page_title: Analytic hierarchy process – car example
section_title: Safety
hierarchical_section_title: Analytic hierarchy process – car example / Pairwise comparing the Alternatives with respect to the Criteria / Safety
caption_attribution_description: Part of a series of images to illustrate an article on the Analytic Hierarchy Process
context_page_description: This is a worked-through example showing the use of the analytic hierarchy process in a practical decision situation.
  See Analytic hierarchy process#Practical examples for context for this example.
context_section_description: Comparing the alternatives on the basis of Safety is much less objective than comparing them on Purchase Price. Purchase prices are measured in dollars and can be determined to the penny. People can easily agree on the meaning of a $20,360 purchase price, and can rationally compare it to all the other prices, using methods and calculations that are understood and accepted by all.
  But "safety" eludes our efforts even to define it in an objective way. Not only that, but the objective measurements of safety are limited and not readily comparable from car to car.
  The government conducts objective crash tests, but they are incomplete measures of the "safety" of a given car. Also, the crash tests only compare the members of a single class of cars, such as Midsize Cars or Minivans. Is a midsize car with 100% 5-star safety ratings equally as safe as a minivan with the same ratings? It's not exactly clear. And when evaluating minivans that have 5-star ratings in all categories but one, who can say if the one with four stars for "Frontal Impact, Driver's Side" is safer than the one whose four stars are in "Side Impact, Rear Occupant?" There's really no way to tell.
  In spite of these difficulties, the AHP provides a rational way to evaluate the relative safety of different cars.
  Let's assume that the Jones family has researched the Safety of the six Hondas they are considering. They will have found that all of them are among the safest cars on the road. All six are "Top Safety Picks" of the IIHS safety standards organization. All of them do very well in the crash testing programs of the National Highway Traffic Safety Administration. But there are differences between them, and the family wants to factor the differences into their decision. "Your car can never be too safe."
  The worksheet below includes the data that the family has decided to evaluate. They believe that a heavier car is a safer car, so they've documented the curb weights of their alternatives. They have investigated the results of government crash tests, and they've summarized the results on the worksheet:
  The family will consider everything in the worksheet as they compare their alternatives. They are not safety experts, but they can apply their life experience to making decisions about the safety ratings. They all feel safer when driving a car that is significantly heavier than another one. One family member has seen two gruesome rollover accidents, and is terrified of a vehicle rolling over with her inside. She insists that the family car has the highest possible Rollover Rating.
  Here are the weights that the Jones family enters for the alternatives regarding Safety (throughout this example, orange shading is used for judgments where A is favored; yellow shading is used for B):
  When the judgments shown above are entered, the AHP software returns the following priorities for the six alternatives with respect to Safety:
  The local priorities show how much the safety of each model contributes to the Criterion of Safety. The global priorities show how much the Safety of each model contributes to the overall goal of choosing the best car for the Jones family.
caption: Safety judgments entered by the Jones family, with the intensity and rationale for each. From the Fundamental Scale, 1 expresses that A and B are equally preferred, 3 that the better of the pair is moderately preferred to the worse, 5 that the better is strongly preferred, 7 that the better is very strongly preferred, and 9 that the better is extremely preferred to the worse. Intensities 2, 4, 6, and 8 express intermediate values.
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