Statistics 495, Applied Statistics for Industry I         Name:

Exam 1, Fall 1997                                         Site: 

1. [35 pts] A manufacturing firm buys steel parts from two suppliers. One of the important characteristics of the steel parts they buy is the tensile strength. Before accepting a lot of steel parts from a supplier, the firm tests 15 randomly selected parts for tensile strength. If the average strength is greater than 290, the lot is accepted. Below are strength data for samples from the two suppliers.

                  Supplier 1                    Supplier 2
   
            293.2   291.4   290.3          290.6   293.1   292.4
            290.9   291.8   293.9          292.1   291.9   294.3
            290.7   292.1   291.5          293.0   293.4   293.0
            289.5   289.3   291.6          292.6   295.4   292.6
            292.4   291.7   292.7          294.3   292.6   293.6
   
                average=291.5                  average=293.0
   
   

   • a) [6] Construct stem plots for each of the lots. Use the stems below.

     
                   Supplier 1                     Supplier 2 
     
                288                            288
                289                            289
                290                            290
                291                            291
                292                            292
                293                            293
                294                            294
                295                            295
                296                            296
     
     

   • b) [6] Which sample has the higher average strength? Does one sample show more variability than the other? Are the shapes symmetric or skewed?

   • c) [4] If we were to say that the statements made in (b) extend to the two lots from which the samples were taken, would this be an enumerative inference or an analytic prediction? Explain briefly.

   • d) [6] At a meeting, these data are presented and someone suggests that all future lots should be purchased from the supplier with the highest average tensile strength as determined from the samples on page 1. The person in charge of testing suggests going with Supplier 1 since for the last 10 samples tested the average strength for Supplier 1 was 293.5 while Supplier 2 had an average strength of only 292.6. Below are the average strengths for the last 10 samples from each of the suppliers. Construct run charts on the axes provided.

          Lot   1      2      3      4      5      6      7      8      9      10
   Supplier 1 300.4  289.8  296.9  300.2  288.1  289.7  289.6  291.6  297.2  291.5
   Supplier 2 292.7  293.4  291.9  292.2  292.5  292.0  293.1  292.8  292.4  293.0
   
   
   
               Supplier 1                               Supplier 2
       |                                       |
       |                                       |
   300 +                                   300 +
       |                                       |
       |                                       |
       |                                       |
       |                                       |
       |                                       |
   295 +                                   295 +
       |                                       |
       |                                       |
       |                                       |
       |                                       |
       |                                       |
   290 + - - - - - - - - - - - - - - -     290 + - - - - - - - - - - - - - - - 
       |                                       |
       |                                       |
       |                                       |
       |                                       |
       |                                       | 
   285 +--+--+--+--+--+--+--+--+--+--+-    285 +--+--+--+--+--+--+--+--+--+--+-
          1  2  3  4  5  6  7  8  9  10           1  2  3  4  5  6  7  8  9  10
   
   

   • e) [8] Describe the patterns that you see in the run charts. Be sure to comment if either Supplier has any lots that would be rejected because the average tensile strength of the sample is too low.

   • f) [5] Which supplier would you choose to provide future lots? Why?

2. [20 pts] A chemical operation tests three machines that can be used to measure concentration automatically. A batch of a chemical with a known concentration of 10 is used for all tests. Each machine determines the concentration of the test solution 25 times.
   • a) [15] On the next page are run charts of the determinations for each machine. Next to each machine comment on the accuracy and precision of that machine. Explain briefly what in each run chart indicates high/low precision and high/low accuracy.

   • b) [5] If you had to pick one machine (for this question you do) to use, which would you pick and why?

    

                  
3. [15 pts] Hornpad assemblies, which are purchased by vehicle manufacturers for use in their steering wheels, are inspected for various types of defects. The types of defects are listed below. The step in the hornpad manufacturing process where the defect was likely to occur is listed in parentheses.

   
   A   Urethane spray      (Spraying)    F   Trim plate      (Trim)
   B   Improper assembly   (Assembly)    G   Blow pressure   (Spraying)
   C   Missing parts       (Assembly)    H   Loose nuts      (Assembly)
   D   Surface defects     (Molding)     I   Other           (Other)
   E   Excessive flash     (Molding)
   
   

   • a) [3] Looking at the Pareto chart below, what types of defects are the `vital few,' i.e. accounting for over 70% of the defects?

      

        
   • b) [8] On the graph below, create a Pareto chart by process step. Be sure to fill in the Count, Percent and Cum \% rows below the chart.

   • c) [4] To what step(s) of the process should we direct our improvement efforts? Why?

        
4. [10 pts] For each of the following scenarios briefly describe the type(s) of variability present. Indicate whether the cause of variability is common (random or system related) or special (attributable to an unusual circumstance). Explain briefly your reasoning.
   • a) [5] The local newspaper guarantees delivery by 6 am each morning. Although the paper may not arrive at exactly the same time each morning, they usually meet this guarantee. Occasionally the paper arrives late. On days that the paper arrives late the explanation given by the newspaper office is that the regular carrier is sick or on vacation and did not find a substitute.

   • b) [5] A manufacturer of truck and car accessories packages hardware (nuts, bolts, washers, etc.} to accompany their product. The packaging process is automated using electronic eyes to count parts. The process is having difficulties packaging the correct number of washers. This is an on going problem that affects day to day operation. Possible causes suggested include vibration of the system, lack of sensitivity due to the age of the electronic eye and the standard process settings.

5. [10 pts] Customer satisfaction is an important concern for any business. Suppose that over the past year 1,000,000 customers buy a particular product. One hundred customers, chosen at random from the 10,000 customers who returned product registration cards, are contacted by telephone and asked about their satisfaction with the product.
   • a) [3] What are the Universe, Frame and Sample for this situation?

   • b) [7] Suppose that 85 of the 100 customers contacted are satisfied or very satisfied with the product. What can be said about the satisfaction level of the 1,000,000 customers who bought the product that year?

6. [10 pts] Consider a process that is producing parts that are all within specifications (i.e. there are no nonconfomities or defects). A histogram of recent measurements of the quality characteristic for parts shipped to customers appears on the next page. Management believes ``If it ain't broke, don't fix it!'' Is there room for improvement? Give a reasoned argument, directed to management, for studying this process. Direct your answer toward the possible benefits derived from studying a process even when it is meeting specifications.