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SEMI E10-0304 E © SEMI 1986, 2004 9 Table 1 RAM Measurement Metric Su mmary EQUIPMENT RELIABILITY Metric How It Is Measured Ref # MTBF p : Mean (productive) time between f ailures productive time/ # of failures that occu…

SEMI E10-0304

6.4 EQUIPMENT MAINTAINABILITY — The probability that the equipment will be retained in, or restored to, a

condition where it can perform its intended function within a specified period of time.

6.4.1 MTTR — Mean time to repair; the average time to correct a failure and return the equipment to a condition

where it can perform its intended function; the sum of all repair time (elapsed time not necessarily total man hours)

incurred during a specified time period (including equipment and process test time, but not including maintenance

delay downtime), divided by the number of failures during that period.

failuresof

timerepairtotal

MTTR

6.4.2 E-MTTR — Mean time to repair equipment-related failures; the average time to correct an equipment-related

failure and return the equipment to a condition where it can perform its intended function; the sum of all equipment-

related failure repair time (elapsed time, not necessarily total man hours) incurred during a specified time period

(including equipment and process test time, but not including maintenance delay downtime), divided by the number

of equipment-related failures during that period.

total repair time for equipment-related failures

# of equipment-related failures

–MTTR =

6.4.3 MTOL — Mean time off-line; the average time to maintain the equipment in or return the equipment to a

condition where it can perform its intended function when downtime is incurred; the sum of all downtime

(scheduled and unscheduled) during a specified time period, divided by the number of downtime events during that

period.

TOL

tota

equ

pmen

ownt

events

6.4.4 Equipment Dependent Scheduled Downtime — The percent of time the equipment is not available to perform its

intended function due to scheduled downtime events such as preventive maintenance. This time period does not

include any maintenance delay downtime caused either by supplier or user. This calculation is intended to reflect

the need for preventive maintenance based solely on equipment design.

equipment dependent scheduled downtime (%) =

equipment scheduled downtime × 100

(oper-time – (all maint-delay DT + out-of-spec input DT + fac-rel DT))

6.4.5 Supplier Dependent Scheduled Downtime — The percent of time the equipment is not available to perform its

intended function due to scheduled downtime events, such as preventive maintenance. This time period does not

include any maintenance delay downtime caused by the user. This calculation is intended to reflect the need for

preventive maintenance based solely on equipment design and supplier response to service.

supplier dependent scheduled downtime (%) =

equipment scheduled downtime × 100

(oper-time – (user maint-delay DT + out-of-spec input DT + fac-rel DT))

6.5 EQUIPMENT UTILIZATION — The percent of time the equipment is performing its intended function during a

specified time period.

6.5.1 Operational Utilization — The percent of productive time during operations time. This calculation is intended

to be used for equipment utilization comparisons between operations with different work shift configurations, since

it does not include non-scheduled time.

operational utilization

(%)

roductive time

operations time

6.5.2 Total Utilization — The percent of productive time during total time. This calculation is intended to reflect

bottom-line equipment utilization.

total utilization

(%)

roductive time

total time

SEMI E10-0304

Table 1 RAM Measurement Metric Summary

EQUIPMENT RELIABILITY

Metric How It Is Measured Ref #

MTBF

: Mean (productive) time between failures

productive time/

# of failures that occur during productive time

6.2.1

E-MTBF

: Mean (productive) time between

equipment-related failures

productive time/

# of equipment-related failures

that occur during productive time

6.2.2

MCBF: Mean cycles between failures total equipment cycles/

# of failures

6.2.3

E-MCBF: Mean cycles between equipment-related

failures

total equipment cycles/

# of equipment-related failures

6.2.4

EQUIPMENT AVAILABILITY

Metric How It Is Measured Ref #

equipment dependent uptime (%) equipment uptime × 100/(oper-time –

(all maint-delay DT + out-of-spec input DT + fac-rel DT))

6.3.1

supplier dependent uptime (%) equipment uptime × 100/(oper-time –

(users maint-delay DT + out-of-spec input DT + fac-rel DT))

6.3.2

operational uptime (%) equipment uptime × 100/

operations time

6.3.3

EQUIPMENT MAINTAINABILITY

Metric How It Is Measured Ref #

MTTR: Mean time to repair total repair time/

# of failures

6.4.1

E-MTTR: Mean time to repair for equipment-related

failures

total repair time for equipment-related failures/

# of equipment-related failures

6.4.2

MTOL: Mean time off-line total equipment downtime/

# of DT events

6.4.3

equipment dependent scheduled downtime (%) equipment scheduled downtime × 100/(oper-time –

(all maint-delay DT + out-of-spec input DT + fac-rel DT))

6.4.4

supplier dependent scheduled downtime (%) equipment scheduled downtime × 100/(oper-time –

(user maint-delay DT + out-of-spec input DT + fac-rel DT))

6.4.5

EQUIPMENT UTILIZATION

Metric How It Is Measured Ref #

operational utilization (%) productive time × 100/

operations time

6.5.1

total utilization (%) productive time × 100/

total time

6.5.2

NOTE: oper-time = operational time, DT = Downtime, fac-rel = facilities related, maint-delay = maintenance delay

SEMI E10-0304

7 Uncertainty Measurement

7.1 The measures of equipment reliability, availability,

and maintainability defined in Section 6 are single

value estimates. They do not indicate the uncertainty or

precision of the estimate. Precision varies depending

upon the number of failures observed and the amount of

productive time contained within the observation

period.

