Reliability engineering involves selecting designs, procedures, plans and methods based on time and economic restrictions. The need for engineering economy comes from the fact that engineers and managers do not work in an economic vacuum. Their decisions are influenced by the allocation of scarce resources used in production and distribution.

Managerial decision making is usually discharged within a framework of:

- Defining the alternatives clearly
- Identifying the aspects common to all alternatives
- Establishing appropriate viewpoints and decision criteria
- Considering the consequences of actions taken

Given the frequent conflicts among requirements and the potential impact on costs, project schedules and plant performance, the reliability alternatives and their consequences should be studied in detail and be well understood.

#### Economics of reliability improvement

Reliability improvement is an investment. Like anything in which we invest money and resources, we expect to receive benefits that are greater than our investment. The following financial overview provides information on various analytical tools and the data financial experts need to provide assistance.

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Making reliability investment tradeoffs requires considering the time value of money. Whether the organization is for-profit or not-for-profit, resources cost money. The three dimensions of payback analysis are:

- Cash flow required to improve reliablity
- Period over which the cash flow occurs
- Cost of money expected during the period

Reliability analysis usually requires either a simple “yes/no” decision, or selecting one of several alternatives. The time value of invested money and the future returns generated by a reliability improvement must be quantified clearly. The time value of money simply means that a dollar in your pocket today is worth more than one a year from now. Another consideration is that forecasting potential outcomes is more accurate in the short term than it is in the long term.

Decision-making methods include:

- Payback
- Percent rate of return (PRR)
- Average return on investment (ROI)
- Cost/benefit ratio (CBR)

The corporate controller often determines the financial rules used in justifying capital projects. Companies have rules like “Return on investment must be at least 20 percent before we will consider a project” or “Any proposal must pay back within 18 months.” Reliability evaluations should normally use the same set of rules for consistency and to help obtain management support. It is also important to realize that the political or financial motives behind these rules may not be entirely logical for your decision level.

#### Payback

Payback simply determines the number of years required to recover the original investment. Thus, if you pay $50,000 for a test instrument that saves downtime and increases production by $25,000 a year, the payback is:

$50,000/$25,000 = 2 years

This is easy to understand. Unfortunately, it disregards the fact that the $25,000 gained the second year needs to be adjusted for the time value of money. It also assumes a uniform payback stream. Finally, it ignores any returns after the two years. Why two years instead of some other number? There may be no good reason except “The controller says so.” If simple payback is negative, then you probably do not want to make the investment.

#### Percent rate of return

Rate of return, as a percentage, is the reciprocal of the payback period. In our case above:

$25,000/$50,000 =.50 = 50 percent rate of return

This is often called the naive rate of return because it ignores the cost of money and a finite payback period.

#### Return on investment

Return on investment is a step better since it considers depreciation, salvage value and all benefit periods. If we acquire a test instrument for $80,000 that has a five-year life and a $5,000 salvage value, then the cost calculation, excluding depreciation, is:

($80,000-$5,000)/5 years = $15,000 per year

If the economic benefit is $135,000 for the same period, the average increment is:

($135,000-$75,000) = $60,000/5 years =$12,000 per year

The average annual ROI is:

$75,000/$135,000 = .55 = 55 percent

Ask your accountant how they handle depreciation, since it can make a major difference in the calculation.

#### Cost-benefit ratio

CBR takes the present value (initial project cost plus net present value) divided by the initial project cost. For example, if the project will cost $250,000 and the net present value (NPV) is $350,000, then:

($250,000 + $350,000)/$250,000 = 2.4

It may appear that the CBR is merely a mirror image of the NPV. However, CBR considers the size of the financial investment required. For example, two competing projects could have the same NPV. But, if one required $1 million and the other $250,000, the absolute amount might influence the choice. Compare the example above with this $1 million project:

($1,000,000 + 350,000)/$1,000,000 = 1.35

There should be little question that you would take the $250,000 project (a 2.4 return) instead of the $1 million one (1.35 return). This calculation requires that we make a management judgment on the inflation/interest rate for the payback period and what the payback pattern will be. For example, if we spend $5,000 today to modify a machine to reduce breakdowns, the payback will come from future improved production revenues and reduced maintenance costs.

#### Measuring reliability

Reliability is defined in many ways, but the most widely accepted version states that it is the ability or capacity of a plant’s production system to perform the specified function in the designated environment for a minimum length of time or number of cycles.

The “life” of an individual system or one of its components cannot be determined except by operating it for the desired time or until it fails. Obviously, you cannot wear out the system to prove that it will meet specifications; therefore, just as in quality assurance, you must rely on data generated by testing. As a result, reliability is measured as the probability that the system and its components will function normally for the required time interval.

Thus, reliability can be calculated by using one or more of the following:

- Mean-time-to-failure (MTTF)
- Mean-time-between-failures (MTBF)
- Mean-time-between-maintenance action (MTBMA)
- Mean-time-before-repair (MTBR)

As a reliability measure, the MTTF of critical production systems must be greater than the planned production interval defined in the annual business plan. If it is less, the probability of production interruptions and a resultant loss of capacity must be considered. Typically, MTTF is determined by using failure modes and effects analysis (FMEA), which calculates the failure probability of each component that makes up a production system. In many cases, it’s provided by the system’s vendor, but you can calculate it at any point during the equipment’s life cycle.

MTBF is the historical average of actual failure intervals. Whereas MTTF is the probability of failure intervals for a specific class of machine or system, MTBF is based on the actual history in a particular plant or application.

MTBMA defines the preventive maintenance level required to meet the MTBF or MTTF criteria. In some cases, statistical data is available for specific machinery or production systems, but more often, it’s a measurement of actual, in-plant maintenance activities.

MTBR criteria are similar to MTBMA, but is limited to corrective maintenance, such as rebuilds, replacement of major-wear parts, and other non-preventive activities. In most cases, this is a measurement of the actual, in-plant history, but many vendors provide statistical MTBR data for their equipment.

Practical measurement of equipment reliability is dependent on accurate record keeping. While these criteria can be calculated as theoretical values, the only true measurement is actual history.