So, for the process of inflating the tires on cars in an assembly line, a study may reveal that of the 352 cars that went through the tire inflation process during a day’s production, 347 were later found to have a pressure within the required specification limits. In this case, the traditional yield is

Y=

Out In

347 352

0.986 or 98.6%

Converting from a proportion like 0.986 to perhaps a more familiar percentage scale is done by simply multiplying the proportion by 100. To go from percentage back to proportion, divide the percentage by 100.

Always perform mathematical operations on proportions, not on percentages.

The traditional calculation of yield is often employed on the last, final inspection step of a process to measure the effectiveness of the overall process.

The Six Sigma perspective: First time yield (FT\l)

The results of calculating yield the traditional way are misleading. Take a closer look at the tire-inflating example process in Figure 6-5.

Items in

(352)

Figure 6-5:

Detailed

View of a tire-inflation

Process.

R

(5)

1

Scrap

Items out

(347)

After inflation, the tire is immediately inspected to make sure it meets the required pressure specification limits. In the example, 103 tires are detected that don’t comply with the pressure specification. Of course, the operators of the process reviewed each of these 103 and corrected (or Reworked) 98 of them, leaving only five that were not able to be brought back within the correct pressure range and had to be scrapped.

With this detailed information, you now know that the proportion of tires going through the inflation process correctly the First time Is

249 0 707 or 70 70/ 352 = 0.707 or 707/0

This calculation of yield is appropriately called First time yield Or FTY for short. First time yield is often much different than traditional yield. That’s because, unlike traditional yield, it captures the harsh reality of the effectiveness of

The process, including inspection and rework. Uncovering the hidden factory

Figure 6-6 shows the tire inflation process again, this time with the previously hidden, but now revealed, part of the process clearly identified.

Items in (352)

Figure 6-6:

The hidden factory caused by inspection

And rework.

I (98)

(103)

_L_

Rework

(5) ±

Scrap

Tire inflation
Process
-	Inspection	1 1

Items out

(347)

The hidden factory

I I

The hidden factory is a natural outgrowth of the inability to correctly comply

With required specifications the first time through the process. Here and there throughout organizations, hidden factories arise and become entrenched as tacit appendages of the standard processes. Measuring yield using the first

Time yield method forces you to objectively review and acknowledge the effectiveness of your processes.

In the case of the example tire inflation process, the hidden factor of in-process inspection and rework accounts for 98.6/ – 70.7/ = 27.9/ of production. All

Together, value-sapping hidden factories within organizations combine to consume valuable resources and time.

Rotted throughput uietd (RT\l)

In reality, individual process steps are strung together to create an overall

Process structure for accomplishing complex tasks. One way Six Sigma quantifies the complexity of a system is to count the number of processes involved.

For example, Figure 6-7 illustrates a purchase order process that is made up of five individual process steps.

Figure 6-7:

Several

Smaller

Process steps link together to create a complex process.

How do you calculate the overall yield for a string of processes? The answer: You multiply the first time yields for each step together, creating what is called the Rolled throughput yield (RTY).

For the purchase order example given in the preceding section, the rolled throughput yield for this five-step process is

RTY = FTYI X FTY-2 X FTY:i X FTY4 x FTY5 RTY = 0.75 X 0.95 X 0.85 X 0.95 X 0.90 RTY = 0.518

That means that the chance of a purchase order going through the process the first time with no rework or scrap is only 51.8 percent! (The last "confirmation"

Step in the process acts as a final test. With this last step having a 90 percent yield, there must be a lot of hidden factory stuff going on to drop the RTY down to 51.8 percent.)

Like a chain that is only as strong as its weakest link, rolled throughput yield can never be greater than the lowest first time yield within the system. To immediately improve the overall system performance, focus first on the individual process step with the lowest first time yield. Then move on to the step

With the next lowest first time yield.

The formula for rolled throughput yield can be simplified as

I – 1 I I

I = \

Where the Greek letter pi (I I) tells you to multiply all the first time yields of the system together. (See Table 6-1 for a summary of yield metrics.)

