(Illustration) To Indentify Potential X's

To Indentify Potential X's

Master: In the Improve Phase, we have three steps to lead us toward our goal.
Master: In Step one, we will take the list of potential causes we brainstormed in Analyze, step six, and determine which of them have the potential to be our vital Xs. This allows us to narrow our focus to the X's that may significantly impact the CTQ's.
Master: In step two, we will use a variety of tools to sicover the variable relationships and then propose one or more solutions to our problem. Just knowing the importance of a factor does not provide enough information to allow us to recommend a solution. We need to run additional tests in order to optimize our proposals.
Master: And finally in step three, we will establish operating tolerances for our revised process and pilot the solution.

Master: So your assignment in the Improve phase is to use all the information that has been acquired and calculated to identify the vital Xs, propose a solution, establish the operating tolerances and prove the solution through the pilot process.
Master : Frank will be your instructor in this phase. So I'm going to turn things over to Frank and let him introduce himself and then take you on through the Improve steps. You're up, Frank!
Instructor: Hi, I'm Frank Finding out all you can about your process and it's limitations is important, but I like to get to the point where we're fixing the actual problem. I have extensive experience in Design of Experiments and Statistical Tolerancing, which is where you determine how you're going to improve the process.

Instructor : At the end of the Analyze phase, you brainstormed a list of potential causes of variation. These are the candidates for the position of "Vital X." In step one, we do further analysis on these candidates and select the winner, or winners for the "Vital X" designation. The Fishbone, or Cause and Effect diagram, will help us link these potential Vital X's to the targeted effect, our Y.

Instructor : Let's quickly look through this Step's learning objectives. We will
>Identify the Vital X's for a given Y.
>We will also select the appropriate improvement strategy based upon characterizing the X's as either operating parameters or critical elements.
>We will review the applicability of a statistical techniques called Design of Experiments, or D O E, which allows us to test causality and which provides a solid statistical foundation to identify which factors are the Vital X's,
>Design and execute a screening DOE with factorial designs, and
>Define, describe, and explain the significance of a lurking variable.

Instructor : This is the fishbone chart we developed as a result of our brainstorming of potential X's. The team started analyzing the individual factors with an eye to narrowing down the choices for our project.

Instructor : The fishbone exercise is the first part of a brainstorming session. It serves as the container for all suggested factors. The second part of brainstorming involves tapping historical data, process knowledge, and process documents to eliminate as many factors as possible. Any factors not conclusively eliminated will be tested with a technique called Design of Experiments to validate their significance.
Instructor : The first area they looked at was the Tools branch.
Instructor : The shift supervisor and the mechanic said that none of the items listed under tools was a significant problem since existing procedures replace all worn or otherwise defective tools.
Instructor : The team then turned its attention to the question of environmental factors. The team's field engineer had been checking data on environmental factors and stated that he saw no potential for high benefits from attempting to control these items with the exception of ambient temperature. An engineer suggested that ambient temperature could affect the tightness between the stud and the nut, so they tentatively decided to leave it in.
Instructor : So the team looked at people. The shift supervisor and Jim had thought about these factors. They searched the records and found all technicians properly trained and certified through testing, and they decided to eliminate them as well,so this left Method and Materials.
Instructor : First, the team looked at the methods. The Shift Supervisor and the Mechanic pointed out that heating and cutting only took place if a nut was jammed or otherwise frozen to the stud, and had already been worked on too long.
Instructor : So removing that individual nut was already going to be out of spec if those steps were necessary.
Instructor : That left Torquing. The Supervisor pointed out that torquing only took place during nut installation, not removal. The Mechanic and the Field Engineer both agreed that the amount of force used to tighten the nuts could address the difficulty in removal. The Field Engineer was assigned to determine how to test removal of nuts tightened to specific torque levels. This factor will be included in the test plan to determine if it is a Vital X.

