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Transcript of y=f(x)
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32 GEARS July 2007
This formula y = f(x) read y is a function of x is one of the foundations of Six Sigma, and one of the key elements of Whats Working and Making It Work. But it isnt the formula itself thats important; its the thinking it represents.
If you look at the formula, youll notice it has three variables: y, f, and x. They represent the three components of a results-oriented project:
f stands for function and is the process of the project. Think of it as the things you do or the steps you take.
x represents the components you put into the process.
y represents the outcome, the results youre looking for, the yield.
Lets use a rather silly example for this, but one thatll make the point real-ly well. Suppose youre baking a cake. You have a list of ingredients, such as 2 eggs, 1 cup of milk, 3 cups of flour, cup of sugar, etc. These are the compo-nents the xs of the formula.
Youre then going to follow the directions, which includes things like mixing the ingredients, putting the mix in a pan and baking it for 45 minutes at 350F. This is the process you follow; its the f of the formula.
By combining the ingredients with the process you wind up with a cake, the outcome the yield. You can dupli-cate the outcome over and over, pro-vided you use the same ingredients and follow the same directions. In fact, you
can have the same outcome regardless of whether you, your sister, or your neighbor down the street does it, as long as they follow the same process and use the same ingredients.
Now lets make a few changes. Suppose we use the same ingredients (xs) but follow a different process. Lets take all the ingredients, toss them in a bowl without mixing them and place the bowl in the oven at 200F for 3 hours. Needless to say, the cake (if you could call it that) wouldnt be the same as the first one; our yield wouldnt be satisfactory.
Now lets follow the same process but modify the ingredients. Instead of 2 eggs we use 1. Instead of 1 cup of milk we use 2 and instead of 3 cups of flour we use 4. We follow the direc-tions exactly as before, but use differ-ent quantities of the ingredients. As you would suspect, the cake wouldnt come out the same as the first; our yield would be different.
So far, everything weve covered is pretty obvious. What isnt so obvious is the part thats most important: The outcome, the yield, depends completely on the parts and process; the x and f. The outcome cant be altered directly! You cant change the cake unless you change the ingredients or the process for making it.
This may seem straightforward at first, but all too often we focus on the results and try to change them without recognizing that the results cant be changed directly; they can only be monitored. If you want to change the results you must change the process or the components that go into the pro-
cess. This formula, y = f(x), is a rule that were bound by, whether we under-stand it or not. Its sort of like the laws of physics: If you step off a cliff, youre going to the bottom whether youve taken a physics class or even recognize the laws of gravity. Lets look at this further and really get a handle on it.
The y of this formula, the yield, should really be thought of as what the customer wants; his needs. Success is based on fulfilling the needs of the customer. And if the needs of the customer change, then so must the process and components that provide that need. We can bake a great cake, but if the customer wants ice cream, we dont get the sale. This is why the 80s method of running a shop may not give you the success it did back in 1980 because the needs of the customer have changed.
Understanding this principle has really answered some questions for me. For example: How is it that two management trainers can have two completely different methods of train-ing, and yet both claim their program delivers success? That is, how can two people whove run successful shops, and have helped others achieve greater success in their shops, argue that the other doesnt know what hes talking about, and their management proce-dure doesnt work?
Well heres how: If a shop owner has achieved success, its by virtue of refining his (or her) processes and what he put into those processes that results in the successful outcome; the yield. After years of tweaking the process, he has a road map for success. This
y = f(x) by Dennis MaddenMAKING IT WORK
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34 GEARS July 2007
road map is proven and repeatable. It can be taught, and it provides success to those who follow it at least most of the time.
The two trainers refined their road maps over the years, each achieving success, yet their road maps are dif-ferent. Because theyve realized the success of their road maps, they know with certainty that they work, and they tend to reject other road maps that dont follow their paths.
Their road maps are different because there were things related to their customers or regional constraints that were different. Whether they real-ized it or not, they were bound by the rule that y = f(x). They paid attention to the outcome and changed their pro-cesses and the things they put into their processes until they developed the out-comes they were looking for.
Does this mean both maps will work if you follow the directions care-fully? For that, well use another silly example: Lets say theres a guy who makes an annual trek from Arizona to Alaska. Over a 10-year period hes been stuck in the snow, run out of gas, and had several other situations that either ruined his trip or slowed him down.