Even if the first time yields of the individual process steps are high, if the overall process becomes more and more complex (that is, more and more

Process steps), the system rolled throughput yield will continue to erode.

Figure 6-8 charts how complexity degrades rolled throughput yield for different levels of individual first time yield.

For very complex systems — like automobiles, aircraft, data switching systems, enterprise-level business processes, and so on — a very high individual first time yield must be achieved in order to have any hope of an acceptable

Rolled throughput yield.

Table 6-1 Summary of Yield Metrics
Metric Name	Calculation Formula Description
Traditional yield (Y)	Y_ Out _ in – scrap _ 1 scrap in in in	Is a misleading perspective that obscures the impact of inspection and rework.
First time yield (FTY)	_ in – scrap – rew°rk _ 1 – scrap + rework in in	Shows the likelihood of an item passing Through a process Successfully the very first time. Includes the effects of inspection, rework and scrap.
Rolled throughput	N RTY_ n FTY, I _ 1	The combined overall Yield of an entire

Yield (RTY) Process stream. Tells

You the likelihood of an item passing through all process steps successfully the first time.

Measuring defect rate

The complimentary measurement of yield is defects. If your yield is 90 percent, there naturally must be 10 percent defects. Measuring defects and calculating the rate or how often they occur is like looking at the flip side

Ofthe yield coin. Defects etfuat failure

When a process or characteristic doesn’t perform within its specifications, it is considered defective. Or in other words, it produces a non-compliant condition, called a Defect.

Defining a defect as a non-compliance with specifications may seem overly simplified. Just because a characteristic exceeds a specification doesn’t necessarily mean that the system it is part of will break or stop functioning. It may or may not. For example, misspelling a customer’s name on a billing statement (a defect or non-compliance with specifications) may or may not turn into a complaint (a failure) that costs money to correct.

But over and over again, experts have verified that product or process failures are directly related to compliance with specifications; the less you are compliant with specifications, the more likely you are to have a failure or

Breakdown.

So given the difficulty in directly linking compliance with specifications to

Product or process performance, the safe thing to do is to make sure you strive

To comply with specifications. The absence or reduction of non-compliance

With specifications will always reduce failures or breakdowns in your customers’ experiences.

Defects per ubiquitous unit (DPU)

Six Sigma applies to all areas of business and productivity — manufacturing,

Design, sales, office administration, accounts receivable, healthcare, finance,

And so on. Each of these areas works on and produces different things —

Products, services, processes, environments, solutions, among others.

To bridge these diverse disciplines, in Six Sigma you call the item you are working on a Unit. A unit may be a discretely manufactured product. Or it may be an invoice that crosses your desk. It may be a month’s worth of continually produced product. It may be a hospital patient or a new design. Whatever it is you do, in Six Sigma it is called a Unit.

A basic assessment of characteristic or process capability is to measure the

Total number of defects that occur over a known number of units. This is then

Transformed into a calculation of how often defects occur on a single unit,

Like this

Dpu_ Number of defects observed

Where DPU stands for defects per unit.

For example, if you process 23 loan applications during a month and find 11 defects — misspelled names, missing prior residence information, incorrect

Loan amounts — then the DPU for your loan application process is

DPU_ 11 _ 0.478

That means that for every two loans that leave your desk, you expect to see

About one defect.

Leveling the field: Defects per opportunity (DPO) and per million opportunities (DPMO)

A DPU of 0.478 for an automobile is viewed very differently than the same

Perunit defect rate on a bicycle. That’s because the automobile, with all its thousands of parts, dimensions, and integrated systems, has many more

Opportunities for defects than the bicycle has. A DPU of 0.478 on an automobile is evidence of a much lower defect rate than the same DPU On a relatively simpler bicycle. It’s just not a fair comparison.

So how do you compare or contrast the defect rates of things that have very different levels of complexity? The key is in transforming the defect rate into terms that are common to any unit, whatever it is or however complex it may be.

