# Explanation of Series System Reliability Property 1 for Plant and Equipment Reliability Improvement

### You must lift the reliability of the worst performing items in a series system if you are to improve the system reliability.

#### Slide 32 – The Implications of Series System Reliability Property 1 When You Want Maximum Plant and Equipment Reliability

Series System Reliability Property 1 is best explained with a simple example. The components shown in a series in the above slide have the reliability indicated in the boxes. The series system reliability formula is used to determine what the total system reliability will be. Its reliability is shown in the system box. You can see from the numbers in the boxes that the system reliability can never be higher than the least reliable component in the system.

#### The Business Effects of Series System Reliability Property 1

In the top two-item series system arrangement, the component with the lowest reliability is improved from 0.8 to 0.9. This is a 12% increase in reliability for the component. The consequential system reliability improvement is also 12%. When one of the components in the lower four-item series system arrangement is improved from 0.8 to 0.9 its reliability rises by 12.5%. The consequentially system reliability also improves 12.5%.

Series System Reliability Property 1 tells us that improving the least reliable component in a series improves the series reliability by the increased reliability of the component. The least reliable item in a series will limit the series reliability performance because system reliability can be no higher than the lowest reliable component.

When a “Bad Actor” item of plant has such low reliability it prevents the plant from achieving its best performance Series System Reliability Property 1 tells you to improve the reliability of the Bad Actor. Until its reliability is raised the operating plant’s reliability is always going to be lower than that of the Bad Actor equipment.

#### The Economics of Series System Reliability Improvement

The reliability of a series configuration can also be raised by other than fixing the Bad Actor item. You will surely lift system reliability by improving the 0.9 reliable item in the two-component system to 0.95 reliability. The system reliability will stay below 0.8, but it will rise from 0.72 to 0.76 (0.95 x 0.8 = 0.76). You don’t only need to focus on Bad Actor items to improve system performance.

We now arrive at an important economic issue when choosing which reliability improvements to make. When you spend money on improving equipment reliability the investment must have a strong business case justifying the expenditure versus its return-on-investment—the project’s ROI must have a great payback.

Say in the upper two-component system shown on the slide it costs \$100,000 to take the Bad Actor equipment from reliability 0.8 up to 0.9 and lift system reliability to 0.81. If instead, you could invest \$10,000 in the reliability improvement of the neighbouring equipment and lift its reliability of 0.9 to 0.95, what should you do? We can put some numbers into the system series reliability equation to determine the scale of the payback from each investment.

At present the system reliability is, 0.9 x 0.8 = 0.72. We know the \$100,000 investment in the Bad Actor gets a system reliability up to 0.81. For the \$10,000 investment in the 0.9 reliable item the new system reliability becomes 0.95 x 0.8 = 0.76, a 5.5% system reliability improvement. The \$10,000 investment increases system reliability 5.5% while the \$100,000 investment delivers 12.5% system reliability improvement. The lower cost investment delivers a better economic return.

 This slide is a companion to the new Industrial and Manufacturing Wellness book. The book has extensive information, all the necessary templates, and useful examples of how to design and build your own Plant Wellness Way enterprise asset life cycle management system-of-reliability. Get the book from its publisher, Industrial Press, and Amazon Books. Use the head office email address on the Contact Us page if you have questions about this slide.