By the 11th year hes fully pre-pared. He knows to bring 4 blankets, chains for his tires, extra food and
water, a five-gallon can of gas, a CB radio, extra batteries for his flashlight, and another dozen items that he found necessary over this 10-year period.
Over the next few years he offers travel consultation and actual travel packs to people interested in extended road trips. The trouble is, the people headed to Florida are wondering why the travel packs contain tire chains. And who needs all those blankets? And wheres the mosquito repellant? You get the idea. Even for the travel-ers headed to Alaska, the travel packs are less appealing, because now there
are gas stations and motels every 10 miles along the route. Theres no need for the gas can and extra food, and one blanket will do; the customers needs have changed.
This is why youll find contradic-tory managing strategies and proce-dures from training classes, and sugges-tions you cant implement in your own shop. There may be nothing wrong with the information they provide; in fact, it may be fantastic. But if it doesnt fit your needs, it may be of little value. What good is a screwdriver when you need a hammer?
So first we must have a clear under-standing of the outcome were looking for. Whats Working is the part of this project that monitors the outcome. The survey is aimed at establishing what successful shops are doing in todays marketplace that brings them success. Not everything will fit your needs, but there are enough trends out there to define the outcome youre looking for. And for you left-brain people (like me), figure 1 shows an illustration that clari-fies the process of y = f(x).
In the next issue of Making It Work, well discuss the measuring process and the steps you take to change the outcome the yield. As the data from Whats Working continues to come in and be refined, well look at different ways of Making It Work for you.
MAKING IT WORK: y = f(x)
If you want to change the results
you must change the process or the com-ponents that go into
the process. This formula, y = f(x),
is a rule that were bound by, whether we understand it
or not.
The illustrations above represent three Function machines. Inside each machine is a mathematical equation that represents its function; the f of the formula. A number is placed into the machine on top; thats the x of the formula. The yield drops out of the bottom of the machine. As you can see the yield is completely dependant upon the x put into the machine and the function of the machine. These simple illustrations demonstrate the idea behind the equation y = f(x).
x=2 x=5x=3
x3 + 1
9 2828
x2 + 3x3 + 1
Figure 1
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T I M E T E S T E D I N D U S T R Y T R U S T E D TM
COrrection
Cause
The kit that fits and fixes slips
When the TCC PWM solenoid is energized and TCC signal fluid pressure is present, itstrokes the TCC regulator valve and regulates line pressure into the converter clutchapply passage. Due to the pulse width modulation of the solenoid, the regulator valve iscontinuously oscillating. Excessive wear at the large spool diameter can prevent propervalve movement, causing no TCC, slips or soft apply. Excessive wear at the balance endof the bore can lead to harsh apply. Additionally, the OEM valve stops against the TCCPWM solenoid screen, resulting in damage that can cause debris to become lodged atthe reverse lockout valve, resulting in no reverse. The Sonnax TCC regulator valve &sleeve kit includes a highly wear-resistant sleeve with significantly more valve support toreduce leakage and prevent wear. The modified valve is made of anodized aluminum to resist wear and prevent leakage, and the modified replacement springrestores proper converter clutch apply pressure with the undersized valve. The protective spacer eliminates solenoid screen damage.
COMPLAINT TCC slip and ratio codes SECONDARY COMPLAINTs Transmission and converter overheat Delayed or no reverse Reverse lockout valve sticking
Wear at the TCC regulator valve borereduces apply pressure or TCC sole-noid is damaged from valve contact.
This kit includes a wear-resistantsleeve, modified valve and spring to re-establish proper apply pressure to thetorque converter clutch, and preventsdamage to the TCC PWM solenoid.
TCC RegulatorValve & SleeveKit
55211-04K1 Sleeve1 Valve2 Retaining Clips1 Spring1 Spacer
F-55211-TL41 Reamer Jig1 Guide Pin1 Reamer
The Sonnax TCC Regulator Valve & Sleeve Kit for the 5L40-E re-establishes control over TCC apply pressure.
REQUIRE
D
TOOL
REQUIRE
D
TOOL
TCC PWM Soleniod
TCC Regulator Sleeve
Retaining Clip
TCC RegulatorValve
Spacer
Solenoid Retainer
TCC RegulatorValve Spring
Reamer Jig
Guide Pin
Reamer
5L40-E
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