The common ground between any different units is opportunity. For any product, process, service, transaction, or environment, an Opportunity Is a specific characteristic that could either turn out as a defect or as a success. Success or failure for the opportunity is defined as compliance to the opportunity’s specification.

Examples of opportunities include:

In a product, the critical dimension of diameter on an automobile axle.

In a transactional process, the applicant’s mailing address on a loan approval form.

F In a hospital, getting the correct medial history records into the patient’s file.

V In the design of a retail store environment, the placement of clearance

Sale racks.

F In a manufacturing process, the tightening of a bolt to the correct torque.

The number of opportunities inherent to a unit, whatever that unit may be, isa direct measure of its complexity. In fact, when you want to know how complex a unit is, you count or estimate how may opportunities there are forsuccess or failure. Individual characteristics that are critical to the

Performance of the system are opportunities. Characteristics that have a

Specification represent opportunities.

The way to level the playing field so you can directly compare the defect rates of systems with very different complexities is to create a per-opportunity defect rate. This measurement of capability is called Defects per opportunity (or DPO)

And is calculated as

Dpn _ Number of defects observed on a unit O number of opportunities on a unit

With a calculated DPO measurement, you can now fairly compare how capable an automobile is to a bicycle. For example, you may observe 158 out-of -

Specification characteristics on an automobile. After some study, you also

Determine that there are 14,550 opportunities for success or failure within that automobile. Its DPO Is then

DPO _ 158 _ 0 011 DPO 14,550 0.011

For a bicycle, on the other hand, you may find only two non-compliant characteristics among its 173 critical characteristics. So its DPO Is

DPO _ _ 0.012

Even though an automobile and a bicycle are two very different items with very different levels of complexity, the DPO Calculations tell you that they both have about the same real defect rate. You only observe more defects on the automobile because there are many more opportunities for defects.

Be careful not to overly estimate the number of opportunities on a unit. You can artificially make the DPO Of your product, process, or service look better than it really is by inflating its number of opportunities. For example, you could count the correct name on a patient record as a single opportunity for

Success or failure; whether the name on the form is right or wrong. Or you

Could say that there’s one opportunity for the correct spelling, another for

The correct font, another for the correct darkness of the printed text, another for the name’s placement within the form box, and so on. Playing opportunity

Counting games only shrinks your ability to make an honest assessment and

Begin to make real improvement.

When the number of opportunities on a unit gets large and the number of observed defects gets small, calculated DPO Measurements become so small

They are hard to work with. For example, two commercial airline crashes (defects) observed out of 6 million flights in a year translates into

DPO _ 6 000 000 _ 0.000000333

0.000000333 is definitely an inconvenient number to work with!

You may also want to estimate out into the future, to know how many defects will pile up after running the process or observing the characteristic for a long time. After all, DPU And DPO Look only at a single unit or a single opportunity.

A simple way to solve both of these problems is to count the number of defects over a larger number of opportunities. For example, how many defects occur

Over a set of one million opportunities? This defect rate measurement is called

Defects per million opportunities (or DPMO) And is used very frequently in Six

Sigma.

When a process is repeated over and over again many times — like an automobile assembly process, or an Internet order process, or a hospital check-in process — DPMO Becomes a convenient way to measure capability. Six Sigma

Is famous for its defect rate goal of 3.4 defects per million opportunities.

When calculating DPMO, You don’t want to actually measure the defects over a million opportunities. That would take way too long. Instead, the way you

Calculate DPMO Is using DPO As an estimate, like this

DPMO = DPO x 1,000,000

This also means you can track backward, going from DPMO to DPO:

DPO_ Tij0MO0

A common alternative form of DPMO Is DPPM— Defective parts per million. DPPMIs often used when assessing the defect rate of a continuous material

Or process where the "part" is the opportunity. Like in ongoing shipments of bolts to a supplier, the cumulative number of defective bolts found compared

To the total number shipped over time can be translated into DPPM. (See

Table 6-2 for a summary of defect rate metrics.)

