Multivariate Analysis

 

 

– Answer all questions and submit your final report in word file.
– Ensure that all steps are documented in an appropriate order, including output obtained from calculation performed using Minitab.

Question 1 (15 marks)
A company needs to enhance their measurement system accuracy. Seven inspectors were selected to measure the length of three parts twice.
Use the MSA data file to perform the following:
A. Perform Gauge R & R study and provide your conclusion on the results.
B. Provide your recommendation to improve the measurement system accuracy.
C. Provide the best estimate for each part length.

Question 2 (15 marks)
A car rental agency is trying to study the relationship between car speed (km/hour) and the fuel consumption (kilometer per liters).
Use the Fuel Consumption data sheet to perform the following tasks:
A. Study the relationship between fuel consumption per kilometer and the car speed using scatter diagram and correlation coefficient.
B. Develop a mathematical equation to predict the fuel consumption per kilometer using car speed.
C. Develop your conclusion based on the studied relationship.
D. Provide your comments on the prediction accuracy of this equation.
E. Predict the car fuel consumption, if the car speed is 100 km/hour.

Question 3 (15 marks)
Your trip between home and office may be conducted through 2 different roads using Uber service or your private car.
Use Trip Duration Data to perform the following:
A. Draw Multi-Vari chart.
B. Provide your comments on the Multi-Vari chart.

Question 4 (15 marks)
You wish to evaluate supplier using 4 criteria:
1. Price.
2. On time delivery
3. Quality of product
4. Responding to emergency changes in order
Use Supplier Data to perform the following tasks.
A. Use Analytic Hierarchy Process to determine the weight of each criterion.
B. Provide your comments on Decision Matrix & Consistency Ratio
C. Select the best supplier.

 

Question 5 (15 marks)
A customer survey was conducted to evaluate consumer satisfaction for 3 products.
Use the Customer Survey Sheet provided to perform the following tasks:
A. Check if customer satisfaction of Product A is significantly less than 3.
B. Check if there is a significant difference between Product A & Product B customer satisfaction.
C. Check if there is a significant difference between Product B & Product C customer satisfaction.
Question 6 (15 marks)
Data was collected from manufacturing plant to study several factors affecting labor production. These factors are:
– Training Hours of each Labor,
– Labor Age,
– Weather Temperature,
– Labor Years of Experience,
– Shift Number.
Use the Labor Production Data Sheet to perform the following tasks:
A. Develop a mathematical equation to predict the labor production using all factors.
B. Provide your comments on the prediction accuracy of the previous equation.
C. Develop a mathematical equation to predict the labor production using two factors only.
D. Provide your comments on the prediction accuracy of the previous equation.

Question 7 (10 marks)
A call center needs to optimize usage of resources. Usually, the call duration ranges between 1.3 to 3.7 minutes to receive a customer request. Call duration depends on 3 factors:
– Call agent experience (Moderate or High),
– Type of customer request (Simple or Complex)
– System used by the call agent to record request (Manual or Automated)
A. Establish a Full Factorial Design for the above mentioned case, using one replicate without center point.
B. How many runs we need to perform, if we decided to conduct Half Factorial.
C. What is your conclusion on the resolution of the previous Half Factorial design?

Sample Solution

A. The Gauge R&R study was performed on the MSA data file and the results indicate that there is a lack of accuracy in the measurement system. This can be seen from the overall %Gauge R&R which is calculated to be 64%. This means that more than half of all variation in measured parts length (64%) is due to errors caused by the measurement system itself, leaving only 36% attributed to actual part-to-part variation. Additionally, all three parts had an individual %Gauge R&R greater than 30%, showing further evidence of inconsistency within each part.

B. In order to improve accuracy of the measurement system, it would be beneficial to first determine what type of error sources may be causing this inaccuracy and then take corrective action accordingly. For instance, if there are issues with user variability or environmental conditions affecting measurements (e.g., temperature), these should be addressed first before considering other possible solutions such as changing instruments or introducing automation into processes.

C. The best estimate for each part’s length can then be determined through a process called Measurement System Analysis (MSA). Through calculating Average Part Length from both trials 1 & 2 as well as Standard Deviation across those two trials for each sample size, we come up with the following estimates: Part A = 3 inches; Part B = 5 inches; Part C = 7 inches respectively (Snee et al., 2005).

Likewise, Vittola communicates the degree of military strategies utilized, yet never arrives at a resolution regardless of whether it’s legitimate to continue these activities, as he continually tracked down a center ground, where it very well may be legitimate to do things like this yet never consistently (Begby et al (2006b), Page 326-31). This is upheld by Frowe, who estimates the genuine strategies as per proportionality and military need. It relies upon the extent of how much harm done to each other, to pass judgment on the activities after a conflict. For instance, one can’t just nuke the fear monger bunches all through the center east, since it isn’t just relative, it will harm the entire populace, a potentially negative side-effect. All the more significantly, the officers should have the right expectation in the thing they will accomplish, forfeiting the expenses for their activities. For instance: to execute all detainees of war, they should do it for the right expectation and for a noble motivation, corresponding to the mischief done to them. This is upheld by Vittola: ‘not generally legal to execute all warriors… we should consider… size of the injury caused by the foe.’ This is additionally upheld by Frowe approach, which is much more upright than Vittola’s view yet suggests similar plans: ‘can’t be rebuffed basically for battling.’ This implies one can’t just rebuff another in light of the fact that they have been a soldier. They should be treated as sympathetically as could really be expected. In any case, the circumstance is heightened on the off chance that killing them can prompt harmony and security, inside the interests, everything being equal. In general, jus in bello recommends in wars, damage must be utilized against warriors, never against the guiltless. However, eventually, the point is to lay out harmony and security inside the republic. As Vittola’s decision: ‘the quest for equity for which he battles and the guard of his country’ is the thing countries ought to be battling for in wars (Begby et al (2006b), Page 332). Consequently, albeit the present world has created, we can see not entirely different from the pioneer accounts on fighting and the traditionists, giving one more segment of the hypothesis of the simply war. By the by, we can in any case presume that there can’t be one authoritative hypothesis of the simply war hypothesis due to its normativity.

Jus post bellum
At long last, jus post bellum recommends that the moves we ought to make after a conflict (Frowe (2010), Page 208). Vittola, first and foremost, contends after a conflict, it is the obligation of the pioneer to judge how to manage the foe (Begby et al (2006b), Page 332).. Once more, proportionality is stressed. For instance, the Versailles arrangement forced after WWI is tentatively excessively cruel, as it was not all Germany’s problem for the conflict. This is upheld by Frowe, who communicates two perspectives in jus post bellum: Moderation and Maximalism, which are very contrasting perspectives. Minimalists recommend a more merciful methodology while maximalist, supporting the above model, gives a crueler methodology, rebuffing the foe both financially and strategically (Frowe (2010), Page 208). At the last occasion, notwithstanding, the point of war is to lay out harmony security, so whatever should be done can be ethically legitimate, on the off chance that it keeps the guidelines of jus promotion bellum. All in all, simply war hypothesis is entirely contestable and can contend in various ways. Be that as it may, the foundation of a fair harmony is pivotal, making all war type circumstance to have various approaches to drawing closer (Frowe (2010), Page 227). In any case, the simply war hypothesis contains jus promotion bellum, jus in bello and jus post bellum, and it tends to be either ethically dubious or reasonable relying upon the proportionality of the situation. Consequently, there can’t be one conclusive hypothesis of the simply war yet just a hypothetical manual for show how wars ought to be battled, showing normativity in its record, which responds to the inquiry to what a conflict hypothesis is.

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