Statistical Data Analysis - Data Collection - Assignment Example

Running Head: DATA COLLECTION Data Collection [Name of the writer] [Name of the institution] Task 1 1. Graphing Procedures Excel offers a variety of graphing procedures, which allow us to visually inspect our data for errors/problems and provide us with a visual snapshot of our results. Although several graphs are available, only two common graphs will be outline below (bar graph and Pie chart). (a) - Pie Charts provide a lucid visual summary of the distribution of a variable or a categorical variable with several categories. Pie charts are only used when the values a variable can take are limited. This graphical method appropriate for nominal and ordinal variables where the proportion in each category of a variable is represented as a segment of a circle. By frequency table one can easily examine the results, see table below: Problem Respondents Cumulative Frequency % Cumulative % Late Delivery 20 20 24.09638 24.09638 Faculty Products 25 45 30.12048 54.21686 Per Sales Service 5 50 6.024096 60.24096 Late Invoice 3 53 3.614457 63.85542 Damaged Packaging 5 58 6.024096 69.87951 After Sales Service 6 64 7.228915 77.10843 Incorrect Invoice 10 74 12.04819 89.15662 No Internet Site 9 83 10.84337 100 Total 83 100 Pie Chart This pie chart is a good visual tool for assessing the relative frequencies of each problem. At a glance we observe that the majority about 30% customers highlighted that the problem “Faculty Products”, according to 24% problem persist because of late delivery, 12% customers point of views are observing that its due to “Incorrect Invoice”, 11% respond that problem raised due to “No internet site”, 7% respond tat it persists “After Sales Service”, rest of 6% responds its by “demanding packaging” and same 6% due to “per sales service”. Lastly the least responses about only 4% customers saying that problem persist due to “Late Invoice”. (b) - Bar Chart Bar charts allow us to show the distribution of cases into particular categories. To demonstrate we will examine the customer perceptions and views towards problem to improve current level of customer service. Again one can easily examine through this graph that “Faculty Products” and “Late Delivery” are two major areas to be improved. (c ) - Merits of Using Pie chart and Bar chart As the facilitators of an upcoming presentation, the presentation will describe three quality management tools. Quality management team (QIT) will allow people to see different ways of performing work in a quality way. Each quality improvement charts will give the reader some in-sight on what the quality management tool is and how it is used to improve work processes. By implementing quality management charts a company can improve the process of how work is done to provide customers the best of the best. Two of the charts have been chosen and through this study, a better understanding of the quality improvement charts are presenting. This study presented the definitions of two quality management tools that are used along with others that help improve work processes. Each is used to create a better quality product and/or service that serve customers satisfaction. The two quality management tools selected for this study were pie-chart and histograms. By implementing quality management techniques a company can improve work process that will provide a better product quality and service to their customers. Using these tools Quality improvement Team will allow companies to provide quality products and services that people will benefit from as well as the companies that present the products and services. 2. Pareto Chart (a) - Pareto Analysis The Pareto analysis consists of identifying quality costs by category, or by product, or by type of defect or nonconformity. (b) - Pareto Chart The Pareto chart is simply a frequency distribution (or histogram) of attribute data arranged by category. Pareto Charts allows us to make selections that determine the type of chart we obtain. To illustrate a Pareto chart, consider the above arranged data, see below: Problem Respondents Faculty Products 25 Late Delivery 20 Incorrect Invoice 10 No Internet Site 9 After Sales Service 6 Per Sales Service 5 Damaged Packaging 5 Late Invoice 3 Total 83 Through this chart we Quality Improvement Team (QIT) can quickly and visually identify the most frequently occurring types of problems. In this case, given chart indicates that faculty products and late delivery are the most commonly encountered problems. Thus the causes of these problem types should probably be identified and resolved first. (c ) - Comments on Pareto Chart