3.3 Reporting data

The manner in which reliability data is analyzed and reported will largely have to be tailored to the specific circumstance or organization. However, it is possible to break down the general methods of analysis/reporting into two categories: non-parametric analysis and parametric analysis. Overall, it will be necessary to tailor the analysis and reporting methods by the type of data as well as to the intended audience. Managers or teachers will generally be more interested in actual data and non-parametric analysis results, while parents and students will be more concerned with parametric analysis. Of course this is a rather broad generalization and if the proper training has instilled the organization with an appreciation of the importance of reliability teaching, there should be an interest in all types of reliability reports at all levels of the organization. Nevertheless, managers are usually more interested in the "big picture" information that non-parametric analyses generally tend to provide, while not being particularly interested in the level of technical detail that parametric analyses provide. On the other hand, parents and technicians are usually more concerned with the close-up details and technical information that parametric analyses provide. Both of these types of data analysis have a great deal of importance to any given organization, and it is merely necessary to apply the different types in the proper places.

Non-Parametric Analysis

Data conducive to non-parametric analysis includes information that has not or cannot be rigorously processed or analyzed. Usually, it is simply straight reporting of information, or if it has been manipulated, it is usually by simple mathematics, with no complex statistical analysis. In this respect, many types of field data lend themselves to the non-parametric type of analysis and reporting. In general, this type of information will be...

3.3 Reporting data

...of most interest to managers as it usually requires no special technical know-how to interpret. Another reason it is of particular interest to managers is that most financial data falls into this category. Despite its relative simplicity, the importance of non-parametric data analysis should not be underestimated. Most of the important decisions that are made concerning the works are based on non-parametric analysis of financial data.

Non-Parametric Reliability Analysis:

Although many of the non-parametric analyses that can be performed based on field data are very useful for providing a picture of how the products are behaving in the field, not all of this information can be considered "hard-core" reliability data. As was mentioned earlier, many such data types and analyses are just straight reporting of the facts. However, it is possible to develop standard reliability metrics, such as product reliability and failure rates, from the non-parametric analysis of field data. A common example of this is the "diagonal table" type of analysis that combines shipping and field failure data in order to produce empirical measures of defect rates.

Parametric Analysis:

Data that lends itself to parametric statistical analysis can produce very detailed information about the behavior of the product based on the process utilized to gather the data. This is the "hard-core" reliability data with all the associated charts, graphs and projections that can be used to predict the behavior of the products in the field.

3.3 Reporting data

The origin of this type of data is usually in-house, from reliability testing done in laboratories set up for that specific purpose. For that reason, a great deal more detail will be associated with these data sets than with those that are collected from the field. Unfortunately, when dealing with field data, it is often a matter of taking what you can get, without being able to have much impact on the quality of the data. Of course, setting up a good program for the collection of field data will raise the quality of the field data collected, but generally it will not be nearly as concise or detailed as the data collected in-house.

The exception to this generalization is field data that contains detailed time-of-use information. For example, automotive repairs that have odometer information, aircraft repairs that have associated flight hours or printer repairs that have a related print count can lend themselves to parametric analysis. Caution should be exercised when this type of analysis is performed, however, to make sure that the data are consistent and complete enough to perform a meaningful parametric analysis.

Although it is possible to automate parametric analysis and reporting, care should be taken in automatic processing. Caution is required because of the level of detail inherent in this type of data and the potential "disconnect" between field data and in-house testing data (described in "Field Data"). Presentations of these two types of data should be carefully segregated in order to avoid unnecessary confusion among the end users of the data reports. It is not unusual for end users who are not familiar with statistical analysis to become confused and indignant when presented with seemingly contradictory data on a particular product. The tendency in cases such as these is to accuse one or both sources of data (field or in-house) of being inaccurate. This is, of course, not necessarily true. There will usually tend to be a disparity between field...

3.3 Reporting data

...data and in-house reliability data.

Another reason for the segregation of the field data and the in-house data is the need for human oversight when performing the calculations. Field data sets tend to undergo relatively simple mathematical processing that can be safely automated without having to worry about whether the analysis type is appropriate for the data being analyzed. However, this can be a concern for in-house data sets that are undergoing more complicated statistical analysis. This is not to say that parametric analysis should not be in any way automated. However, a degree of human oversight should be included in the process to insure that the data sets are being analyzed in an appropriate manner. Furthermore, the data should be cross-referenced against the Test Log and Service Log to make sure that irrelevant or "outlier" information is not being included in the data.

Measures of Central Tendency

Researchers are often interested in defining a value that best describes some attribute of the population. Often this attribute is a measure of central tendency or a proportion.

Central Tendency

Measures of central tendency are measures of the location of the middle or the center of a distribution. The definition of "middle" or "center" is purposely left somewhat vague so that the term "central tendency" can refer to a wide variety of measures. The mean is the most commonly used measure of central tendency.

3.3 Reporting data

The following measures of central tendency are discussed in this text:

Mean

Median

Mode

Several different measures of central tendency are defined below.

Arithmetic Mean

The arithmetic mean is what is commonly called the average: When the word "mean" is used without a modifier, it can be assumed that it refers to the arithmetic mean. The mean is the sum of all the scores divided by the number of scores. The formula in summation notation is:

where μ is the population mean ,X is the scores and N is the number of scores.

If the scores are from a sample, then the symbol M refers to the mean and N refers to the sample size. The formula for M is the same as the formula for μ.

3.3 Reporting data

The mean is a good measure of central tendency for roughly symmetric distributions but can be misleading in skewed distributions since it can be greatly influenced by scores in the tail. Therefore, other statistics such as the median may be more informative for distributions such as reaction time or family income that are frequently very skewed.

a.	To find the median, we arrange the observations in order from smallest to largest value. If there are an odd

number of observations, the median is the middle value. If there is an even number of observations, the

median is the average of the two middle values. Thus, in the sample of five women weights,

(150,140,100,100,130) the median value would be 130 pounds; since 130 pounds is the middle weight.

When there is an even number of numbers, the median is the mean of the two middle numbers. Thus, the

median of the numbers 2, 4, 7, 12 is (4+7)/2 = 5.5.

The median is the middle of a distribution: half the scores are above the median and half are below the

median. The median is less sensitive to extreme scores than the mean and this makes it a better measure

than the mean for highly skewed distributions. The median income is usually more informative than the

mean income, for example :The sum of the absolute deviations of each number from the median is lower

than is the sum of absolute deviations from any other number.

3.3 Reporting data

b.	The mode is the most frequently appearing value in the population or sample. Suppose we draw a sample

of five women and measure their weights. They weigh 100 pounds, 100 pounds, 130 pounds, 140 pounds,

and 150 pounds. Since more women weigh 100 pounds than any other weight, the mode would equal

100 pounds.

The mean, median, and mode are equal in symmetric distributions. The mean is typically higher than the

median in positively skewed distributions and lower than the median in negatively skewed distributions,

although this may not be the case in bimodal distributions.

Proportions and Percentages

When the focus is on the degree to which a population possesses a particular attribute, the measure of interest is a percentage or a proportion.

A proportion refers to the fraction of the total that possesses a certain attribute. For example, we might

ask what proportion of women in our sample weigh less than 135 pounds. Since 3 women weigh less

than 135 pounds, the proportion would be 3/5 or 0.60.