Problem 1: [10 marks] Unplanned shutdowns of reactors have been a chronic problem for a nuclear plant. After much discussion, 'cylinder changes' and 'human error have been identified as the primary causes. A diagnostic approach based on facts was instituted. Here are data on the causes of previous shutdowns: Frequency Cause Cylinder changes Human error Initiator system Hot melt system Interlock malfunction Other 19 23 a. Convert the preceding table into a Pareto chart (by calculating the cumulative percentage of the frequency of occurrence for each cause), and based on the chart identify the main causes for the unplanned shutdowns. Discuss the findings. b. For the unplanned shutdowns caused by human error,' the data related to the time between shutdowns in weeks is shown in the following table: [ 19 22 20 33 27 40 24 15 18 28 25 1 21 31 16 27 Fill in the table below to determine the frequency of the data for the provided data cells, and afterwards draw a histogram to visually represent the distribution of the time between shutdowns due to human error. Time between shutdowns (weeks) Frequency 10-15 21-25 25-30 31-35 36-40 c. Draw an Ishikawa diagram to address the problem of low quality of acquired materials by a Purchasing Department at an organization