Análisis De Datos

CHAPTER 5

Interpreting Data and Demonstrating Reliability
5.1 The Four Cases
interpreting k failures and T which includes two cases. If k is large (say, more than five) then the sampling inaccuracy in such a wide-tolerance parameter may be ignored. Chapter 4 has emphasized the wide ranges that apply and thus, for large values of k = k T and =Tk

can be used. When k is small (even zero), theneed arises to make some statistical interpretation of the data and that is the purpose of this chapter. The table also shows the second case where constant failure rate cannot be assumed. Again there may be few or many failures to interpret. Chapter 6 deals with this problem where the concept of a failure rate parameter is not relevant to describe the failure distribution.
Constant Failure RateMany failures Few failures Use = k/T Variable Failure Rate Chapter 6 (use probability plotting) (Inadequate data so assume constant failure)

Chapter 5 (statistical interpretation)

5.2 Inference and Confidence Levels
ˆ) was introduced. In Section 2.2 the concept of a point estimate of failure rate ( ˆ 2 showed N items having k failures in T cumulative hours. The observed failure rate ˆ) ofthat sample measurement was k/T. If the test were to be repeated, and another value ( of k/T would yield a number of values of estimates of failure rates. Since these estimates are the result of sampling they are called point estimates and have the symbols ˆ and ˆ . It is the true everything to fail and then to evaluate k/T or T/k Ns(t) ____ dt N

0
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Chapter 5

a test will, of course, yield accurate data but, alas, no items left to use. In practice, we are

is required when only sample data are available. In many cases, where there is high reliability and hence few failures, the time required to accumulate several failures would be unrealistic. The process of making a statement about a population of items based on theevidence of a sample is known as statistical inference. It involves, therefore, the additional concept of confidence level. 1, which shows a distribution of heights of a group of people in histogram form. Superimposed onto the histogram is a curve of the normal distribution. The practice in statistical inference is to select a mathematical distribution that closely fits the data. Statements basedon the distribution are then assumed to apply to the data. In the figure there is a good fit between the normal curve, which has a mean of 5 10 and a standard deviation (measure of spread) of 1 , and the heights of the group in question. Consider a person drawn, at random, from the group. It is permissible to state, from a knowledge of the normal distribution, that the person will be 5 10 tall ormore providing that it is stated that the prediction is made with 50% confidence. This really means that we anticipate being correct 50% of the time if we continue to take

5 11 or more at 15.9% confidence 6 0 or more at 2.3% confidence 6 1 or more at 0.1% confidence 9 and 5 11 at 68.2% confidence. The inferred range of measurement and the confidence level can, hence, be traded off against eachother. Thus, the lower the choice of height then the greater is the confidence of not being proved wrong by an unlucky random sample.

Figure 5.1: Distribution of heights

Interpreting Data and Demonstrating Reliability

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analog measurement (like height) but the occurrence of a discrete event with an underlying frequency. 2 illustrates how a stream of events (failures) may lead to threedifferent results according to the random positioning of the sample. Indeed sample (3) ‘sees’ no failures. This emphasizes the fact that a zero-failures sample does not necessarily imply a zero failure rate. There will be a different estimate of failure rate for each choice of probability (i.e. confidence) that the sample size in question would, at random, ‘see’ no failures. This leads to a method...