Business Statistics and Quantitative Analysis - Checking for Quality

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Scenario: A venture capitalist has just given you several million dollars to develop your dream product! Explain in detail what this product is and why people would buy it. (Think Steve Jobs and the iPhone - did people really think we needed “smartphones” back in 2007?)

Main Post: Now your dream product has gone into production and the manager is asking you, as the statistical expert, to use statistical methods to ensure quality control.

1. You will generate a random dataset of N samples of defective proportions by completing the following steps:

a) You will start with a random number by combining the last 2 digits of the year in which you were born plus the day of the month in which you were born. For example, if you were born October 3, 1990, your number would be 90 + 3 = 93. (If your number exceeds 100, subtract 100 from the total.) Call this X and it will seed your random number generation. MY DATE OF BIRTH IS 9/4/1978.

b) Choose a number of samples, N. (N should be between 5 and 10 samples.)

c) In Excel, type =RAND()*X in a cell. Repeat N times. This will generate the proportion of defective products (out of 100) for your N samples.

2. Use Excel to create a p-chart for a sample size, 100, and the number of samples, N.

3. Write a professional memo to your business/company owner describing the production quality so far and prioritizing any control measures necessary to guarantee high quality products.

Address the following items and questions in your professional memo:

  • Describe your product, its use, and societal value. (Humor is encouraged.)
  • Share and summarize your p-chart.
  • What is your Lower Control Limit (LCL) and Upper Control Limit (UCL)?
  • Is the product in control? If not in control, what sample(s) was outside of the limits, i.e., below LCL or above UCL?
  • What measures could be taken now to address the data points that out of control?
  • What recommendations would you suggest to optimize quality in future production?

