Failure or Fatigue Failure of a Valve Shaft

The type of failures you will get will in a high degree be depending of the quality of the valves different parts and quality and how suited they are compared to the process media and conditions.

As the process seems to have a larger number of different smaller valves, one way could be to build on existing experiance and routines, and change complete valves and check types of wear/failures after a preplanned periode and system.
I gather your purpose is to preplan maintenance. This again to have as few unplanned stops as possible and select valve and parts quality, maintenance or new valves to have best cost/lifetime value.
part of this would also be to chart how much wear is acceptable before the process get disturbed.
Apart from this, you will probably have a failure rate, a bit different on the different types of valves, but perhaps mainly (if valves materials are selected to suit process)
Sealings: wear of stem sealings and seat sealings.
Seats: wear of seats.
Wear of stem (depending of valve/stemtype) mostly caused by penetration of seals and deposits on stem.
Same as above for balls.
Corrosion (only by uncorrect or poorer quality of (inner?)part of body (material and/or protection) compared to fluid requirements.
Cavitation (by wrong selection or throtteling of valve comared to flow and delta p)
Remember that dirt, deposits, and particle abrasion and 'non optimum clean' fluid condition often are the strongest contribution to wear.

API standard 609 covers design, materials, face-to-face dimensions, pressure-temperature ratings, and examination, inspection and test requirements for gray iron, ductile iron, bronze, steel, nickel-based alloy, or special alloy butterfly valves. The following two categories of butterfly valves are included:

a) Category A—Manufacturer’s rated cold working pressure (CWP) butterfly valves, usually with a concentric disc and seat configuration. Sizes covered are NPS 2 to NPS 48 for valves having ASME Class 125 or Class 150 flange bolting patterns.

b) Category B—ASME Class and pressure-temperature rated butterfly valves that have an offset seat and either an eccentric or a concentric disc configuration. These valves may have a seat rating less than the body rating. Sizes covered are listed below.  For lug and wafer, Class 150: NPS 3 to NPS 48.  For lug and wafer, Class 300 and Class 600: NPS 3 to NPS 48.  For double-flanged long pattern, Class 150, 300, and 600: NPS 3 to NPS 36.  For double-flanged short pattern, Class 150 and Class 300: NPS 3 to NPS 48.  For double-flanged short pattern, Class 600: NPS 3 to NPS 24.

The ASME B31.1 code lists three valves standards, excluding cast iron and bronze valves. The standards are: 1) ASME B16.34, Valves–Flanged, Threaded, and Weld End; 2) MSS SP67–Butterfly Valves; and 3) MSS SP68–High Pressure Butterfly Valves with Offset Design. As stated in B31.1, para 107.1, “Valves not complying with above [the list] shall be of a design, or equal to the design, that the manufacturer recommends for the service as stipulated in para. 102.2.2. Such valves shall be pressure tested in accordance with MSS SP-61.

The AWWA C 504 establishes minimum requirements for rubber-seated butterfly valves, 3 in. (75 mm) through 72 in. (1,800 mm) in diameter, with various body and end types, for fresh water having a pH range from 6-12 and a temperature range from 33º-125ºF (0.6º-52ºC). This standard covers rubber-seated butterfly valves suitable for a maximum steady-state fluid working pressure of 250 psig (1,723 kPa), a maximum steady-state differential pressure of 250 psi (1,723 kPa), and a maximum fully open fluid velocity of 16 ft/sec (4.9 m/sec) based on nominal valve size.