Table 6-2 Summary of Defect Rate Metrics

Metric Name	Calculation Formula	Description
Defects per unit (DPU)	DPU_ number of defects observed numberofunitsinspected	DPU Provides a measurement of the average number of defects On a single unit.
Defects per opportunity (DPO)	DPO Number of defects observed on a unit DPO Number of opportunities on a unit	DPO Measure the number of defects that occur per opportunity for Success or failure. DPO Allows you to fairly compare the Defect rates of Things with very Different levels of Complexity.
Defects per million opportunities (DPMO)	DPMO = DPO x 1,000,000	DPMO Is the average number of Defects found over a Million opportunities. It is best used when the process or Characteristic is repeated many times.
Defective parts per million (DPPM)	DPPM = DPO x 1,000,000	DPPMIs Synonymous with DPMO.

Linking yield and defect rate

You can calculate the yield of a process or characteristic. You can also calculate the defect rate of a process or characteristic. Are these two measures related? In fact, they are.

When you have an overall process with a relatively low defect rate, say, a process that produces units with a DPU less than 0.10 (or 10 percent), you can mathematically link the process defect rate to the overall process yield:

RTY _ e ~DPU

Where E In the equation is a mathematical constant equal to 2.718. There will be a function or key for raising E To a number on any scientific calculator or any spreadsheet computer program. (Look for the Ex Key on your calculator.)

The actual value of the constant E Is 2.71828182845905. . . . The decimal digits of E Go on forever, never repeating. But you don’t need to know the details of this curious constant called E To excel at Six Sigma. If, however, you feel yourself compelled to know more, you can proudly claim the title of "math geek." And by all means, find yourself a copy of Calculus For Dummies By Mark Ryan (Wiley) to find out more about the fascinating number E!

The power of this mathematical link between yield and defects, is that if you can only measure or have only measurements of the defect rate of a process, you can still calculate its rolled throughput yield.

A little bit of algebraic contortions provides an equation to calculate DPU Based only upon the rolled throughput yield of a process:

DPU = – ln(RTY)

Where ln is the natural logarithm. (Hint: There’s an ln button on every scientific calculator.)

Sigma (Z) score

From a quality perspective, Six Sigma is defined as 3.4 defects per million opportunities. This is called a Six Sigma level of quality. What is this famous

Sigma level or score? Sigma scores are thrown about so much, you definitely

Need to be comfortable understanding what they are and how they are

Calculated.

Ho© many standard deviations can fit>

Figure 6-9 illustrates a process or characteristic performance distribution

Compared to its one-sided specification.

Figure 6-9:

A characteristic’s performance distribution as defined by its mean X And its

Standard

Deviation cr.

"l-1-1-1-r

Characteristic Scale of Measure

The central tendency of the performance distribution is defined by its mean. The amount of variation in the performance, or the width of the distribution, is defined by its standard deviation cr. The question is, how many standard deviations can you fit between the process or characteristic’s mean and its specification limit SL?

Graphically, in Figure 6-9, you can see that four standard deviations can fit

Between the mean and the specification limit. The exact number can always

Be calculated (even without a graph!) by the formula

Z _ -

O

Mis-

Calculating Z Tells you exactly how many standard deviations can fit between the mean and specification limit of any process or specification. In Six Sigma, you call this value the Sigma score Of the process or characteristic.

Statisticians usually call this same value the Z Score or Normal Score. In Six

Sigma, however, you need to be careful not to confuse the sigma score

(sometimes called a Sigma value, Or even simpler just Sigma) With the standard deviation represented by the Greek letter <r. Z Score, Z Value, Z, Sigma score, sigma value, and sigma are all different names for how many standard

Deviations can fit between the mean and the specification limit. Things get

Confused when practitioners call the standard deviation "sigma." In this

Book, we always call the standard deviation the standard deviation. To avoidthe confusion yourself, whenever you are reading or speaking about

A a, don’t call it "sigma." Instead, call out "standard deviation" for what the symbol always represents.