Pareto charts are widely used in nonmanufacturing applications of quality improvement methods. It is used by Quality Improvement Team in a procurement organization is shown in above chart. Pareto chart is a picture of the unit, showing all relevant views. Then the various types of problem are drawn on the picture and the diagram is analyzed to determine whether the location of the problems on the unit conveys any useful information about the potential causes of the problem to the Quality Improvement Team. Noted that the Pareto chart does not automatically identify the most important problems but rather only those that occur most frequently. For instant in graph above, late invoice occur very infrequently (3 out of 83, of 3.6%). However, late invoice could result in incorrect invoice (that is 10 out of 83, of 12%). 3. Cause and Effect Analysis In general Pareto chart is one of the most useful of the “magnificent seven.” Its applications to quality improvement are limited only by the ingenuity of the analyst. Once a problem, error, or defect has been identified and isolated for further study, we must begin to analyze potential causes of this undesirable effect. In situation where causes are not obvious (sometimes they are), the causes and effect diagram is a formed tool frequently useful in unlayering potential causes. The cause and effect Pareto diagram constructed by a quality improvement team (QIT) assigned to identify potential problem areas in the product quality process mentioned above. Causes and effect analysis is an extremely powerful tool. A highly detailed cause and effect diagram can serve as an effective trouble-shooting aid. Furthermore, the construction of the cause and effect chart as a team experience tends to get people involved in attacking a problem rather than in affixing blame. Pareto charts are widely used in nonmanufacturing applications of quality improvement methods. It is used by Quality Improvement Team in a procurement organization is shown in above chart. Pareto charts are broadly used in nonmanufacturing applications of quality improvement methods. It is used by Quality Improvement Team in a procurement organization is shown in chart. Task 2 1. (a) – Mean Dimension (mm) ‘xi’ Frequency ‘fi’ fi*xi 50.2 1 50.2 50.4 3 151.2 50.5 8 404 50.6 15 759 50.7 13 659.1 50.8 6 304.8 50.9 1 50.9 Total 47 2379.2 = = = 50.621 (b) – Mode: - Mode is defined as a value which occurs most frequently in a data set that is it indicates the most common result. A set of data may have more than one mode or no mode at all when each observation occurs the same number of times. In case of grouped data, the mode would lie in the class that carries the highest frequency. So here the mode will be 50.6. (c) – Standard Deviation: - When the data are grouped into frequency distribution, the formula of standard deviation is: Formula: s = Computation: Dimension (mm) ‘xi’ Frequency ‘fi’ (xi - ) (xi - )2 50.2 1 -0.421 0.177241 0.177241 50.4 3 -0.221 0.048841 0.146523 50.5 8 -0.121 0.014641 0.117128 50.6 15 -0.021 0.000441 0.006615 50.7 13 0.079 0.006241 0.081133 50.8 6 0.179 0.032041 0.192246 50.9 1 0.279 0.077841 0.077841 Total 47 0.798727 s = = 0.130, so the standard deviation is 0.130 for this grouped data case. (d) – Histogram Plot Interpretation Histogram - A single numeric variable is summarized. The histogram shows the number of cases which fall within each interval. This distribution is not highly skewed as evidenced by the histogram. According to histogram, the shape of this distribution is about normal distribution. 2. (a) - Process Capability Index, Cp Process Compatibility Index is a algebraic review that evaluates the performance of a product or behaviour/performance indices / ratios, we generally use it as a genetic terminology. It narrates the voice of the customer to the voice of the process. Its large value of the index indicates that the current process is capable of producing parts that, in all likelihood, will meet or exceed the customer’s requirement. It is convenient because it decreases complex information about the process to a single number. Process Capability Ratios = Cp = Where USL and LSL are upper and lower specific limits respectively. Usually, the process standard deviation  is unknown and must be replaced by an estimated. (b) - To estimate  we typically use the sample standard deviation s, for this case. Therefore Cp is calculated as, Cp = = 1.02279 As above question, we assumed that dimensions (mm) are approximately normal distributed (a reasonable assumption, based on the above histogram). Index = = 97.77 (a large value) Cumulative Relative Frequency Table