||Jerry C. Whitaker
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The approach to probability and statistics used in this chapter is the pragmatic one that probability and statistics are methods of operating in the presence of incomplete knowledge. The most common example is tossing a coin. It will land heads or tails, but the relative frequency is unknown. The two events are often assumed equally likely, but a skilled coin tosser may be able to get heads almost all of the time. The statistical problem in this case is to determine the relative frequency. Given the relative frequency, probability techniques answer such questions as how long can we expect to wait until three heads appear in a row. Another example is light bulbs. The outcome is known: any bulb will eventually fail. If we had complete knowledge of the local universe, it is conceivable that we might compute the lifetime of any bulb. In reality, the manufacturing variations and future operating conditions for a lightbulb are unknown to us. It may be possible, however, to describe the failure history for the general population. In the absence of any data, we can propose a failure process that is due to the accumulated effect of small events (corrosion, metal evaporation, and cracks) where each of these small events is a random process. It is shown in the statistics section that a failure process that is the sum of many events is closely approximated by a distribution known as the normal distribution. A manufacturer can try to improve a product by using better materials and requiring closer tolerances in the assembly. If the light bulbs last longer and there are fewer differences between the bulbs, then the failure curve should move to the right and have less dispersion...