Instructor : So we've got a couple of Vital X candidates.
Instructor : The team then took up the only topic left, materials.
Instructor : The Mechanic said that according to the maintenance log, there had never been a problem with corrosion causing difficulty in nut removal, So the team agreed to drop it.
Instructor : The Field Engineer said that there was an alternative nut called the Torq-Master, which the benchmarked competitors were using for similar heavy-equipment applications. It is possible that they might improve performance in this process.
Instructor : Let's take a quick look at how we characterize Vital X's
Instructor : Critical elements tend to be changed by changing the kind or type of element, as opposed to changing an amount. These are Xs that are not necessarily measurable on a specific scale, but have an affect on the process. Some of these changes would include alternative work flow sequences, process standardization, and other qualitative changes in the process. Vital x's which are critical elements require testing of alternatives in order to determine the best solution.
Instructor : Operating parameters tend to be changed in amount, rather than replacing an element with another. These are Xs that can be set at multiple levels to study how they affect the process Y. Some examples include heat treatment temperature, cycle time, or the cutting speed on a machine tool. Operating parameters call for a mathematical model which helps you find the optimal setting for the vital x's to address the CTQ's.

Instructor : The approach we will use to test the significance of the suggested vital x's is called a Design of Experiments, or D O E. D O E is a statistical approach to test the significance of X's and interactions between and among X's. There are two general kinds of DOEs
Instructor : A screening DOE is used in this step to identify the vital x's for the CTQ. It looks at all of the variables, or factors, to determine those that affect our CTQ. Thus, it allows us to focus on the vital few and avoid wasting time on the trivial many.
Instructor : An optimization DOE is used in Step 8 to determine the optimized settings for the vital x's. These setting are identified through what is called the transfer function, which relates the customer specifications to specific settings for the vital x's. Now we'll look at some key considerations in our DOE.
Instructor : Including the current process conditions, or baseline, is a standard practice for doing experiments. Two benefits of this practice are:
Instructor : It allows you to compare experimental results with real-world process data using the same parameters, and by doing so
Instructor : validates your experimental setup.
Instructor : Remember, you obtained baseline data in order to generate your original process capability report.
Instructor : Let's look at another key consideration.
Instructor : Another key consideration is the overall statistical design approach to your experiments.
Instructor : A full factorial design requires your to test every combination of factors at all levels.
Instructor : If the number of runs required to execute a full factorial design is too large to accommodate, reducing the number of experimental runs is inevitable.
Instructor : Statistical approaches such as fractional factorial design can provide an effective way to reduce the number of experiments while remaining aware of potential shortcomings in the design.
Instructor : Another of the key considerations addresses a number of experimental factors.
Instructor : The number of factors to test is an outcome of the brainstorming session.
Instructor : In a screening DOE, which is what we are doing here, we will look at two different settings for each factor. This is typical of screening DOEs where we are simply determining the Vital X's. When we fine-tune our recommendations through an optimization DOE, more levels are typically used.
Instructor : Finally, we need to define the actual settings or the range of values over which we will test each factor. The range should be sufficient to ensure that we can detect any effect of the change, and it should also be feasible to carry out. Click Next and we'll look at some critical experimental design considerations.

Instructor : Another of the key considerations addresses the experimental setup.
Instructor : Replication is often confused with repetition. Repetition may involve additional observations during a single trial or run. Replication means to reproduce an entire experimental trial, but to do that under the exact same conditions each time.
Instructor : In order to minimize the effect of data gathered at a certain time or in a predetermined order, the order of trials should be randomized.
Instructor : All trials should take place under identical conditions, but that isn't always possible. Temperature, humidity, time of day, shift, individual supervisor or technician, are all nuisance factors that can be eliminated with a blocked design. Block variables lumps all reading taken under identical conditions are part of a block.
Instructor : Adding center points is a way to determine if there is curvature in the results. While it typically isn't done in a screening DOE, it can prove useful in certain situations.

Instructor : We have decided to use both replication and randomization in our screening DOE.
Instructor : Replication, by providing multiple sets of data under identical conditions, will provide an estimate of experimental error, which will become the basis for determining if a difference in observations is significant or not.
Instructor : A lurking variable is a variable which has an important effect on outcomes, but which has not been accounted for in the data. In this case, we will randomize the order in which various experiments take place, so that a time-dependent lurking variable, possibly tied to when a particular activity takes place, does not pollute the results.
Instructor : The Experimenter's Checklist is an excellent resource. You will find it under the Resources menu on the left side.

Instructor : After taking all of these considerations into account, we decided how to address the situation at the Rockledge plant.
Instructor : We will perform a screening DOE with a 2-level factorial design on the three remaining factors to identify the true vital x's
Instructor : We will use both replication and randomization to enhance the reliability of our results.Instructor : To summarize our design, we start out with three factors
Instructor : The type of nut, the torque level used to install the nuts, and the ambient temperature.
Instructor : We will define two possible levels for each factor
Instructor : The nut will be either the current nut or the Torque-Master nut.
Instructor : The installation torque setting will be either fifteen thousand five hundred or eighteen thousand foot pounds of force.
Instructor : And the nut will be removed at an ambient temperature of either fifty degrees Fahrenheit or one hundred degreed Fahrenheit.

Instructor : So how many different test make up a full factorial? Before we discuss the underlying logic, let's see if you can figure it out. We have three factors and two levels we will use for each. So how many different tests do we have to run in order to cover all possible combinations? Each combination must contain a unique combination of values for all three factors.

Instructor : Here are the eight possible combinations which we will test in our screening DOE. If all our screening experiments were limited to three variables and two levels, it would be simple to determine the number of possible combinations. We realize, however, that in the real world there are often far larger numbers of potential causes to test. Is there a simple mathematical formula which we can use to determine how many combinations there are for any number of factors?

Instructor : The general formula for the number of tests, or n, required for full factorial DOE is:
Instructor : n equals the number of levels to the power of the number of factors

Instructor : If we apply the general formula to the Rockledge case, we have two levels for three factors.
Instructor : Taking two to the power of three, results in eight different tests.

Instructor : It would be valid to ask why we only test each factor at two levels. We do so because this is a screening DOE, rather than an optimization DOE. We are only attempting to verify the significance of the factor, not determine the optimal setting.

Instructor : Our next task is to design the experiment. We're going to do a full factorial experiment as our screening exercise. We will use a test casing. Our casing is placed in a testing chamber
Instructor : This will allow us to subject the test to the full range of vibration it would on an actual operating generator
Instructor : Our measurable response will be the time required to remove the nut.
Instructor : According to historical data, nut removal time is not sensitive to the diameter of the nut used.
Instructor : The team decided to use a two point five inch nut for this test.
Instructor : In order to perform the statistical analysis, we must utilize numbers to represent the levels for each factor. In this case, since each factor has two levels, we will code those levels as minus one and one. Let's build a chart to show what we mean.
Instructor : For the nut, minus one will designate the regular nut while one represents using the Torque-Master nut.
Instructor : For the torque setting, minus one will designate fifteen thousand, five hundred foot pounds and one will indicate eighteen thousand foot pounds
Instructor : Finally, minus one will indicate an ambient temperature of fifty degrees Fahrenheit, while one will indicate an ambient temperature of one hundred Fahrenheit. It is good practice to make a note of how you have coded these levels because that information is not captured in Minitab.

Instructor : The first step is to select your factorial design. First click on the Stat menu and then select D O E. From the D O E submenu, select Create Factorial Design.

Instructor : This dialogue box comes up when you select Create a Factorial Design.
Instructor : Since we have only two values, lets select two level factorial design with the default generators.
Instructor : We have three factors to address, so select three from the Number of factors pull-down menu.
Instructor : We still have to select an actual design, so click on Designs.

Instructor : When you click on Designs, this dialogue box appears. First, select Full Factorial from the choices in the large window.
Instructor : Make sure that number of center points is zero.
Instructor : Then select two for the number of replicates. In MiniTab, this automatically requires each individual test to be run two times.
Instructor : Then make sure that number of blocks is set to one.
Instructor : When you click on O K, you will go back to the top design screen.
Instructor : Next, you need to name the three factors. To do this, click on Factors.
Instructor : Clicking on the Factors button brings up this dialogue box.
Instructor : We're going to change only the names here, so we will rename the three factors Nut Type, Torque, and Ambient Temp.
Instructor : When you have changed the names, as shown here, click on the O K button.
Instructor : By default, MiniTab is set to randomize the run order, and to assume there is only one block. We're going to accept those defaults of the program, so the final step is clicking the OK button to accept the design.
Instructor : If you did everything right, you will see this information in the Session window of MiniTab.
Instructor : Factors three indicates that you have three variables
Instructor : The Base Design shows that you have three variables and eight unique tests, which is a full factorial design for this group.
Instructor : The Runs field says you have sixteen actual tests to perform
Instructor : While the Replicates field says that each of the eight unique tests will be run twice. We aren't going to bother with blocks and Center Points in this example.

