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Management system failures.The U.S. Chemical Safety and Hazard Investigation Board (CSB) is responsible for determining the root cause of industrial accidents (Process Safety Progress, December 2004). The accompanying table gives a breakdown of the root causes of 83 incidents caused by management system failures.

Management System Cause Category	Number of Incidents
Engineering & Design Procedures & Practices Management & Oversight Training & Communication	27 24 22 10
Total	83

a.Find the relative frequency of the number of incidents for each cause category.

b.Construct a Pareto diagram for the data.

c.From the Pareto diagram, identify the cause categories with the highest (and lowest) the relative frequency of incidents.

Step by step solution

01

 Step 1: Finding the relative Frequency

$\mathbf{Relative}\mathbf{}\mathbf{Frequency}\mathbf{=}\frac{\mathbf{Frequency}}{\mathbf{Total}\mathbf{}\mathbf{Frequency}}$

Engineering and Design (ED),

$\begin{array}{c}\text{RelativeFrequency=}\frac{\text{27}}{\text{83}}\\ \text{=0.32}\end{array}$

Procedures and Practices (PP),

$\begin{array}{c}\text{RelativeFrequency=}\frac{\text{24}}{\text{83}}\\ \text{=0.29}\end{array}$

Management and Oversight (MO),

$\begin{array}{c}\text{RelativeFrequency=}\frac{\text{22}}{\text{83}}\\ \text{=0.27}\end{array}$

Training and Communication (TC),

$\begin{array}{c}\text{RelativeFrequency=}\frac{\text{10}}{\text{83}}\\ \text{=0.12}\end{array}$

02

Constructing a Pareto Diagram

As the data is already in descending order and based on the relative frequencies above we can find the percentages.

ED = 32%

PP = 29%

MO = 27%

TC = 12%

Using this we will construct the Pareto diagram.

03

Identifying the category with the highest and lowest relative frequency of incidents

The category with the highest relative frequency of incidents is Engineering and Design (0.32).

The category with the lowest relative frequency of incidents is Training and Communication (0.12).

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