Dimension (mm) ‘xi’ Frequency ‘fi’ Relative Frequency Cumulative Relative Frequency 50.2 1 0.021 0.021 50.4 3 0.064 0.085 50.5 8 0.170 0.255 50.6 15 0.319 0.574 50.7 13 0.277 0.851 50.8 6 0.128 0.979 50.9 1 0.021 1 Total 47 (c ) – X-bar and range control chart Sample Mean Range 1 50.61 0.3 2 50.43 0.31 3 50.58 0.28 4 50.62 0.37 5 50.64 0.36 6 50.3 0.38 7 50.49 0.4 8 50.61 0.41 9 50.62 0.41 10 50.63 0.42 Mean =50.553 = 0.364 Control limits for the R chart UCL = D4 = 0.76986, (where D4 and D3 are tabulated values for samples of n = 5) LCL = D3 = 0 Control limits for the chart UCL = +A2 = 50.76303, (where A2 is tabulated for samples of n = 5) LCL = - A2 = 50.34297 Comments When setting up and R control charts, it is best to begin with the r chart. Because the control limits on the chart depend on the process variability, unless process variability is in control, these limits are not having much meaning. The r chart shown above, when the 10m sample ranges are plotted there is no indication of an out-of control condition. Since the r chart indicates that process variability is in control, now we talk about the chart, there is no indication of an out-of control condition is observed. Therefore, since both the and R charts exhibit control, we would conclude that the process is in control at the stated levels and adopt the trial control limits for use in on-line statistical process control. Task 3 Question 1 - Brainstorming In every decision there is a process which is used to determine the best way to go about making that decision. There are many different tools and techniques that can be used to come to a final decision. For purposes of this paper I will use the brainstorming technique. Brainstorming can be done alone with a pad and paper or within a group with a designated facilitator and a white board or chalk board. Individual brainstorming is an art although there is definitely a special dynamic to group brainstorming sessions. In conclusion we can say that decision making is a difficult process that requires as much critical thinking skills and individuality as humanly possible to achieve. Group decision making is the ideal way to achieve a common goal from a group of unique ideas. Individual brainstorming or jotting down ideas before beginning the decision making process is a great way to see what ideas you can come up with on our own while group brainstorming can achieve much more creative outcomes because of the differing ideas and creative thinking. If a group facilitator is capable of keeping the flow of ideas moving in a forward direction the decision can usually be made quickly and efficiently to the satisfaction of everyone involved. There are a few requirements needed in order to use brainstorming as an effective decision making tool. First, there must be a problem to solve. If there is no real problem or if the issue is already clear-cut, there may not be a need to brainstorm. Therefore, the brainstorming activities would be useless. There is also a necessity to be able to work as a team. When brainstorming activities begin for an organization, it is important that the group generates the ability and the want to work as a team, to make a decision. The brainstorming process can be very hectic and almost anarchic. Round robin is a form of brainstorming where a group sets a predetermined order and goes around the room one at a time looking for ideas. This gives each member of the team an opportunity to be heard, and will eliminate the problem of domination from any member. It can inhibit the team by possibly eliminating the opportunity for spontaneity and creativity. Using this form of brainstorming can result in fewer ideas, and can make individuals feel disconnected from the team. Brainstorming is a great way to create, discuss and hopefully exhaust all options to solving problems. Companies that invest the time to hold properly administered brainstorming sessions should see a solid return on their investment. The ingenuity that comes out of these meeting will not only show in the quality of the product or services being sold, but shine a positive light throughout the entire organization itself. Question 2: - Data 14 16 11 24 28 12 21 16 (a) - Mean = =17.75 (b) - Range = maximum value – minimum value = 28 – 11 = 17 (c ) - Variance = s2 = = 36.21429 (d) - Standard deviation = s = = 6.017831 Question 3: Given that Mean = 130 and Standard Deviation = 15 (a) - P (X > 160) = 1- P (X≤160) = 1 – P = 1- P (Z≤2) = 1 – 0.9772 = 0.0228 (b) - P (X < 105) = P (X< 105) = P = P (Z < -1.66) = 0.0485 (c ) - P (130 < X < 140) = P (130 < X< 140) = P = P (0 < Z < 0.666) = P (Z < 0.666) – P (Z Read More