chapt 12) Statistical Quality/Process Control (SPC) (Chapt 15)

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304 The Manufacturing Handbook of Best Practices

Table 14.5 provides a rough comparison of the steps associated with theapproaches, with a brief summary of each step’s purpose Table 14.6 provides someguidelines on the strength of the tools in specific problem-solving situations Here

is a brief description of how the three methods work:

TABLE 14.5

Comparison of Problem-Solving Approaches

6 σ

Plan

Form team Recognize Tie quality to strategy

Define Prioritize projects & resources

Describe problem Define actual

Understand process behaviors

• Key input variables

• Sources of variation

ID root causes Choose & verify

corrective actions

Remove root causes Improve Finalize what to change

Study Implement permanent

corrections

Change procedures

to sustain gains Control Sustain gains

Act Prevent recurrence Standardize Standardize

Become accustomed to new procedures

Integrate Propagate improvements

Celebrate Recognize & encourage

success

TABLE 14.6

Applicability of Problem-Solving Approaches

Application Ford 8D (TOPS) Lean (KaiZen) 6 σ (DMAIC)

Manufacturing quality Strong Strong Strong

Lean manufacturing Moderate Strong Moderate

Transactional Moderate Moderate Strong

Design Moderate Moderate Strong

Infrasturcture Weak Weak Moderate

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Six Sigma Problem Solving 305

14.2.2.1 Six Sigma DMAIC

The primary topic of this chapter, DMAIC, originated as an approach to rectify qualityproblems on the manufacturing floor It has also proven effective in addressing qualityproblems throughout an organization, including transactional and design issues Inconjunction with project management, DMAIC even supports establishing infra-structures

As discussed in Chapter 2, the right kind of management involvement andorganizational infrastructure strongly influences the degree to which problem solvingaffects the bottom line Of course, this pertains to all problem-solving methodologies

14.2.2.2 Ford 8D TOPS

Some consider this to be a variant on a method of problem solving attributed toKepner and Tregoe Although particularly effective at rectifying quality problemsoriginating on the manufacturing floor, it has also had some success in design andtransactional processes Traditionally, 8D has not been a major component of man-agement strategy; instead it is controlled closer to the teams

14.2.2.3 Lean Manufacturing

So-called “lean” encompasses a broad range of topics, including single minuteexchange of die (SMED, or quick changeover), poka-yoke (defect prevention), andkanban (“pull” system production and just-in-time inventory) The theory of con-straints was developed separately from lean, but the approaches are quite compatible.The primary focus is on maximizing how efficiently the organization’s resourcesdeliver output Defect reduction is a means to achieve this end

The problem-solving aspect of lean is called kaizen, in which production floorteams have extensive localized control of their process Whereas lean often is astrategic issue for top management, kaizen tends to be controlled closer to teams.Likewise, while Lean can attack design and some transactional issues, kaizen tends

to emphasize the factory floor

14.3 SELECTING TOOLS AND TECHNIQUES

To some degree, there are two types of decisions to make when approaching selection

of tools and techniques for Six Sigma

The strategic decision occurs at the executive level: whether to favor DMAIC, 8D,lean, or some other fundamental approach to problem solving Here, the coordinatorwields considerable influence with the top staff, who must rely upon his or herjudgment and impartiality

During projects, practitioners, experts, and masters make many tactical sions They have “tool boxes” from which to select, along with skills to aid in theselection Managers need enough understanding of the tools to help teams overcomeobstacles against tool use Table 14.7 shows a list of common problem-solving tools,with some ways each tool might be useful:

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