Use a sigma (z) score only on a characteristic that is approximately normal.

That means its distribution needs to be bell shaped. When the distribution is far from normal, the formula for calculating the sigma score (Z)breaks down.

The quickest way to check whether the distribution is approximately normal is to create a dot plot or histogram. (See Chapter 5 to do this.)

A low sigma (z) score means that a significant part of the tail of the distribution is extending past the specification limit. So the higher the sigma (z) score, the fewer the defects. A process or characteristic gets a good sigma (z) score when the variation distribution is safely away from the edge of the

Specification cliff.

There are three ways a sigma (z) score can change: F The location of the central tendency of the distribution, the mean,

Moves either closer or farther from the specification limit.

V The width of the distribution, as defined by the standard deviation A, Gets either wider or narrower.

F The location of the specification limit SL Moves either closer or farther

From the characteristic or process variation.

Actually, changes to X And a usually happen at the same time, with both simultaneously contributing to a change in the computed sigma (Z) score.

Short-term Versus long-term sigma score

From the mean X And the standard deviation cr, you can calculate a sigma (z) score. A wrinkle here is that you must know what type of standard deviation

You are using to calculate the sigma (Z)score: Is it a short-term standard

Deviation <rST, or is it a long-term standard deviation <%? (To understand the critical differences in short – and long-term standard deviations, and the implications, see Chapter 5.)

If you are using a short-term standard deviation, the sigma (Z)score you

Calculate is a short-term sigma score ZST:

If, however, you have a long-term standard deviation, you can calculate the long-term sigma score Zlt:

Zlt _ Olt

Short-term variation performance, as quantified by the short-term sigma

Score Zst, Represents the best variation performance that you can expect out

Of your currently configured process. It is an Idealistic Measure of capability. It is also the easiest type of data to collect — you just go and quickly grab a relatively small sample of measurements from the process or characteristic.

But in the real world, a process or characteristic doesn’t operate ideally like it does in the short-term. Its performance is degraded by shift, drift, and

Trend influences.

At the heart of Six Sigma is a method that combines the best of both worlds. It allows you to leverage the economy of short-term variation data while projecting realistic, long-term performance versus the process’s or characteristic’s specifications.

Shifty business: Linking short-term capability to long-term performance ©ith the 1.5-sigma shift

Figure 6-10 shows the short-term variation of a process or characteristic and

Its expanded, long-term variation.

Figure 6-10:

A characteristic with short-term variation that complies with specifications, but

With an

Expanded long-term

Variation that creates defects.

Short-term

Long-term

Defects

Characteristic Scale of Measure

The characteristic or process shown in Figure 6-10 stays within specifications

During the short-term. It looks like there aren’t problems. But over the long term, disturbances to the problem cause it to expand and sometimes create defects beyond the specification limit.

One mathematical way to simulate the effect of these degrading, long-term influences is to artificially move the short-term distribution closer to the specification limit until the amount of defects for the short-term distribution

Is the same as that for the long-term distribution. This approach is shown in Figure 6-11.

Early practitioners of Six Sigma proposed that mathematically shifting a characteristic’s or process’s short-term distribution closer to its specification

Limit by a distance of 1.5 times its short-term standard deviation (aST) would approximate the amount of defects occurring in the long term. This breakthrough can be applied directly to the calculation of short-term and long-term

Sigma (Z)scores.

Figure 6-11:

Mathematically shifted

Short-term distribution used to estimate the long-term variation performance.

Characteristic Scale of Measure

Because ZST Represents the number of short-term standard deviations between the variation center and the specification, the sigma (Z) score of the shifted

Distribution is

ZShifted= Zst - 1.5

But with the shifted distribution being equivalent, defect-wise, to the long-term distribution, the preceding equation can be rewritten as

Zn= ZST - 1.5

So what Six Sigma practitioners do is measure the short-term variability of a process or characteristic and calculate its short-term sigma score ZSt. Then they immediately translate this to the expected long-term defect rate performance, using the 1.5 short-term standard deviation shift. This long-term sigma score, Zm Is communicated in terms of defects per million opportunities, DPMO.

