Assignment 1 Excel

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Conestoga College *

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8090

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Statistics

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Feb 20, 2024

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Assignment 1 19 th October 2023 Prepared by Vikas Patel Student no – 8938771 STAT8090 Prepared for Reza Mohaghegh
Compute all descriptive summary measures, box-and-whisker plots and any other tables and charts relating to the cat food cans that you believe would be useful in preparing your report to management. Interpretation: - The interquartile range (IQR) in both samples is relatively narrow, which suggests that most cans are within a consistent range. - There are a few potential outliers in the Shrimp Cat Food sample, which may require investigation. To further analyze the data and prepare a comprehensive report for management, you may consider the following additional steps: 1. Conduct hypothesis tests to determine whether the means of the samples are statistically different from the legal requirement. 2. Analyze the data for trends or patterns by examining shifts and possible root causes of variation. 3. Create control charts to monitor the filling process over time and detect any trends or shifts. 4. Provide recommendations for process improvements to ensure that the company consistently meets legal requirements. 5. Calculate the percentage of underfilled and overfilled cans. 6. Summarize the potential impact of current filling practices on customer satisfaction, product quality, and compliance with legal standards. Incorporating these additional analyses and insights into your report will help management make informed decisions about process improvements and quality control measures. Identify issues with the current process and what needs to be done to improve it? Issues with the current process for filling cat food cans are evident from the data and the analysis. Here are the identified issues and suggestions for improvement: 1. Variability in Fill Weights: The standard deviations for both Kidney and Shrimp cat food cans are relatively high. This indicates a significant level of variability in the fill weights. Variability can lead to inconsistencies in product quality, consumer dissatisfaction, and potential legal issues. Improvement: To address variability, the company should consider the following steps: - Fine-tuning the extruding machine: Ensuring precise control over the amount of food dispensed into each can. - Calibration and maintenance of equipment: Regular maintenance and calibration of the filling machinery to reduce measurement errors.
- Quality control checks: Implement stringent quality control checks at various stages of the filling process to catch and correct discrepancies in real-time. 2. Outliers : The box-and-whisker plots may reveal outliers, which are data points falling outside the whiskers. Outliers can be indicative of irregularities in the filling process or measurement errors. Improvement : Investigate and address the root causes of outliers. This may involve inspecting the production process for unusual events, equipment malfunctions, or measurement errors. 3. Legal Compliance: The company is currently overpacking the cans to ensure they meet the minimum legal requirement, resulting in some cans being overfilled. This can lead to spillage and cost inefficiencies. Improvement : To meet legal requirements efficiently and minimize overpacking and spillage, consider the following: - Adjusting the extruding machine settings to control the fill weight more precisely within the legal range. - Implementing real-time monitoring and feedback systems to ensure that the fill weights remain within the legal limits. 4. Consistency in Shifts: It's also essential to examine the consistency between shifts. The data shows variations in fill weights between different shifts, which might be due to differences in equipment handling or process management. Improvement: To improve consistency between shifts, consider standardizing operating procedures and providing additional training or supervision for workers to ensure uniformity in the filling process. 5. Statistical Process Control: Implementing a statistical process control (SPC) system can help monitor and control the filling process in real-time. This includes setting control limits, monitoring variation, and taking corrective actions when necessary. 6. Root Cause Analysis: Conduct a root cause analysis to identify and address the underlying factors contributing to variability and inconsistencies in fill weights. This may involve examining equipment performance, raw materials, and operator skills. 7. Continuous Improvement: Establish a culture of continuous improvement within the organization. Regularly review and update procedures and processes to enhance product quality and consistency. 8. Customer Feedback: Collect feedback from customers regarding the consistency and quality of the product. Use this feedback to make further adjustments to the process. By addressing these issues and implementing the suggested improvements, the company can achieve better consistency in fill weights, reduce overfilling, minimize underfilling, and ensure compliance with legal requirements. This, in turn, can enhance customer satisfaction and maintain a competitive edge in the gourmet cat food market. Estimate the population standard deviation using the sample characteristics. Make sure you are not mixing two processes. Standard deviation for kidney shift 1 – 0.0181
