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					Quiz: TQM – SQC

  1. In monitoring process quality we might use which of the following statistics?

     A)   Absolute values
     B)   Percentage deviation from tolerance centers
     C)   “k” values for the sample mean
     D)   Logarithmic control intervals
     E)   Difference between the highest and lowest value in a sample***

 2. Quality control charts usually have a central line and upper and lower control
    limit lines. Which of the following is not a reason that the process being
    monitored with the chart should be investigated?

     A)   A large number of plots are close to the upper or lower control lines
     B)   Erratic behavior of the plots
     C)   A single plot falls above or below the control limits
     D)   A change in raw materials or operators***
     E)   A run of five above the central line

 3. Quality control charts usually have a central line and upper and lower control
    limit lines. Which of the following are reasons that the process being
    monitored with the chart should be investigated?

     A)   A single plot falls above or below the control limits***
     B)   Normal behavior
     C)   A large number of plots are on or near the central line
     D)   No real trend in any direction
     E)   A change in raw materials or operators

 4. If there are 120 total defects from 10 samples, each sample consisting of 10
    individual items in a production process, which of the following is the
    fraction defective that can be used in a “p” chart for quality control
    purposes?

     A) 120
     B) 10
     C) 8
   D) 1.2***
   E) 0.8

5. If there are 400 total defects from 8 samples, each sample consisting of 20
   individual items in a production process, which of the following is the
   fraction defective that can be used in a “p” chart for quality control
   purposes?

   A)   400
   B)   160
   C)   2.5***
   D)   1.0
   E)   0.4

6. You want to determine the upper control line for a “p” chart for quality
   control purposes. You take several samples of a size of 100 items in your
   production process. From the samples you determine the fraction defective
   is 0.05 and the standard deviation is 0.01. If the desired confidence level is
   99.7 percent, which of the following is the resulting UCL value for the line?

   A)   0.39
   B)   0.08***
   C)   0.06
   D)   0.05
   E)   None of the above

7. You want to determine the lower control line for a “p” chart for quality
   control purposes. You take several samples of a size of 50 items in your
   production process. From the samples you determine the fraction defective
   is 0.006 and the standard deviation is 0.001. If the desired confidence level
   is 99.7 percent, which of the following is the resulting LCL value for the
   line?

   A)   0.0
   B)   0.002
   C)   0.003***
   D)   0.004
   E)   None of the above


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8. You want to determine the control lines for a “p” chart for quality control
   purposes. If the desired confidence level is 99 percent, which of the
   following values for “z” would you use in computing the UCL and LCL?

    A)   0.99
    B)   2
    C)   2.58***
    D)   3
    E)   None of the above

9. For which of the following should we use a “p” chart to monitor process
   quality?

    A)   Defective electrical switches***
    B)   Errors in the length of a pencil
    C)   Weight errors in cans of soup
    D)   Temperature of entrees in a restaurant
    E)   Letter grades on a final examination

10. For which of the following should we use a “p” chart to monitor process
    quality?

    A)   The dimensions of brick entering a kiln
    B)   Lengths of boards cut in a mill
    C)   The weight of fluid in a container
    D)   Grades in a freshman “pass/fail” course***
    E)   Temperatures in a classroom

11. With which of the following should we use an “X-bar” chart based on sample
    means to monitor process quality?

    A)   Grades in a freshman “pass/fail” course
    B)   Tire pressures in an auto assembly plant***
    C)   Vehicles passing emissions inspection
    D)   Computer software errors
    E)   Number of units with missing operations




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12. Which of the following should we use an “R” chart to monitor process
    quality?

    A)   Grades in a freshman “pass/fail” course
    B)   Tire pressures in an auto assembly plant***
    C)   Vehicles passing emissions inspection
    D)   Computer software errors
    E)   Number of units with missing operations

13. Which of the following should we use an “R” chart to monitor process
    quality?

    A) Weighing trucks at a highway inspection station to determine if they are
       overloaded
    B) Deciding whether an airliner has sufficient fuel for its trip
    C) Student grades measured from 1 to 100***
    D) Determining whether vehicles from a motor pool will run
    E) Determining the accuracy of a forecast of “snow”

14. You are developing an “X-bar” chart based on sample means. You know the
    standard deviation of the sample means is 4, the desired confidence level is
    99.7 percent, and the average of the sample means is 24. Which of the
    following is your UCL?

    A)   36***
    B)   24
    C)   12
    D)   4
    E)   None of the above

15. You are developing an “X-bar” chart based on sample means. You know the
    standard deviation of the sample means is 4, the desired confidence level is
    99 percent, and the average of the sample means is 20. Which of the
    following is your LCL?

    A) 36
    B) 24
    C) 9.68***


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D) 16.79
E) 30.32




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Homework: TQM – SQC

1. Discuss the key differences between common and assignable causes of
   variation. Give examples.

      Common causes of variation are random, which means that there is not a specific reason for
      the variation, such as a malfunctioning machine. If you look at 2-liter bottles of a soft
      drink on a shelf at a retailer, you will notice that they are not filled to the exact same level.
      That is to be expected, since a machine cannot fill each one to exactly 2 liters every time.
      Assignable causes of variation are not random. Some examples of assignable causes are a
      machine in need of repair and defective raw materials from our supplier.