Unit 10 Discussion: Checking for Quality Unit 10 Discussion Example – Main Post Scenario: A venture capitalist has just given you several million dollars to develop your dream product! Explain in detail what this product is and why people would buy it. (Think Steve Jobs and the iPhone - did people really think we needed “smartphones” back in 2007?) Main Post: Now your dream product has gone into production and the manager is asking you, as the statistical expert, to use statistical methods to ensure quality control. You will need to write a professional memo to your business/company owner describing the production quality so far and prioritizing any control measures necessary to guarantee high quality products. You should include your statistical data in the professional memo. See the DB Starter video in the Unit 10 LiveBinder. 1. Describe your product, its use and societal value in at least one paragraph. Humor is encouraged. 2. You will generate a random dataset of N samples of defective proportions by completing the following steps: a) You will start with a random number by combining the last 2 digits of the year in which you were born plus the day of the month in which you were born. For example, if you were born October 3, 1990, your number would be 90 + 3 = 93. (If your number exceeds 100, subtract 100 from the total.) Call this X and it will seed your random number generation. b) Choose a number of samples, N. N should be between 5 and 10. c) In Excel, type =RAND()*X in a cell. Repeat N times. This will generate the proportion of defective products (out of 100) for your N samples. 3. Use Excel to create a p-chart for a sample size, 100, and the number of samples, N. Share your p-chart. See video in Unit 10 Live Binders. 4. Share Lower Control Limit (LCL) and Upper Control Limit (UCL). 5. Is the product in control? If not in control, what sample(s) was outside of the limits, ie below LCL or above UCL? ***************************************************************************************** * 1. My dream product is a TV that can change between a computer monitor and a TV or video display. Wouldn’t it be great to have a computer monitor the size of your TV screen? Oh, also it will be touch sensitive. After all, a computer mouse is a thing of the past! I will call this product the “Do-It-All-Display”! 11 21 43 9 31 2. So, we are now in production mode and the first line of “Do-It-All-Display” been made!! I will create an imaginary random dataset to represent the defective Displays out of N samples. My year is 1962 and month day is 1. (January, 16, 1962) a) X = 62+1 = 63 b) N = 10 62 7 16 products have number of 45 21 Using RAND()*63, my 10 sample proportions are: 3. p-chart: Sample number Number of Defects Number in Sample Percent of defects Average of Defects 1 11 100 0.11 26.60% Below 2 21 100 0.21 26.60% 3 43 100 0.43 26.60% Above 4 9 100 0.09 26.60% Below 5 31 100 0.31 26.60% 6 62 100 0.62 26.60% Above 7 7 100 0.07 26.60% Below 8 16 100 0.16 26.60% 9 45 100 0.45 26.60% Above 10 21 100 0.21 26.60% P-Chart 70 60 50 40 30 20 10 0 0 1 2 3 4 4. Upper Control Limit = 39.88% 5 6 7 8 9 10 11 Above or Below accepted value Lower Control Limit = 13.34% Sample Summary Total defects 266 Total sampled 1000 average proportion 0.266 standard error of the proportion 0.04419 Standard Deviations above and below average 3 Probability of outside of Tolerance (1confidence interval) 0.00270 Upper Limit 39.86% Lower Limit 13.34% 5. The process is not in control. There are 3 samples that are above the acceptable % defective. In this case, it is okay that there are 3 samples that have a defective % less than the lower control limit, since less defective products is okay!
size of tolerance Number of standard deviations 3 Sample Information Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Count 3 14 12 12 Above or Below acceptable value Values for Control Chart mean standard deviation Upper Limit Lower Limit 10.250 10.250 10.250 10.250 3.2016 3.2016 3.2016 3.2016 19.855 19.855 19.855 19.855 0.645 0.645 0.645 0.645 Sample number Number of Defects Information From AverageSamples of Number in Sample Percent of defects Defects 1 9 100 0.0900 0.098 2 9 100 0.0900 0.098 3 10 100 0.1000 0.098 4 11 100 0.1100 0.098 5 10 100 0.1000 0.098 6 7 8 9 10 11 12 13 14 15 16 17 18 19 m Samples Upper Limit Lower Limit 0.156 0.040 0.156 0.040 0.156 0.040 0.156 0.040 0.156 0.040 Sample Sum Above or Below accepted value standa Standard Deviations alpha Probability of outside of Toleran Sample Summary Total defects 49 Total sampled 500 average proportion 0.098 standard error of the proportion 0.02973 Standard Deviations above and below average 1.96 z value calculated 1.96 ity of outside of Tolerance (1-confidence interval) 0.0500 Upper Limit 0.1563 Lower Limit 0.0397 0.05 Color Key: Cells that require student input Excel Intermediate Calculations Excel Calculated Results Major Headings Minor Headings Reference/Check Points Size of Samples Sample Size 3 Raw Data Collected for Sample Sample Number Item 1 Item 2 Item 3 Item 4 1 0.97 1 1.04 2 0.96 0.97 1.01 3 0.99 1.01 1.04 4 1.01 0.98 0.97 5 0.99 1.04 1.04 6 0.99 1.03 0.96 7 0.98 1.05 0.96 8 1.02 1.04 1 9 1.04 1.03 0.98 10 1.04 1.03 0.99 11 1.01 0.97 0.96 12 0.98 0.98 1.01 13 0.95 1.05 1.04 14 0.97 1.01 0.98 15 0.97 1.01 0.95 16 17 18 19 20 21 Item 5 Item 6 Item 7 Item 8 Compiled Sample Information ample Item 9 Item 10 Item 11 Item 12 Sample Range average 1 0.0700 1.0033 2 0.0500 0.9800 3 0.0500 1.0133 4 0.0400 0.9867 5 0.0500 1.0233 6 0.0700 0.9933 7 0.0900 0.9967 8 0.0400 1.0200 9 0.0600 1.0167 10 0.0500 1.0200 11 0.0500 0.9800 12 0.0300 0.9900 13 0.1000 1.0133 14 0.0400 0.9867 15 0.0600 0.9767 16 17 18 19 20 21 Determine Samples that are not in Range Tolerance Upper Lmit Range r bar center line Lower Limit Range 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 0.147 0.057 0.000 Above or Below acceptable value Determine Samples that are not in Mean Tolerance Above or Below Upper Limit x bar center Lower Limit acceptable x bar line x bar value 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 1.058 1.000 0.942 Color Key: Cells that require student input Excel Intermediate Calculations Excel Calculated Results Major Headings Minor Headings Reference/Check Points Size of Samples Sample Size 10 Compiled Sample Information Sample Range Determine Samples that ar Tolerance average Upper Lmit Range r bar center line 1 5 21 8.974 5.050 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 4 2 3.5 7 5.75 3.25 12 5 3 20 23 17 18.5 21.5 20.25 21 19.75 22 8.974 8.974 8.974 8.974 8.974 8.974 8.974 8.974 8.974 5.050 5.050 5.050 5.050 5.050 5.050 5.050 5.050 5.050 amples that are not in Range Tolerance Lower Limit Range Above or Below acceptable value Determine Samples that are not in Tolerance Upper Limit x bar x bar center line 1.126 21.955 20.400 1.126 1.126 1.126 1.126 1.126 1.126 1.126 Above 1.126 1.126 21.955 21.955 21.955 21.955 21.955 21.955 21.955 21.955 21.955 20.400 20.400 20.400 20.400 20.400 20.400 20.400 20.400 20.400 Color Key: Cells that require student input Excel Intermediate Calculations Samples that are not in Mean Tolerance Lower Limit x bar Above or Below acceptable value Major Headings Minor Headings Reference/Check Points 18.845 18.845 18.845 18.845 18.845 18.845 18.845 18.845 18.845 18.845 Excel Calculated Results Above Below Below Above SampeSize 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 A2 1.88 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.285 0.266 0.249 0.235 0.223 0.212 0.203 0.194 0.187 0.18 0.173 0.167 0.162 0.157 0.153 d2 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.97 3.078 3.173 3.258 3.336 3.407 3.472 3.532 3.588 3.64 3.689 3.735 3.778 3.819 3.858 3.895 3.931 D3 0 0 0 0 0 0.076 0.136 0.184 0.223 0.256 0.283 0.307 0.328 0.347 0.363 0.378 0.391 0.403 0.415 0.425 0.434 0.443 0.451 0.459 D4 3.268 2.574 2.282 2.114 2.004 1.924 1.864 1.816 1.777 1.744 1.717 1.693 1.672 1.653 1.637 1.622 1.608 1.597 1.585 1.575 1.566 1.557 1.548 1.541

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School: UC Berkeley

Please let me know if there is anything needs to be changed or added. I will be also appreciated that you can let me know i...

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Anonymous
Tutor went the extra mile to help me with this essay. Citations were a bit shaky but I appreciated how well he handled APA styles and how ok he was to change them even though I didnt specify. Got a B+ which is believable and acceptable.

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