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Statistics for Process Control Engineers
book

Statistics for Process Control Engineers

by Myke King
October 2017
Intermediate to advanced content levelIntermediate to advanced
624 pages
17h 24m
English
Wiley
Content preview from Statistics for Process Control Engineers

14Hazard Function

The hazard function, sometimes described as the conditional failure density function or, more commonly, the failure rate is defined as

The reciprocal of the hazard function is known as the conditional failure density function.

Applying Equation (14.1) to the exponential distribution, described by Equations (12.61) and (12.62), gives

This tells us that the failure rate is constant at λ; it does not vary with time. The process has no memory.

Commonly the EL (exponential‐logarithmic) distribution is used. We will cover this in detail in Section 28.9. From Equations (28.33) and (28.34)

This function is plotted as Figure 14.1, with λ adjusted so that h(x) is 1 when x is zero. As δ → 1, Equation (14.3) becomes Equation (14.2). As δ is reduced below 1, the failure rate reduces over time. This might apply to the number of occasions a control scheme is disabled because of technical issues that are resolved over time. Or it may be because the operators initially did not properly understand its operation and this resolved by ongoing training.

Hazard function derived from EL distribution displaying two descending curves labeled λ = 0.5, δ = 0.28 and λ = 0.16, δ = 0.01.

Figure ...

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Publisher Resources

ISBN: 9781119383505