2. It is generally not appropriate to apply control charts to the same data that
   were used to derive the mean and limits. Why? What are two possible
   outcomes if this is done, how likely is each, and what are the appropriate
   interpretations?

      The data used to generate the control charts may themselves be out of control and thus
      generating false control chart information. Only data that is known to be in control should
      be used to set up the control charts. If the charts are applied in retrospect, either the
      data will fall within the limits (and no judgment can be made as to whether it is in control or
      not) or it may be so erratic that it may even fall outside the limits, in which case the
      process is terribly out of control.


3. Firms regularly employ a taster for drinkable food products. What is the
   purpose of the taster?

      The coffee (and other such) taster tells the firm when the process or raw materials need to
      be corrected, not when to scrap a batch of product. The task is to change the process
      before a batch has to be scrapped.




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Exercise: TQM – SQC

Tom Dooley just graduated from Arizona State and accepted a job with Meyerson
Candy Company. One of their major products is gum drops that are packaged in an
assortment of colors, each color being a different flavor. Most of the process is
automated with machines producing the gum drops, mixing the different flavors,
and packaging them in plastic bags. Each bag should contain 16 ounces of candy;
each gum drop is about 1/2 ounce. The mix in each bag should be approximately
20% red (cherry), 20% orange, 20% white, 20% yellow (lemon) and 10% each of
black (licorice), and green (lime).

Recently, the company has received customer complaints along two lines:

   1. Many are complaining that the bags do not appear full and they believe that
      they are not getting a fair measure for what they are paying, but no one has
      verified this.

   2. Several customers have complained about "too many green ones" in the
      package. Some have even reported counting the total number of gum drops
      and the number of green ones in a package. No one has ever complained
      about too few green ones.

Tom has been given copies of the complaint letters and the assignment to "fix the
problem." He decides his first step is to determine if there really is a problem with
the process. To do that he will need to use the tools and ideas he learned in his
Operations Management course.

Tom has been trying to figure out what information he needs, how to analyze it,
and how to create a system to monitor the quality of the product to assure that
these customer complaints do not arise in the future. At first, he was not sure
whether to count the gum drops, weigh them, or use some other measure. After
giving it more thought, Tom has decided to take random samples of 10 bags
throughout the day and use their weights to monitor "fair measure."

The problem of "too many green ones" is a bit more difficult for Tom to
formulate. He thought about calling the green ones "defects" but then he would
have to say that each bag should contain about 10% "defects" that wouldn't sound
right in a report to management. A better approach, he thought, would be to say


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that since the bag should contain about 32 gum drops and 10% of those should be
green, any bag containing 2 or 3 or 4 green ones would be a “good” bag. Therefore,
if a bag contained less than 2 or more than 4 green ones, the bag would be
considered "bad" or "defective" with respect to the product specifications.

Now, Tom has to determine if he needs a p-chart, an X-bar chart, an R-chart or
what. He needs your help.

THE "FAIR MEASURE" PROBLEM

1. What kind of chart(s) does Tom need to analyze this problem? Explain why you
   chose the chart(s) he should use.

      Tom should use both the x-bar and R-charts since weight is a variable measure of quality.
      These charts must be used together.


2. Specifically, what information will Tom need to construct the chart(s) and how
   will he gather it?

      Tom will need to take random samples of 10 bags each from the process. For each bag, he
      will measure the weight and record it. Then he will calculate the average weight of those 10
      bags by averaging the 10 recorded weights. Finally, he will calculate the range of the
      weights by subtracting the smallest of the 10 weights from the largest of the 10 weights.


3. Explain the calculations Tom will need to make -- including formulas and tables
   he will need -- to construct the chart(s).

      Answer should show the formulas for the x-bar and R-charts. In addition, the answer
      should explain that Tom will need to look up information in a table to estimate 3 standard
      deviations from the mean for the control limits.


4. After he has the chart(s) completed, what should Tom do over the next week or
   so?

      Tom should continue taking samples at regular intervals to determine whether the process is
      still in control or not. If it is out of control, Tom will need to take action to fix the
      assignable cause of the variation.




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"TOO MANY GREEN ONES" PROBLEM

1. Should Tom use the same or different type of chart(s) to analyze this problem?
   Explain why.

      Tom should use the p-chart. He must use a different chart since the quality characteristic
      being measured is an attribute. The background information suggests that he should not
      use a c-chart since he does not think it is reasonable to count each green gum drop as a
      defect.


2. Specifically, what information will Tom need to construct the chart(s) for this
   problem and how will he gather it?

      Tom will need to gather random samples of 10 bags. For each bag, he will count the number
      of green gum drops. If the number is less than 2 or more than 4, then the bag is considered
      defective. Each plot on the p-chart will then show the proportion of the 10 bags that were
      defective. For example, if 2 out of the 10 bags have the wrong number of green ones, then
      the proportion defective is 0.20 (20%).


3. Explain the calculations Tom will need to make -- including formulas and tables
   he will need -- to construct the chart(s).

      The answer should show the formulas for the center line and control limits for the p-chart.


4. After he has the chart(s) completed, what should Tom do over the next week or
   so?

      Tom should continue taking samples at regular intervals to determine whether the process is
      still in control or not. If it is out of control, Tom will need to take action to fix the
      assignable cause of the variation.




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