LOGINV

Calculates the inverse of the LOGNORMDIST function.

Syntax:

LOGINV(p, μ, σ)

A variable is lognormally distributed if its natural logarithm is normally distributed. Parameters of the distribution are μ (mean) and σ (standard deviation).

LOGINV returns the value x, such that LOGNORMDIST(x, μ, σ) is p.

Example:

LOGINV(0.5, 0, 1)

returns 1.

LOGNORMDIST(1, 0, 1)

returns 0.5.

Application:

Product Lifespan Analysis

Scenario: A manufacturer of high-end electronic components knows from historical data that the lifespan of a particular component follows a log-normal distribution. They want to determine the lifespan value below which 5% of their products are expected to fail. This is a critical quality control metric.

Understanding the Parameters:

Probability (p): This is the cumulative probability we are interested in. In this case, it's 5%, or 0.05. This represents the fraction of components we expect to fail by a certain time.
Mean (μ): This is the mean of the natural logarithm of the lifespan values. From their data analysis, the manufacturer has found this to be 6.5.
Standard Deviation (σ): This is the standard deviation of the natural logarithm of the lifespan values. They have calculated this to be 0.8.

The Problem: The manufacturer wants to find the lifespan value (x) such that the probability of a component failing at or before that lifespan is 0.05.

Using the LOGINV Function:

The LOGINV function helps us find this value. Its syntax is LOGINV(probability, mean_log, standard_dev_log).

probability = 0.05
mean_log = 6.5
standard_dev_log = 0.8

Calculation:

LOGINV(0.05, 6.5, 0.8)

Result:

The function returns the value x in the original units (hours, in this case). The result of this calculation is approximately 178.42 hours.

Summary Table:

	Parameter	Description	Value
	A	B	C
1	Probability	The cumulative probability of failure we are interested in.	0.05
2	Mean (log-scale)	The mean of the natural logarithm of the component's lifespan.	6.5
3	Standard Deviation (log-scale)	The standard deviation of the natural logarithm of the component's lifespan.	0.8
4	Result (LOGINV)	The lifespan in hours corresponding to the 5% probability.	178.42

Conclusion:

Based on the log-normal distribution of component lifespans, the manufacturer can expect that 5% of their components will fail at or before 178.42 hours of operation. This information is crucial for setting warranty periods, predicting failure rates, and implementing preventative maintenance schedules. The LOGINV function directly provides the threshold value for a given probability, which is the inverse of what the LOGNORMDIST function would provide (calculating the probability for a given lifespan).