Descriptive Statistics

Descriptive statistics refers to the methods employed to summarize quantitative data in such a w'ay as to define the characteristics of data distribution. The characteristics of data mostly taken into consideration are the central value of data (e.g., averages);

FIGURE 1.1 QET; statistical and non-statistical techniques.

and the dispersion of data (e.g., domains or standard deviations). Another feature of interest is the shape of the distribution of data (e.g., symmetries). The information obtained from descriptive statistics can often be easily and effectively influenced by resorting to various types of graphical methods including histogram charts, Pareto graphs, dispersion charts, causation charts or trend graphs. These graphical methods are useful since they are capable of discovering unusual aspects in the data that are vague in quantitative analyses. These methods are widely used in data analysis when the researcher decides to discover or verify the relationship among variables and intend to estimate the parameters used to describe these relationships.

FIGURE 1.2 QET.

1.2.1.1.1 Applications

In general, descriptive statistics are used to summarize and describe data attributes. This method is normally the first step in analyzing quantitative data. Therefore, as a first step and introduction to each analysis, these statistical methods are utilized. Examples of such applications are as follows:

• • Summarizing the key indices of product features (e.g., average and standard deviations).
• • Describing the function of some process parameters (e.g., temperature)

• • Describing the delivery and response times (e.g., services)
• • Summarizing the customer evaluation date (e.g., satisfaction or dissatisfaction)
• • Displaying the measuring data (e.g., equipment calibration data)
• • Displaying the distribution of features related to a process through a histogram
• • Viewing the performance results of a given product over some time through a trend graph
• • Evaluating the relationship between independent variables (e.g., temperature) and the output of that process as a dependent variable
• 1.2.1.1.2 Advantages

Using descriptive statistics is a convenient and simple way to summarize and describe data. It is also a good choice of procedure for providing information, especially by supplying graphical means for data and transferring information. Furthermore, this method is helpful in analyzing and interpreting data, which proves useful in making decisions.

1.2.1.1.3 Disadvantages

Descriptive statistics provides characteristics of sample data (for instance, means and standard deviations). However, these tools are contingent upon limitations such as sample size, and sampling method. These quantitative tools are considered valid when considered in relation to statistical assumptions.

Design and Analysis of Experiments

The design and analysis of experiments refer to all studies that are planned and carried out based on statistical calculations related to the results at a specified level. This technique involves making changes to the system under investigation and accordingly evaluating the effect of these changes on the system. Verifying some features of a system or examining the effect of one or more factors on these features can be defined as another goal of this technique. The arrangement and the tests that are conducted for this technique are extremely dependent on the purpose and the conditions of testing. There are various supplementary tools for analyzing data from variance analysis perspective such as checking the probability of points with having graphical natures.

1.2.1.2.1 Applications

Descriptive statistics can be used to evaluate the assessments of a product, process, or a system for verifying a specified standard or evaluating the comparisons made of several systems at a certain level. Confirmation of the effect of medical treatments and agricultural products, and evaluation of various types of methods in industrial productions are among the practical applications of this technique. The most practical aspect of this technique is its ability to examine complex systems whose outputs may be affected by multiple potential factors. As such, the purpose of the design of experiments under this condition is to optimize a feature or reduce its variability. In this case, descriptive statistics is used to analyze the factors that have the greatest impacts on the characteristics of the system. The results may be used to facilitate the design and development of a product or process to control or improve an existing system. Examples of this may be to control or improve the average or reduce the variability in certain process characteristics such as process efficiency, product strength, or durability in factory products manufactured, for instance, by electronics, automotive, or chemical industries.

1.2.1.2.2 Advantages

One of the most striking advantages of designing and analyzing experiments is the creation of high-efficiency, economical procedure to examine the effects of several factors in a process, compared to the study of these factors. Also, the ability of this technique to identify the interactions between certain factors can lead to a deeper understanding of the process. Using the correct method of applying this technique, the risk of error in finding a random relationship between two or more variables is considerably reduced.

1.2.1.2.3 Disadvantages

There are some levels of variability inherent in all systems, w hich in some cases can prevent the attainment of accurate conclusions. While there may be misleading effects of some unknown factors, as well as the interactive effects of various factors in a system, choosing the right sample size and including other considerations might reduce the risk of errors in the final conclusions of the technique making it an acceptable outcome, although they cannot be totally eliminated. And in such cases, extending the generalization of the technique should always be limited to the internal workings of the selected scope.