Table 6-3 is a look-up table that Six Sigma practitioners carry around in their pockets and use over and over until they have it memorized (or until it is worn out, whichever happens first). They figure the ZST For any process or

Characteristic, and then translate that into a long-term defect rate DPMO. Or,

In reverse, they first find the DPMO, and then translate that back to a short-term sigma score ZST.

Table 6-3_Sigma Score Table: Z — DPMO

Z_DPMO_

0.0_933,193_

0.5 841,345

ZDPMO

1.0 691,462

1.5 500,000

2.0308,538

2.5158,655

3.0 66,807

3.5 22,750

4.06,210

4.51,350

5.0233

5.532

6.0 3.4

Note: Paired table values are long-term for DPMO and short-term for Z (example, a long-term DPMO of 6,210 is the result of a process with a short-term sigma score of 4.0). Add 1.5 to corresponding Z values to obtain short-term equivalents (example, a short-term DPMO of 32 is the result of a process with a short-term sigma score of 4.0).

What’s your sigma, bab§>

As you work in Six Sigma, you may hear someone ask, "What’s the sigma of the process?" And the response you’ll hear back is, "2 sigma" or "3.3 sigma" or such-and-such sigmas. The question these people are really asking is, "What is the short-term sigma score ZST Corresponding to the long-term

Defect rate of the process?"

After only a few times looking up sigma score values in Table 6-3, you begin to get a feel for this famous scale of capability. You may even be able to

Approximate sigma scores for defect rate values that fall between the rows

Of the table. Like a DPMO Of 20,000. Its sigma score is about 3.6, a value just a little larger than the 3.5 corresponding to the DPMO Of 22,750 in the table.

The sigma score can be applied to the performance of anything that has a specification and a defect rate: the performance of the mail system in delivering letters to the correct address, the ability of an automobile manufacturer to produce a door that fits to the body within a required dimensional tolerance,

Or a repeated budgeting process that must be completed within its specified schedule window.

All these sigma scores can be directly compared to see how capable the process or characteristic is. And when you communicate this capability with a sigma score, everyone else in Six Sigma knows exactly what you’re talking

About.

Capability indices

Yet another set of measures exists to quantify the capability of a process or characteristic to meet its specifications. This last set are indices that directly compare the voice of the process to the voice of the customer.

Short-term capability index (CP)

The simplest capability index is called CP. It compares the width of a two-sided specification to the effective short-term width of the process. Determining the width between the two rigid specification limits is easy. It is simply the distance between the upper specification limit USL And the lower specification limit LSL. But with variation that trails out at the tails, how do you determine the width of the Process?

To get over this hurdle, Six Sigma practitioners have defined the effective Limits Of any process as being three standard deviations away from the average level. At this setting, these limits surround 99.7 percent, or virtually all, of the variation in the process. This is shown graphically in Figure 6-12.

Figure 6-12:

The effective width of a process or characteristic is ±3 standard deviations, containing 99.7 percent of the process

Variation.

Standard Deviations

So to compare the width of the specification to the short-term width of the process, you use the formula:

Ce = 6CJst

Where Usl - Lsl Represents the voice of the customer’s requirements and 6crST represents the inherent voice of the process.

A calculated CP Value equal to 1 means that the voice of the customer is equal to the voice of the process. A CP Value less than 1 means that the process is wider than the specification, with defects spilling out over the edges. A CP

Value greater than 1 means that the effective width of the process variation isless than the required specification, with fewer defects occurring.

CP Is a measure of short-term process or characteristic capability. Use only the short-term standard deviation to calculate its value. Using a long-term

Standard deviation in its calculation gives you incorrect results.