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Standard deviation for kidney shift 2 – 0.0234 Standard deviation for shrimp shift 1 – 0.0338 Standard deviation for shrimp shift 2 – 0.0363 To meet the legal requirements, what must the company do to improve the filling processes for each type of canned food? And what should be the enhanced process mean and standard deviation? To meet the legal requirements for filling processes for each type of canned food (Kidney and Shrimp Cat Food), the company must ensure that the fill weights fall within the specified range, which is between 2.95 ounces (minimum) and 3.10 ounces (maximum). Here's what the company should do to improve the filling processes: 1. Fine-Tune the Filling Equipment: Adjust the extruding machine settings to control the fill weight more precisely. Calibrate the equipment regularly to maintain accuracy. 2. Implement Real-Time Monitoring: Use real-time monitoring and feedback systems to ensure that the fill weights remain within the legal limits. Implement statistical process control (SPC) to detect variations and make immediate adjustments. 3. Quality Control Checks: Conduct stringent quality control checks at various stages of the filling process. Perform regular inspections to ensure the equipment is functioning correctly. 4. Consistency in Shifts: Standardize operating procedures across different shifts. Provide additional training or supervision to workers to ensure uniformity in the filling process. 5. Root Cause Analysis: Conduct a root cause analysis to identify and address factors contributing to variability and inconsistencies in fill weights, such as equipment performance, raw materials, and operator skills. Now, let's discuss what the enhanced process mean and standard deviation should be to meet the legal requirements for filling each type of canned food:
Kidney Cat Food: - To meet the legal requirements, the enhanced process mean for Kidney Cat Food should target the midpoint of the legal range, which is the mean of 2.95 ounces and 3.10 ounces: \((2.95 + 3.10) / 2 = 3.025\) ounces. - The enhanced process standard deviation should be reduced from the current value to ensure that the majority of cans fall within the specified range. The exact target standard deviation will depend on the analysis of the process data, but it should be set to minimize underfilling and overfilling. Shrimp Cat Food: - Similarly, for Shrimp Cat Food, the enhanced process mean should also target the midpoint of the legal range, which is 3.025 ounces. - The enhanced process standard deviation should be reduced to ensure that most cans fall within the legal range, based on the analysis of the process data. It's important to emphasize that the company must continuously monitor and adjust the filling process to maintain the enhanced process mean and standard deviation. Ongoing quality control, data analysis, and process improvement efforts are essential to meet legal requirements and provide consistently high- quality products. What percentage of each type of canned food is underfilled, and what percentage is overfilled? To calculate the percentage of each type of canned food that is underfilled and overfilled, we'll use the sample data for Kidney Cat Food and Shrimp Cat Food separately and compare it to the legal requirements for a 3-ounce can (2.95 ounces minimum and 3.10 ounces maximum). Kidney Cat Food: 1. Count the number of Kidney Cat Food cans that are underfilled (below 2.95 ounces). 2. Count the number of Kidney Cat Food cans that are overfilled (above 3.10 ounces). 3. Calculate the total number of Kidney Cat Food cans in the sample (which is 50). Calculate these percentages for Kidney Cat Food Shift 1: - Number of Kidney Cat Food cans underfilled: 0 - Number of Kidney Cat Food cans overfilled: 0 - Total number of Kidney Cat Food cans: 50 Percentage of underfilled Kidney Cat Food cans:
Percentage of Underfilled Kidney Cat Food Shift 1 = 0/50 × 100% = 0% Percentage of overfilled Kidney Cat Food cans: Percentage of Overfilled Kidney Cat Food Shift 1 = 0/50 × 100% = 0% Calculate these percentages for Kidney Cat Food Shift 2: - Number of Kidney Cat Food cans underfilled: 0 - Number of Kidney Cat Food cans overfilled: 1 - Total number of Kidney Cat Food cans: 50 Percentage of underfilled Kidney Cat Food cans: Percentage of Underfilled Kidney Cat Food Shift 2 = 0/50 × 100% = 0% Percentage of overfilled Kidney Cat Food cans: Percentage of Overfilled Kidney Cat Food Shift 2 = 1/50 × 100% = 2% Shrimp Cat Food: 1. Count the number of Shrimp Cat Food cans that are underfilled (below 2.95 ounces). 2. Count the number of Shrimp Cat Food cans that are overfilled (above 3.10 ounces). 3. Calculate the total number of Shrimp Cat Food cans in the sample (which is 50). Calculate these percentages for Shrimp Cat Food Shift 1: - Number of Shrimp Cat Food cans underfilled: 0 - Number of Shrimp Cat Food cans overfilled: 2 - Total number of Shrimp Cat Food cans: 50 Percentage of underfilled Shrimp Cat Food cans: Percentage of Underfilled Shrimp Cat Food Shift 1 = 2/50 × 100% = 4% Percentage of overfilled Shrimp Cat Food cans: Percentage of Overfilled Shrimp Cat Food Shift 1 = 0/50 × 100% = 0% Calculate these percentages for Shrimp Cat Food Shift 2: - Number of Shrimp Cat Food cans underfilled: 3 - Number of Shrimp Cat Food cans overfilled: 0 - Total number of Shrimp Cat Food cans: 50 Percentage of underfilled Shrimp Cat Food cans:
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Percentage of Underfilled Shrimp Cat Food Shift 2 = 3/50 × 100% = 6% Percentage of overfilled Shrimp Cat Food cans: Percentage of Overfilled Shrimp Cat Food Shift 2 = 0/50 × 100% = 0%