This is “Software and Technology Exercises”, section 10.7 from the book Beginning Project Management (v. 1.1). For details on it (including licensing), click here.
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Real production processes are never perfect. In some cases, a few products that are too small or that do not work will just cause inconvenience, but in other cases they might be life threatening. Samples of the production process will show how much variation occurs. If it appears that the variations are distributed equally above and below the mean (average), it might be assumed that the statistics of a normal distribution can be used to predict the percentage of products that will be defective when many of them are produced even if none of the samples are defective.
Some projects are initiated to increase the quality by reducing the variation in production. To understand the language of statistics and how it is used to justify a project, it is useful to gain a “feel” for how the distribution of samples is described by the standard deviation. A spreadsheet can be used to simulate samples of production runs where the mean and standard deviation can be chosen to show their relationship in a normal distribution. By trying different values for the standard deviation and observing the effect on the distribution of estimated samples in a chart, you can develop a sense of how the two are related.
Recall that a standard deviation is called a sigma and represented by the Greek letter σ and the 68-95-99.7 rule refers to the percentage of samples that will be within one, two, and three standard deviations of the mean.
Complete the exercise by following these instructions:
Notice the following features of the spreadsheet:
Compare the chart in the spreadsheet to the chart in Figure 10.13 "Normal Distribution of Gasoline Samples" that was used in the text. Observe that the standard deviation, σ, is .2 and that almost all the sample values occur between 86.4 and 87.6—three σ on either side of the mean.
Figure 10.13 Normal Distribution of Gasoline Samples
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Switch back to the spreadsheet. To see the effect of a better production process that would have a σ of .1 instead of .2, click cell L3. Type .1 and then, on the Formula bar, click the Enter button. The distribution narrows so that almost all the estimated samples are within .3 on either side of the mean (87.0), as shown in Figure 10.14 "Normal Distribution with Smaller Standard Deviation".
Figure 10.14 Normal Distribution with Smaller Standard Deviation
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In the spreadsheet, in cell L3, type .4 and then, on the Formula bar, click the Enter button. Notice that a larger standard deviation means the distribution is more spread out. Three standard deviations is 1.2 (3 × .4), so almost all the samples will be within 1.2 on either side of the mean, as shown in Figure 10.15 "Normal Distribution with Larger Standard Deviation".
Figure 10.15 Normal Distribution with Larger Standard Deviation
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The effects of a lower-than-expected octane rating in a passenger car might be engine knock during acceleration and less power climbing a hill, but the effect of lower-than-expected octane fuel in a military aircraft might mean that the plane could not achieve the desired altitude or speed in a critical situation. Aviation gasoline is designed for use in high-performance engines that require 100 octane fuel. Use the spreadsheet to examine the estimated distribution of gasoline samples with a different mean and σ.
Complete the exercise by following these instructions:
Review your work and use the following rubric to determine its adequacy:
Element | Best | Adequate | Poor |
---|---|---|---|
File name | Ch10STDStudentName.doc | Same or .docx file format | Student name missing |
Predict likely range of values in a normal distribution | Five screen captures plus a reflective essay on what you learned about predicting the upper and lower limits defined by 3 σ | Same as Best | Missing pictures; essay does not describe how the upper and lower limits of 3 σ are calculated |
W. Edwards Deming teaches that some variation is inevitable due to chance cause. A manager needs to recognize the difference between variations that are due to chance and those that indicate the presence of an assignable cause or a trend. If it appears that there is an assignable cause for variation in quality, a project manager might be required to identify and fix the problem. To communicate with process managers who are monitoring and sampling production, it is useful to understand the use of control charts.
A run chart is a type of chart that shows variations from the mean as a function of time. The value of each sample is plotted to show the day it was taken and how it differs from the mean. If the variation is random, there will be roughly the same number of points above and below the mean.
A spreadsheet can be used to simulate random variations in production. In this exercise, the spreadsheet uses its random number function to pick two numbers that are positive and two that are negative and adds them to the mean. Each number represents a variation that is between the control limits. Most of the time the positive and negative numbers cancel each other out and result in a sum that is close to the mean, but occasionally the four random factors add up to values that are far from the mean.
In this part of the exercise, you observe variations in a run chart and frequency distribution chart that are due to random effects. You generate the random numbers several times to see what production runs with random (unassignable) variations look like.
Complete the exercise by following these instructions:
Scroll the screen or adjust the zoom so that you can see both charts. See Figure 10.16 "Screen Adjusted to Show Both Charts".
Figure 10.16 Screen Adjusted to Show Both Charts
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Press the F9 key several more times until you get a set of samples that are grouped close to the mean like the example shown in Figure 10.17 "Most Samples near the Mean".
Figure 10.17 Most Samples near the Mean
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Press the F9 key again and stop at a set of samples that has a greater variation, such as the example shown in Figure 10.15 "Normal Distribution with Larger Standard Deviation".
Figure 10.18 Greater Variation
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Complete the exercise by following these instructions:
An assignable cause can be mixed in with the chance-cause random effects. In this part, you introduce a factor that causes the samples to display a trend. You run the simulation several times to learn how to recognize a set of data that is a mix of random (chance-cause) factors and a trend that is probably from an assignable cause.
Press the F9 key several times and observe how this trend appears within the samples such as the example in Figure 10.19 "Trend That Is Probably Due to an Assignable Cause".
Figure 10.19 Trend That Is Probably Due to an Assignable Cause
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Review your work and use the following rubric to determine its adequacy:
Element | Best | Adequate | Poor |
---|---|---|---|
File name | Ch10RunChartStudentName.doc | Ch10RunChartStudentName.docx | Did not include name in file name |
Recognize assignable and unassignable causes of statistical variation | Three screen captures that show two random causes and one assignable cause; an essay that describes how to recognize the difference and the effect on worker morale if a run with low random variation is chosen as a standard | Same as Best | Missing screen; essay does not address both requirements |