Instructor : The system then generates the testing design.
Instructor : Numbers in the first column represent the combinations of factors; the numbers in the second are the order of the run. You can see from these two columns that the runs have been randomized to avoid lurking variables. Since we are not using center points or blocks, all of the entries in those columns are one.
Instructor : The last three columns indicate the actual level of each of the three variables. We already defined what minus one and one mean for each variable, so this is a simple way to record the test conditions.
Instructor : Remember that we assigned two levels for each factor, coded to minus one and one. Let's take a look at how that works.
Instructor : For example, if we look at row four, the levels indicated in columns five, six and seven are minus one, minus one, and one. The minus one in column five means that this run will use the standard nut. The minus one in column six means that the nut will be tightened to 15,500 ft-lbs, and the one in column seven indicates that the ambient temperature will be 100 degrees Fahrenheit.

Instructor : So here are the results of all our tests. The actual removal time has been added as column C eight. Our next step will be to analyze this data.

Instructor : Now that we have the data in place, it's time to analyze our factorial screening.
Instructor : From the Stat menu, select DOE
Instructor : And then from the sub menu, select Analyze Factorial Design
Instructor : When you make your selection, the now-familiar MiniTab dialogue box will appear.
Instructor : You select Nut Removal as your response by clicking on column C eight in the selection box and then clicking on Select.
Instructor : When your dialogue box looks like this, you should click on Terms to make sure that they are correct.
Instructor : A key item here is to determine which terms will be analyzed by MiniTab. This is defined in the pull down menu at the upper right.
Instructor : If one is selected, only the main effects, or the individual variables in isolation, will be analyzed. There will be no analysis of the interactions between variables.
Instructor : If two is selected, the two way interactions between all pairs of variables will also be analyzed.
Instructor : The default is three, which means that all interactions, including the three way combination of all variables, is analyzed.
Instructor : Clicking on OK here will take you back to the previous screen. Clicking on OK in the main dialogue box will generate the analysis of your factorial screening.
Instructor : The DOE analysis uses the hypothesis test to determine the significance of each factor and interaction between and among factors. As you have seen previously, the P value is a test of significance. In this case, a P value of less than zero point zero five means that the corresponding term is a vital X.
Instructor : Of the three main effects, the nut type and torque show a P less than zero point zero five and are therefore considered vital X's.
Instructor : The Ambient Temperature is not a vital X
Instructor : The combination of nut type and torque is also a vital X, but none of the other interactions qualify.
Instructor : So our conclusion from this analysis is that nut type, torque, and the interaction of nut type and torque are the vital X's. Interactions are a critical concept here.

Instructor : The combination of time and temperature in cooking is a good example of an interaction.
Instructor : If we have a specific temperature set, it will take a certain amount of time to properly cook an egg. Therefore the time required, in this case, is dependent upon the temperature used.
Instructor : If we raise the temperature, it takes less time.
Instructor : If we decide to leave the eggs cooking longer, we must reduce the temperature. Neither factor can be optimized without taking into account the other.

Instructor : A common practice is to rerun the analysis, removing the term with the highest P value each time, until the results show only those terms with a P value of less than zero point zero five. Click Next to see those results.

Instructor : So here are the final results. These are the terms with P values less than zero point zero five. So we conclude that these are the vital X's. The effect column measures the overall effect on the Y of moving from the low, or minus one, level to the high, or positive one, level. In the case of the Nut Type, for example, the time required to remove the nut will decrease by approximately eighteen minutes on average, when the standard nut is replaced by the Torque Master nut. We will now build an equation to predict the nut removal time for the Torque Master nut installed at the lower torque level.
Instructor : We start with the Constant Coefficient.
Instructor : We then add to that the product of the Nut Type Coefficient and the assigned value of the nut type. In this case, the torque master nut type is one and the regular nut is minus one, so we will use one.
Instructor : In a similar manner, we add to that the product of the Torque Coefficient and the assigned value of the lower torque level, which is minus one.
Instructor : Finally, we add the product of the Coefficient of the interaction of the nut type and torque, which means changing simultaneously from the standard nut to the torque master and from the low to the higher torque value, and the product of the assigned value of each.
Instructor : By taking all the products first, we simplify the equation to this straight forward string of additions and subtractions
Instructor : Which adds up to twenty four point six minutes.

