Page 13 RMI 2101 Fall 2016 Homework Assignment 520 Points

P A G E 1 3rmi 2101fall 2016homework Assignment 520 Pointsdue On Mo

Analyze the problem related to Amazon.com's truck stations in Pennsylvania and New Jersey, focusing on accident frequencies, probability distributions, expected values, variances, risk assessments, and associated financial losses. Complete calculations based on provided accident data, construct probability distributions, determine risk levels, and evaluate expected losses both in dollar terms and in terms of severity based on reported accident costs.

Paper For Above instruction

Amazon.com, a major e-commerce retailer, operates extensive logistics networks that include truck stations in various states, notably Pennsylvania (PA) and New Jersey (NJ). Analyzing the risks associated with their truck operations involves understanding accident frequencies, their probabilities, and the financial impact of these incidents. The following comprehensive assessment covers the key elements of risk management in this context, including probability distributions, expected values, variances, and financial implications.

Introduction

Risk assessment in logistics and transportation management requires quantification of accident frequencies, their probabilities, and potential financial losses. For Amazon's truck stations in PA and NJ, the statistical analysis is crucial for operational planning, safety improvements, and financial planning. The data provided allows for a qualitative and quantitative comparison of risk levels between the two stations. This assessment considers accident frequency distributions, calculates expected accident rates, evaluates variance and risk, and estimates the expected financial losses resulting from accidents. The ultimate goal is to inform decision-making processes that enhance safety and minimize costs.

Probability Distribution of Accident Frequencies

The data presents the number of accidents per truck, along with the number of trucks experiencing that frequency, for both stations. For the PA station, with 250 trucks, and the NJ station, with 180 trucks, the probability distribution functions (PDFs) for accident frequencies can be derived. This entails calculating the probability that a randomly selected truck from each station falls into each accident frequency category:

• PA station: The probabilities for each accident count are obtained by dividing the number of trucks with specific accident counts by the total trucks (250). For example, if 2 trucks had 0 accidents, then P(X=0) = 2/250 = 0.008.
• NJ station: Similarly, probabilities are derived based on the trucks and accidents data (180 trucks).

This distillation results in discrete probability distributions that are essential for subsequent calculations of expected values and variances.

Expected Value of Accident Frequency

The expected number of accidents per truck is calculated as the sum of each accident count times its probability:

Expected Accidents (PA) = Σ (number of accidents) × P(accident count)

This metric provides an average accident frequency per truck, serving as a central measure for risk comparison.

Units of measurement are accidents per truck per year, quantifying the frequency of accidents in a standardized manner.

Variance and Risk Analysis

The variance quantifies the dispersion of accident frequencies around the mean, with higher variance indicating greater risk or variability. For the PA station, the variance is given as 0.6324, indicating the degree of fluctuation in accident frequencies. The units for variance match those of the squared accident count units, i.e., accidents² per truck. A higher variance suggests greater unpredictable risk, which could lead to more significant financial implications.

Similarly, the NJ station has a variance of 0.57, providing a basis for risk comparison. The station with the higher variance is inherently riskier, as the accidents are less predictable and potentially more costly.

Comparison of Risk Between PA and NJ Stations

Comparing the variances of accident frequencies in the two stations reveals that PA has a slightly higher variance (0.6324) than NJ (0.57). This indicates that PA's accident frequency exhibits marginally more variability, implying a slightly higher risk. However, other factors such as the total number of trucks and the expected accident rate should also inform the assessment.

The station with the higher expected accident frequency and variance presents a more substantial risk profile, influencing safety protocols and risk mitigation strategies.

Expected Financial Losses from Accidents

Assuming each accident incurs a fixed cost of $2,500, the expected loss per truck can be calculated by multiplying the expected number of accidents by this fixed cost:

Expected Loss (PA) per truck = E(Accidents) × $2,500

This provides a monetary measure of risk exposure at the individual truck level.

The total expected loss across all trucks is obtained by multiplying the per-truck loss by the total number of trucks at each station, offering insights into the overall financial risk for the operation.

Severity and Financial Impact Based on Reported Accidents

When considering reported accident costs, a weighted mean or expected value of severity is computed based on the reported dollar amounts and their respective frequencies. For example, calculations involving the reported dollar amounts (ranging from $300 to $5,500) and their occurrence counts provide an average severity per accident.

The expected severity is obtained by summing the product of each dollar amount and its probability, which in turn influences the expected financial loss per truck when considering actual accident costs.

This analysis allows Amazon to estimate potential financial exposure from accidents more accurately, involving both frequency and severity considerations.

Conclusion

Evaluating risk in Amazon’s truck operations involves a nuanced understanding of accident frequency distributions, probabilities, variances, and financial implications. The slightly higher variance at PA suggests marginally increased unpredictability, which combined with higher expected accident rates, indicates a greater risk profile compared to NJ. Consequently, targeted risk mitigation initiatives, safety protocols, and insurance considerations should prioritize the PA station, while likewise addressing NJ’s vulnerabilities. Continuous data monitoring and statistical analysis are essential components for dynamic risk management in large-scale logistics operations.

References

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