Quantative Methods (Statistical Analysis) Assignment

Quantative Methods (Statistical Analysis) - Assignment Example The Common Cause Variations are those instances that are affected by naturally occurring situations and the attributes of the products or raw materials themselves. The Special Cause variations are the ones that need to be attended to, as these are variations caused by issues or problems with the manufacturing process; like the wear and tear of appliances and changes in material quality. Slight variations in product are expected due to the natural cause variations; and SPC can be used to identify when action needs be taken to rectify the processes; and also to identify when the variations are not significant enough to require attention. It is thus also a means of saving resources that may otherwise have been spent in addressing a small issue that is not cost effective. Constant mapping of product quality helps in identifying points in time that could be cause for concern by isolating times of excessive variation. When such a situation is spotted, Pareto Diagrams – amongst other techniques can help in identifying the causes of these variations; and the feasibility of responding to them. A Pareto chart is a chart that maps both the individual categories under survey as well as the cumulative total of the categories. Each category is represented as a bar; and the categories are ranked from the one causing most variation to the one causing the least. The cumulative total is represented as a line graph; and is most often curved to form a concave line. The left vertical axis represents the frequencies and the right vertical axis, the cumulative percentage. The horizontal axis represents the categories under study. The chart thus helps us identify the categories that are most in need of being addressed. It also helps us identify which categories it would not be cost effective to focus on. There are two types of Pareto charts – the Counts chart, and the Cost chart. The Counts chart helps in understanding which of the units have the most flaws; while the Co st chart helps in identifying the category that is incurring the most cost. At times, there may be different categories implicated by the two charts for a single analysis; so the organization then has to prioritze which they would like to address first. An example would be a shirts manufacturing unit; which manufactures shirts in a variety of price ranges. In a given month; the SPC finds that reject units have significantly gone up; and further analysis is conducted. The Pareto charts show that three types of shirts are most to blame for this increase in wastage – a simple cotton shirt, a linen shirt and a high end silk shirt. It is also identified that while far more units of the cotton shirt are being rejected; the costs incurred from the rejected units of the silk shirts is significantly higher. The organization can now choose which to focus on. It is decided that immediate attention should be focused on rectifying the problem with the silk shirt production; and then the q uality control team should focus on the problems with the cotton shirt production. The charts also helped in identifying that the problems with the linen shirt would not be cost effective to address in the given situation; and so the company chooses not to address those problems; but monitor the production to ensure that there are no further issues. Question 1: B i. The probability of any randomly selected phone call having a response rate of less than the target rate of 19 minutes is found to be 0.9772. This means that 97.72% of the times, the