Adjusted short-term capability index (C„)

A problem with the short-term capability index CP Is that it only compares the widths of the specification and the process. Figure 6-13 illustrates this

Problem.

Figure 6-13:

Two

Distributions, one centered and one offset

From the

Specification limits.

In Figure 6-13, both the distribution drawn with the solid line and the distribution drawn with the dotted line have the same calculated Cp. That’s because

They both have the same specification width and the same process width. But the are not equally capable. Because it is offset from the center of the specification, the dotted line distribution has many more defects than the solid

Distribution.

You can compensate for this by adjusting the CP Calculation for how far it is offset. To do this, you simply compare the distance from the distribution center X To each of the specification limits with the half-width of the short-term variation that should exist between the center of the distribution and the specification limit, like this

The smallest value you calculate of CPU And CPL Is called the adjusted short-term capability index CPK. So the formula for CPK Can be written as

CPk = Min ( CPu , CP

Where the Min In the equation tells you to choose the smallest of the values

In parentheses.

^Sty* If the characteristic or process variation is centered between its specification

Limits, the calculated value for CPK Will be equal to the calculated value for CP. But as soon as the process variation moves off the specification center, it’s penalized in proportion to how far it is offset.

CPK Is very useful and very widely used. That’s because it compares the width

Of the specification with the width of the process while also accounting for

Any error in the location of the central tendency. This is a much more realistic approach than what the CP Method offers.

Generally, a CPK Greater than 1.33 indicates that a process or characteristic is capable in the short-term. Values less than this tell you that the variation is

Either too wide compared to the specification or that the location of the variation is offset from the center of the specification. Or it may be a combination of both width and location. The only way to know for sure is to create a graph and begin to review the details.

Long-term capability indices 0PP and PPK)

The same capability indices that you calculate for short-term variation, CP

And Cpk, Can also be calculated for long-term variation. To differentiate them

From their short-term counterparts, these long-term capability indices are called PP And PPK. The only difference in their formulas is that you use in place of crST.

Long-term capability indices are important because no process or characteristic operates in just the short term. Every process extends out over time to create long-term performance. Table 6-4 summarizes each of the short – and long-term capability indices.

Table 6-4 Summary of Short – and Long-Term Capability Indices

Index Name Formula_Description_

Short-term CP = crT Compares the width of

Capability index ST the specification to the

Short-term width of the

Process

Index Name Formula_Description_

Adjusted short – CPK = Min (U^_~ *, *~LSL) Compares the width of

Term capability V ST ST ‘ the specification to the

Indexshort-term width of the

Process and accounts for off-centering of the process from the specification

Long-term Pp = US^~~LSL Compares the width of

Capability LT the specification to the

Index long-term width of the

Process

Adjusted long – PPK = Min (US-~ *, *-7rrLSL) Compares the width of

Term capability V LT LT ‘ the specification to the

Index long-term width of the

Process and accounts for off-centering of the process from the

Specification

Prescribing a capability improvement plan

When you know what the short – and long-term capability indices of a process or characteristic are, what do you do? How can you use these four indices to chart out a plan for improvement?

Table 6-5 outlines the various scenarios that may occur when measuring the capability of a process or characteristic. The table also describes an improvement plan for each scenario.

Table 6-5_Prescriptive Capability Improvement Plan

Symptom Diagnosis_Prescription_

CP = CPK Overall, your process or As needed, focus on reducing

And characteristic is centered the long-term variation in

PP = PPK Within its specifications. your process or characteristic

While maintaining on-center performance.

Continued

Table 6-5 (continued)
Symptom Diagnosis Prescription
CP = PP	Your process or character – Focus on correcting the set
And istic suffers from a consis – point of your process or char -
Cpk = PPK	Tent offset in its center acteristic until it is centered.
Location.
Cp = Ppk	Your process is operating at Continue to monitor the capa -
Its entitlement level of bility of your process. Redesign
Variation. your process to improve
Its entitlement level of
Performance.