The following symbols and notations are common to test methods 1  3 contained in this appendix:
X = the random variable which denotes the maintenance
characteristics of interest (e.g., X can denote corrective maintenance time,
preventive maintenance time, fault location time, manhours per maintenance
task, etc.).
X_{i} = the i^{th}; observation or value of the random variable X.
n = the sample size.
X = the sample mean
E(random variable) = the expected value of the variable
^{2} = E[(lnX  )^{2}] = the true variance of lnX.
µ = E(X) = the true mean of X.
^{2} = Var (X) = E[( X  µ^{2}] = the true variance of X.
^{2} = the sample variance of X (i.e., d^{2} =
^{2} = the prior estimate of the variance of the maintenance time.
X_{p} = the (1p)th percentile of X (i.e., X_{.50} = the 95th percentile of X).
= X_{.50} = the median of X.
Y = lnX = the natural logarithm of X.
= the sample mean of Y
= E(lnX) = the true mean of lnX
^{2} = the prior estimate of the variance of the logarithm of maintenance times.
s^{2} = the sample variance of lnX.
Z_{p} = the standardized normal deviate exceeded with probability p (i.e.,
Z_{} = Z_{(1  )} =
standardized normal deviate exceeded with probabilities and (1  _{}) respectively.
= the producer's risk; the probability that the equipment will be rejected when it has a true value equal to the desired value (H_{0}).
= the consumer's risk; the probability that the equipment will be accepted when it has a true value equal to the maximum tolerable value (H_{1}).
H_{0} = the desired value specified in the contract or specification and is expressed as a mean, critical percentile, or critical maintenance time.
H_{1} = the maximum tolerable value. Note: H_{0} < H_{1}.
When X is a lognormally distributed random variable:
If Y = lnX, the probability density of Y is normal with mean and ^{2} variance
Y ~ N( , ^{2 })
Properties of the lognormal distribution:
mean = µ = e
variance = d^{2} = e 

median = = e^{}
mode = M = e
(1p)th percentile = X_{p} = e
Table BVIII  Standardized Normal
Derivatives
P 
Z_{p} 
00.1 
2.33 
0.05 
1.65 
0.10 
1.28 
0.15 
1.04 
0.20 
0.84 
0.30 
0.52 
The following symbols are common to test methods 4, 8  11 contained in this appendix.
X_{ci} = Maintenance downtime per corrective maintenance task (of the i^{th} task).
X_{pmi} = Maintenance downtime per preventive maintenance task (of the i^{th} task).
n_{c} = Number of corrective maintenance tasks sampled.
n_{pm} = Number of preventive maintenance tasks sampled.
_{ } =
Consumer's risk
= That value, corresponding to risk, which is obtained from a table of normal distribution for a onetail test.
f_{c} = Number of expected corrective maintenance tasks occurring during a representative operating time (T).
f_{pm} = Number of expected preventive maintenance tasks occurring during a representative operating time (T).
T = Item representative operating time period.
D_{t} = Total maintenance downtime in the representative operating time (T).
_{c}, _{pm}, _{p/c} = Mean downtimes of sample. (Corrective, Preventive, and combined Corrective/Preventive Maintenance Times.)
M'_{Maxc} = Sample calculated maximum corrective maintenance downtime.
µ_{c} = Specified mean corrective maintenance time.
µ_{pm} = Specified mean preventive maintenance time.
µ_{p/c} = Specified mean maintenance time. (Taking both corrective and preventive maintenance time into account.)
M_{Max} = A requirement levied in terms of a maximum value of a percentile of task time (i.e., 95% of all corrective task times must be less than 60 minutes) usually taken as the 90th or 95th percentile.
M_{Maxc} = Specified M_{Max} of corrective maintenance downtimes.
M_{Maxpm} = Specified M_{Max} of preventive maintenance downtimes.
_{c} = E(ln X_{c} ) = Expected value of the logarithm of corrective maintenance tasks.
Log X_{ci}, Log X_{c} =
Log to the base 10 of X_{ci}, X_{c}.
ln X_{ci}, ln X_{c} =
Natural logs of X_{ci}, X_{c}.
_{ct} =
Median value of corrective maintenance tasks.
_{pm} =
Median value of preventive maintenance tasks.