Instructor : Be cautious when using the preliminary transfer function. It is limited in that it will not reveal any curvature. We use it to help identify a Vital X, but not to optimize the actual setting.
Instructor : You can use optimization D O E or other tools to optimize the setting of a Vital X. We will do that in the next step, coming up soon.

Instructor : Another thing we can now do is generate a graphical representation of the actual factorial screening. This often provides visually dramatic results. However, graphical representations must always be backed by statistical results. From the Stat Menu, select D O E and then Factorial Plots
Instructor : When you select Factorial Plots, the following dialogue screen will appear. There are three kinds of plots that you can do. In this particular case, we'll go ahead and select all three by clicking in each white box.
Instructor : Upon selecting a plot, the SETUP buttons become active. So let's click on the top SETUP button.
Instructor : When you click on SETUP, MiniTab displays the following dialogue box. Let's go through the proper setup.
Instructor : First, we need to select a Response. This is the CTQ we believe our Vital X's will influence.
Instructor : The Response value is in column C eight, so we place our cursor in the Responses Field
Instructor : and click on C eight
Instructor : and then click on the SELECT button on the lower left. you can also double click on an item, which will perform the same function as selecting the item first and then clicking on SELECT.
Instructor : After successfully entering our Response, we look at which factors to include in the plots.
Instructor : Our three factors are in the AVAILABLE box. We want to look at all three variables, so you can either click on the arrow three times or the double arrow once to transfer them over to the selected window.
Instructor : This screen shows all proper choices selected. When you press O K, you will return to the Factorial Plot Main Menu.
Instructor : From this screen, check the settings for the other two plots by clicking on SETUP. Make certain that all three have the same factors defined. Once you have completed the setup,
Instructor : click on O K to execute the plot. Click next and we'll start looking at the data.Instructor : This first graph shows us the individual factors plotted against the nut removal time. The slope or height of the line demonstrates the impact of the change.
Instructor : It appears that there is a sizable decrease in removal time when we switch from the regular nut to the Torque-Master nut.
Instructor : Is also appears that there is some increase in removal time due to increase in torque applied.
Instructor : And finally, there does not appear to be any direct effect of changing ambient temperature.
Instructor : The second plot shows interactions between pairs of variables. You can determine which two by simply looking either up or to the right of each variable to see where it is used. Interactions are significant when lines are not parallel. This means that the lines either cross, or if extended would cross. A right angle would be the strongest interaction.
Instructor : The first result shows some interaction between Nut Type
Instructor : and Torque.
Instructor : The next shows no detectable interaction between the Nut Type
Instructor : and Ambient Temperature.
Instructor : The third shows the same lack of interaction between the Torque
Instructor : and the Ambient Temperature.
Instructor : So here in step one, our primary task was to identify the Vital X's for our Y.
Instructor : We also looked at a strategy for determining our exact improvement plan.
Instructor : We reviewed the applicability of using a Design of Experiments approach to this process,
Instructor : and executed a full factorial screening DOE
Instructor : As part of the design our or screening experiment we took steps to limit the possible effect of any lurking variable.
Instructor : So we designed and executed a full factorial screening on our three potential Vital X's.
Instructor : We used replication and randomization to enhance the reliability and credibility of our experimental results.
Instructor : We determined that the Nut Type and Torque were both significant factors,
Instructor : but Ambient Temperature was not.
Instructor : So we're about ready to wrap up this section of the course and the case, and move forward to the next step of the Analyze phase.

Instructor : Well that wraps up step seven. Congratulations. We have correctly identified two vital X's which we will optimize in the next stage to lead us to fulfillment of our process objectives.