7.2 Precision is described by calculating a lower and

upper confidence limit for the MTBF

and presenting

this interval along with the MTBF

point estimate.

7.3 These procedures assume that the failure rate is

constant and the times between failures are

independently distributed according to the exponential

distribution. Therefore, there are no improvement or

degradation trends and it is meaningful to calculate

MTBF

. Section 8 applies when the failure times

indicate that a non-constant failure rate is present (for

example, when there is reliability growth or

degradation). Section 8 would typically apply during

prototype reliability improvement testing.

7.4 Since MTTR distributions are unlikely to follow an

exponential distribution assumption, applying these

procedures to put confidence limits on MTTR would be

inappropriate.

7.5 Note that all procedures and tables referred to in

this section apply equally well to measuring the

precision of estimates for similar metrics, where hours

are replaced by cycles or units, for example. These

procedures apply to E-MTBF

or E-MCBF in the same

way. It is also appropriate to combine data from

identical tools being used the same way, in order to

improve the precision of MTBF

estimates.

7.6 Calculation of Lower and Upper Confidence Limits

— To obtain lower and upper MTBF

limits, multiply

the MTBF

estimate by factors obtained by table look-

up (Tables A1-1 and A1-2 in Appendix 1). For the case

when there are zero failures during the measurement

period, lower confidence limit factors for the MTBF

are given in the first row of Table A1-1 (they multiply

the amount of productive time that had no failures to

obtain the desired MTBF

lower limit). There is no

upper limit estimate for performance when there are

zero failures.

7.6.1 Calculation of the MTBF

Lower Limit — Use

Table A1-1 in Appendix 1 to obtain a k

r;conf

factor,

where r is the number of failures observed during the

measurement period and conf is the confidence level

desired. The rows of Table A1-1 correspond to

different values of r and the columns correspond to

different values of conf. Confidence levels ranging

from 80 percent to 95 percent are typical choices.

7.6.1.1 Since the equipment being measured has

demonstrated (at a given confidence level) that it is at

least as good as the MTBF

lower limit, this lower limit

is an important and useful performance statistic, and is

often used contractually.

7.6.1.2 Note that the factors in Table A1-1 for 90%

confidence are less than 0.5 until the number of failures

equals or exceeds 4. This means that when the number

of failures is under 4, the MTBF

lower limit will be

less than half the MTBF

estimate, and confidence

intervals will be wide. From the point of view of

precision, it is advantageous to have had 4 or more

failures.

7.6.1.3 Example: During a given calendar quarter, a

tool was productive for 1200 hours and had 6 failures.

The MTBF

estimate is 1200/6 = 200 hours. A 90

percent lower limit factor from Table A1-1

(corresponding to r = 6 failures) is 0.570. That means

that 200 × 0.570 = 114.0 hours is a 90 percent lower

confidence limit for the true tool MTBF

7.6.2 Calculation of the MTBF

Upper Limit — Use

Table A1-2 in Appendix 1 to obtain a k

r;conf

factor,

where r is the number of failures observed during the

measurement period and conf is the confidence level

desired. The rows of Table A1-2 correspond to

different values of r and the columns correspond to

different values of conf. Confidence levels ranging

from 80 percent to 95 percent are typical choices.

7.6.2.1 Example: During a given calendar quarter, a

tool was productive for 1200 hours and had 6 failures.

The MTBF

estimate is 1200/6 = 200 hours. A 90

percent upper limit factor from Table A1-2

(corresponding to r = 6 failures) is 1.904. That means

that 200 × 1.904 = 380.8 hours is a 90 percent upper

confidence limit for the true tool MTBF

7.6.3 Calculation of a Confidence Interval for the

MTBF

— Lower and upper 100 × (1 – α/2) confidence

limits for the MTBF

can be combined to give a 100 ×

(1 – α) confidence interval. Here α/2 is the chance of

missing on either end of the interval. A 90 percent

lower limit has an α/2 = 0.1 chance of not being low

enough to capture the true MTBF

, and the same is true

for a 90 percent upper limit. Therefore, a 90 percent

lower limit and a 90 percent upper limit combine to

give an 80 percent confidence interval. Similarly, a 95

percent lower limit and a 95 percent upper limit would

combine to give a 90 percent confidence interval.

7.6.3.1 Example: During a calendar quarter, a tool was

productive for 1200 hours and had 6 failures. The

MTBF

estimate is 1200/6 = 200 hours. The 90 percent

lower and upper limits are 114 and 380.8 respectively

(see Sections 7.6.1 and 7.6.2). The interval (114,