6 CHAPTER I THE ROLE OF STATISTICS IN ENGINEERING 3.Production maintains the two temperatures as closely as possible to desired targets or set points.Because the temperatures change so little,it may be difficult to assess their real impact on acetone concentration. 4.Within the narrow ranges that they do vary,the condensate temperature tends to in- crease with the reboil temperature.Consequently,the effects of these two process variables on acetone concentration may be difficult to separate. As you can see,a retrospective study may involve a lot of data,but that data may contain relatively little useful information about the problem.Furthermore,some of the relevant data may be missing,there may be transcription or recording errors resulting in outliers (or unusual values),or data on other important factors may not have been collected and archived.In the distillation column,for example,the specific concentrations of butyl alco- hol and acetone in the input feed stream are a very important factor,but they are not archived because the concentrations are too hard to obtain on a routine basis.As a result of these types of issues,statistical analysis of historical data sometimes identify interesting phenomena,but solid and reliable explanations of these phenomena are often difficult to obtain. 1-2.3 Observational Study In an observational study,the engineer observes the process or population,disturbing it as lit- tle as possible,and records the quantities of interest.Because these studies are usually con- ducted for a relatively short time period,sometimes variables that are not routinely measured can be included.In the distillation column,the engineer would design a form to record the two temperatures and the reflux rate when acetone concentration measurements are made.It may even be possible to measure the input feed stream concentrations so that the impact of this fac- tor could be studied.Generally,an observational study tends to solve problems 1 and 2 above and goes a long way toward obtaining accurate and reliable data.However,observational studies may not help resolve problems 3 and 4. 1.2.4 Designed Experiments In a designed experiment the engineer makes deliberate or purposeful changes in the control- lable variables of the system or process,observes the resulting system output data,and then makes an inference or decision about which variables are responsible for the observed changes in output performance.The nylon connector example in Section 1-1 illustrates a designed ex- periment;that is,a deliberate change was made in the wall thickness of the connector with the objective of discovering whether or not a greater pull-off force could be obtained.Designed experiments play a very important role in engineering design and development and in the improvement of manufacturing processes.Generally,when products and processes are designed and developed with designed experiments,they enjoy better performance,higher reliability,and lower overall costs.Designed experiments also play a crucial role in reducing the lead time for engineering design and development activities. For example,consider the problem involving the choice of wall thickness for the nylon connector.This is a simple illustration of a designed experiment.The engineer chose two wall thicknesses for the connector and performed a series of tests to obtain pull-off force measurements at each wall thickness.In this simple comparative experiment,the
6 CHAPTER 1 THE ROLE OF STATISTICS IN ENGINEERING 3. Production maintains the two temperatures as closely as possible to desired targets or set points. Because the temperatures change so little, it may be difficult to assess their real impact on acetone concentration. 4. Within the narrow ranges that they do vary, the condensate temperature tends to increase with the reboil temperature. Consequently, the effects of these two process variables on acetone concentration may be difficult to separate. As you can see, a retrospective study may involve a lot of data, but that data may contain relatively little useful information about the problem. Furthermore, some of the relevant data may be missing, there may be transcription or recording errors resulting in outliers (or unusual values), or data on other important factors may not have been collected and archived. In the distillation column, for example, the specific concentrations of butyl alcohol and acetone in the input feed stream are a very important factor, but they are not archived because the concentrations are too hard to obtain on a routine basis. As a result of these types of issues, statistical analysis of historical data sometimes identify interesting phenomena, but solid and reliable explanations of these phenomena are often difficult to obtain. 1-2.3 Observational Study In an observational study, the engineer observes the process or population, disturbing it as little as possible, and records the quantities of interest. Because these studies are usually conducted for a relatively short time period, sometimes variables that are not routinely measured can be included. In the distillation column, the engineer would design a form to record the two temperatures and the reflux rate when acetone concentration measurements are made. It may even be possible to measure the input feed stream concentrations so that the impact of this factor could be studied. Generally, an observational study tends to solve problems 1 and 2 above and goes a long way toward obtaining accurate and reliable data. However, observational studies may not help resolve problems 3 and 4. 1-2.4 Designed Experiments In a designed experiment the engineer makes deliberate or purposeful changes in the controllable variables of the system or process, observes the resulting system output data, and then makes an inference or decision about which variables are responsible for the observed changes in output performance. The nylon connector example in Section 1-1 illustrates a designed experiment; that is, a deliberate change was made in the wall thickness of the connector with the objective of discovering whether or not a greater pull-off force could be obtained. Designed experiments play a very important role in engineering design and development and in the improvement of manufacturing processes. Generally, when products and processes are designed and developed with designed experiments, they enjoy better performance, higher reliability, and lower overall costs. Designed experiments also play a crucial role in reducing the lead time for engineering design and development activities. For example, consider the problem involving the choice of wall thickness for the nylon connector. This is a simple illustration of a designed experiment. The engineer chose two wall thicknesses for the connector and performed a series of tests to obtain pull-off force measurements at each wall thickness. In this simple comparative experiment, the c01.qxd 5/9/02 1:28 PM Page 6 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH 1 12 FIN L:
1-2 COLLECTING ENGINEERING DATA 7 engineer is interested in determining if there is any difference between the 3/32-and 1/8-inch designs.An approach that could be used in analyzing the data from this experi- ment is to compare the mean pull-off force for the 3/32-inch design to the mean pull-off force for the 1/8-inch design using statistical hypothesis testing,which is discussed in detail in Chapters 9 and 10.Generally,a hypothesis is a statement about some aspect of the system in which we are interested.For example,the engineer might want to know if the mean pull-off force of a 3/32-inch design exceeds the typical maximum load expected to be encountered in this application,say 12.75 pounds.Thus,we would be interested in test- ing the hypothesis that the mean strength exceeds 12.75 pounds.This is called a single- sample hypothesis testing problem.It is also an example of an analytic study.Chapter 9 presents techniques for this type of problem.Alternatively,the engineer might be inter- ested in testing the hypothesis that increasing the wall thickness from 3/32-to 1/8-inch results in an increase in mean pull-off force.Clearly,this is an analytic study;it is also an example of a two-sample hypothesis testing problem.Two-sample hypothesis testing problems are discussed in Chapter 10. Designed experiments are a very powerful approach to studying complex systems,such as the distillation column.This process has three factors,the two temperatures and the reflux rate,and we want to investigate the effect of these three factors on output acetone concentra- tion.A good experimental design for this problem must ensure that we can separate the effects of all three factors on the acetone concentration.The specified values of the three factors used in the experiment are called factor levels.Typically,we use a small number of levels for each factor,such as two or three.For the distillation column problem,suppose we use a"high,"and "low,"level(denoted +1 and-1,respectively)for each of the factors.We thus would use two levels for each of the three factors.A very reasonable experiment design strategy uses every possible combination of the factor levels to form a basic experiment with eight different set- tings for the process.This type of experiment is called a factorial experiment.Table 1-1 pres- ents this experimental design. Figure 1-6,on page 8,illustrates that this design forms a cube in terms of these high and low levels.With each setting of the process conditions,we allow the column to reach equilib- rium,take a sample of the product stream,and determine the acetone concentration.We then can draw specific inferences about the effect of these factors.Such an approach allows us to proactively study a population or process.Designed experiments play a very important role in engineering and science.Chapters 13 and 14 discuss many of the important principles and techniques of experimental design. Table 1-1 The Designed Experiment(Factorial Design)for the Distillation Column Reboil Temp. Condensate Temp. Reflux Rate -1 -1 -1 +1 -1 -1 -1 +1 -1 +1 +1 -1 -1 -1 +1 +1 -1 -1 +1 +1 +1 +1 +1
engineer is interested in determining if there is any difference between the 332- and 18-inch designs. An approach that could be used in analyzing the data from this experiment is to compare the mean pull-off force for the 332-inch design to the mean pull-off force for the 18-inch design using statistical hypothesis testing, which is discussed in detail in Chapters 9 and 10. Generally, a hypothesis is a statement about some aspect of the system in which we are interested. For example, the engineer might want to know if the mean pull-off force of a 332-inch design exceeds the typical maximum load expected to be encountered in this application, say 12.75 pounds. Thus, we would be interested in testing the hypothesis that the mean strength exceeds 12.75 pounds. This is called a singlesample hypothesis testing problem. It is also an example of an analytic study. Chapter 9 presents techniques for this type of problem. Alternatively, the engineer might be interested in testing the hypothesis that increasing the wall thickness from 332- to 18-inch results in an increase in mean pull-off force. Clearly, this is an analytic study; it is also an example of a two-sample hypothesis testing problem. Two-sample hypothesis testing problems are discussed in Chapter 10. Designed experiments are a very powerful approach to studying complex systems, such as the distillation column. This process has three factors, the two temperatures and the reflux rate, and we want to investigate the effect of these three factors on output acetone concentration. A good experimental design for this problem must ensure that we can separate the effects of all three factors on the acetone concentration. The specified values of the three factors used in the experiment are called factor levels. Typically, we use a small number of levels for each factor, such as two or three. For the distillation column problem, suppose we use a “high,’’ and “low,’’ level (denoted +1 and 1, respectively) for each of the factors. We thus would use two levels for each of the three factors. A very reasonable experiment design strategy uses every possible combination of the factor levels to form a basic experiment with eight different settings for the process. This type of experiment is called a factorial experiment. Table 1-1 presents this experimental design. Figure 1-6, on page 8, illustrates that this design forms a cube in terms of these high and low levels. With each setting of the process conditions, we allow the column to reach equilibrium, take a sample of the product stream, and determine the acetone concentration. We then can draw specific inferences about the effect of these factors. Such an approach allows us to proactively study a population or process. Designed experiments play a very important role in engineering and science. Chapters 13 and 14 discuss many of the important principles and techniques of experimental design. 1-2 COLLECTING ENGINEERING DATA 7 Table 1-1 The Designed Experiment (Factorial Design) for the Distillation Column Reboil Temp. Condensate Temp. Reflux Rate 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 c01.qxd 5/9/02 1:28 PM Page 7 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH 1 12 FIN L: