Reliability Mathematics Chapter 2 Reliability Mathematics © 2012 John Wiley & Sons, Ltd.

Figure 2.1 Samples with defectives (black squares).

Figure 2.2 Dual redundant system.

Figure 2.3 (a) Frequency histogram of a random sample, (b) frequency histogram of another random sample from the same population, (c) data of many samples shown with measurement intervals of 0.5.

Figure 2.4 Continuous probability distribution.

Figure 2.5 Measures of central tendency.

Figure 2.6 Typical cumulative distribution function (cdf).

Figure 2.7 Probability Density Function (pdf) and its application to reliability.

Figure 2.8 The normal (Gaussian) distribution.

Figure 2.9 (a) The pdf f(x) versus x; (b) the cdf F(x) versus x (see Example 2.5).

Figure 2.10 Extreme value distributions.

Figure 2.11a Shapes of common failure distributions, reliability and hazard rate functions (shown in relation to t).

Figure 2.11b (Continued).

Figure 2.12 Curtailed normal distribution.

Figure 2.13 Effect of selection.

Figure 2.14 Skewed distribution.

Figure 2.15 Bi-modal distribution.

Figure 2.16 Four distributions with the same means and SDs (after W. A. Shewhart).

Figure 2.17 Utilizing Excel’s Goal Seek to find Z-value corresponding to the 95% confidence interval.

Figure 2.18 Confidence levels for normal distribution.

Figure 2.19 Arrival and interarrival values.

Figure 2.20 Rate of occurrence for superimposed processes.