Introduction to Statistics

I: Introduction to Statistics

 

1. A high jumper, John “Hoppin” Hermann, completes the jumps on the excel worksheet “High Jumps” for histrack season.  Using your statistical analysis package in Minitab 15, complete a normal probability and box plotof the data and perform Stat=>Basic Statistics=>Graphical Summay. Paste the results below.  Discuss the results in detail.  Are the data normal?  Discuss the chances of Hoppin Hermann breaking  Javier Sotomayor’s world record of 8.0383 feet.(20pts)

II: DMAIC:

 

While visiting the MIT Mousetrap Company as a consultant you are approached by the Quality Control Supervisor, Wes Jones.  Mr. Jones has noticed that some (3 per 100) of the new humane catch-n-release traps are below specification (less than acceptable cheese holding ability) and has approached you to assist in fixing this expensive problem (MIT sells millions of these C-n-Rs each year).

a) DMAIC — define each letter of the acronym (D,M,A,I, and C) and write 1-2 sentences related to the above scenario, i.e. talk about the steps you would recommend taking for each part of the process and discuss what resources you might use to complete that task.(15pts)

1. b) Discuss more extensively how you might determine measures and gather data in the “M” portion of this problem solving framework and what tools you might use (and how). (10pts)

 

III: SPC

1. A. Discuss the differences between special cause and common cause failures or variation, giving at least one example of each. How might you see the difference in your measurements? (5pts)

 

1. Discussion the difference between attribute and variables data. How do they work together in an effective SPC Program? (5pts)

 

 

1. What is a Pareto Chart? How is it used in a continuous improvement program? (5)

 

 

1. The USGA announced that they are going to be very “tough” in enforcing the rule that the maximum coefficient of restoration (COR) for golf club drivers by 0.83.  (some drivers were measured by them as 0.85, this COR gives a drive 5 yards or so advantage over one that is “in spec.”.  Assume that the lower spec limit is 0.80)The USGA will allow the upper spec limit on any manufacturer’s driver to be 0.83 as long as the Cpk is at least 2.0.  Ping has developed a very repeatable process for making the driver heads that they believe can achieve a Cpk of 2 with the average COR being 0.828.

 

1. If this is true what must s be? (5pts)
2. Ping is encouraged as they believe their competitors s is at least 0.004. If this is true what COR average must the competitor aim for to have a Cpk no greater than 2. (10pts)
3. For every 0.01 loss in COR the driver loses 2.5 yards. How much less yardage will the competitions driver hit a ball on average as compared to Pings? (10pts)
4. Ping manufactures 10,000 drivers. The data are in the spreadsheet in tab “Golf Club COR” .  Analyze the data.  Assume with subgroup size = 1.  Did they achieve their goal?  Comment on the data Re: normality, etc.  Are there Shewhart violations?  If so discuss them.  State any assumptions.  Copy and paste appropriate data and/or graphs.Use an upper spec of 0.83 and a lower spec of 0.82.(15pts)

 

IV:DOE

A full factorial experiment is proposed to optimize stencil printing for a 0.3mm process.  The assembly will be in Singapore, so management wonders if temperature and humidity control will be needed.  The stencil aperture is 6x4x30 mils, +/- 10% of this volume is the proposed spec.  The factors are Type 4 paste (1=ACME, 2=AJAX, 3=Kostco), stencil (efab, laser), humidity (30, 45, 60 RH), temperature (20, 25, 30 C).  The two replicate data are in the worksheet “Solder Paste DOE.”  Set up the experiment with the factors in this order and do not randomize runs. Analyze the data, look for interactions and non linear effects.  Comment on the results. What are your recommendations?  There is a rumor in the industry that the AJAX paste does not print well at 20C.  What do the data tell you in this regard?  Do you propose further experiments, what are they? (40pts)

 

V:General

 

Explain Lean, Six Sigma, and how the two work together in a way that your 15 year old neighbor would understand. (10pts)

 

VI: Lean

You are a Six Sigma practitioner working for a retail chain that sells home furniture. The company has been losing market share recently, and it has been determined that this is due to poor customer satisfaction during the product ordering process.  You have just been assigned a project to improve the process of quoting price and delivery for new dining room tables to retail customers.

 

• What is the most probable primary metric (or key process output variable) for this process? (5pts) ___________________________________

 

• How would you begin to determine possible sources of waste in this process? (Select the best answer) (5pts)
  1. Conduct a DOE to determine sources of variation at the factory.
  2. Map the value stream of the quoting process.
  3. Run a 2 sample T test on process time before and after improvements.
  4. Look at what has been done in the past when sales have fallen and repeat those actions.
  5. Ask the owner what he would do.
• Create a rough process map of the ordering process, and identify the NVA, BNVA and VA steps (can be simply “step 1 à step à”, no fancy graphics required). Comment on which could be eliminated or reduced. (10pts)

 

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