Optimistic Time given Standard Deviation Calculator

✖The Standard Deviation is a measure of how spread out numbers are.ⓘ Standard Deviation [σ]			+10% -10%
✖A Pessimistic Time is the longest time that an activity could take if everything is wrong.ⓘ Pessimistic Time [t_p]			+10% -10%

✖Optimistic Time is the shortest possible time to complete the activity if all goes well.ⓘ Optimistic Time given Standard Deviation [t₀]

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Formula

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Optimistic Time given Standard Deviation

Formula

`"t"_{"0"} = -(6*"σ"-"t"_{"p"})`

Example

`"2.02d"=-(6*"1.33"-"10d")`

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Optimistic Time given Standard Deviation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Optimistic Time = -(6*Standard Deviation-Pessimistic Time)
t₀ = -(6*σ-t_p)
This formula uses 3 Variables

Variables Used

Optimistic Time - (Measured in Day) - Optimistic Time is the shortest possible time to complete the activity if all goes well.
Standard Deviation - The Standard Deviation is a measure of how spread out numbers are.
Pessimistic Time - (Measured in Day) - A Pessimistic Time is the longest time that an activity could take if everything is wrong.

STEP 1: Convert Input(s) to Base Unit

Standard Deviation: 1.33 --> No Conversion Required
Pessimistic Time: 10 Day --> 10 Day No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t₀ = -(6*σ-t_p) --> -(6*1.33-10)

Evaluating ... ...

t₀ = 2.02

STEP 3: Convert Result to Output's Unit

174528 Second -->2.02 Day (Check conversion here)

FINAL ANSWER

2.02 Day <-- Optimistic Time

(Calculation completed in 00.004 seconds)

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Credits

Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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< 17 Project Evaluation and Review Technique Calculators

Optimistic Time given Expected Time

Go Optimistic Time = (6*Mean Time)-(4*Most Likely Time)-Pessimistic Time

Mean or Expected Time

Go Mean Time = (Optimistic Time+(4*Most Likely Time)+Pessimistic Time)/6

Most Likely Time given Expected Time

Go Most Likely Time = (6*Mean Time-Optimistic Time-Pessimistic Time)/4

Standard Deviation given Probability Factor

Go Standard Deviation = (Scheduled Time-Mean Time)/Probability Factor

Scheduled Time given Probability Factor

Go Scheduled Time = (Standard Deviation*Probability Factor)+Mean Time

Expected Time given Probability Factor

Go Mean Time = Scheduled Time-(Standard Deviation*Probability Factor)

Probability Factor

Go Probability Factor = (Scheduled Time-Mean Time)/Standard Deviation

Pessimistic Time given Expected Time

Go Pessimistic Time = 6*Mean Time-Optimistic Time-4*Most Likely Time

Earliest Expected Occurrence Time of Event j

Go Earliest Occurrence Time of j = Earliest Occurrence Time of i+Duration of i-j

Earliest Expected Occurrence Time of Event i

Go Earliest Occurrence Time of i = Earliest Occurrence Time of j-Duration of i-j

Expected Time of Activity i-j

Go Duration of i-j = Earliest Occurrence Time of j-Earliest Occurrence Time of i

Slack of Event i or j

Go Slack of an Event = LOT of Event j-Earliest Occurrence Time of j

Optimistic Time given Standard Deviation

Go Optimistic Time = -(6*Standard Deviation-Pessimistic Time)

Standard Deviation of Activity

Go Standard Deviation = (Pessimistic Time-Optimistic Time)/6

Pessimistic Time given Standard Deviation

Go Pessimistic Time = 6*Standard Deviation+Optimistic Time

Least Allowable Occurrence Time of Event i

Go LOT of Event i = LOT of Event j-Duration of i-j

Least Allowable Occurrence Time of Event j

Go LOT of Event j = LOT of Event i+Duration of i-j

Optimistic Time given Standard Deviation Formula

Optimistic Time = -(6*Standard Deviation-Pessimistic Time)
t₀ = -(6*σ-t_p)

What is Programme Evaluation and Review Technique (PERT)?

It is a numerical technique used in projects in which time cannot be estimated accurately such as research and development projects. It is an event-oriented network. Cost is assumed to be directly proportional to time.
Three time estimates are made in PERT.
1. Optimistic time (to): This is the minimum possible time in which an activity can be completed under the most ideal conditions.
2. Pessimistic time (tp): This is the maximum time required to complete an activity under the worst possible conditions.
3. Most likely time (tm): This is the time required to complete an activity under normal working conditions. It's value lies between to and tp It is near to the expected time.

What is Central Limit Theorem and Critical Path?

Central Limit Theorem: The theorem states that a project consists of a large number of activities, where each activity has its own mean time (te), standard deviation (σ), variance (σ2) and also its own ß-distribution curve.
Critical Path: The time-wise longest path is the critical path. In this path, any type of delay in any event will cause a delay in the project. These are shown by double lines or dark lines in a network

How to Calculate Optimistic Time given Standard Deviation?

Optimistic Time given Standard Deviation calculator uses Optimistic Time = -(6*Standard Deviation-Pessimistic Time) to calculate the Optimistic Time, The Optimistic Time given Standard Deviation formula is defined as it gives the minimum possible time to finish the project under most ideal conditions. Optimistic Time is denoted by t₀ symbol.

How to calculate Optimistic Time given Standard Deviation using this online calculator? To use this online calculator for Optimistic Time given Standard Deviation, enter Standard Deviation (σ) & Pessimistic Time (t_p) and hit the calculate button. Here is how the Optimistic Time given Standard Deviation calculation can be explained with given input values -> 2.3E-5 = -(6*1.33-864000).

FAQ

What is Optimistic Time given Standard Deviation?

The Optimistic Time given Standard Deviation formula is defined as it gives the minimum possible time to finish the project under most ideal conditions and is represented as t₀ = -(6*σ-t_p) or Optimistic Time = -(6*Standard Deviation-Pessimistic Time). The Standard Deviation is a measure of how spread out numbers are & A Pessimistic Time is the longest time that an activity could take if everything is wrong.

How to calculate Optimistic Time given Standard Deviation?

The Optimistic Time given Standard Deviation formula is defined as it gives the minimum possible time to finish the project under most ideal conditions is calculated using Optimistic Time = -(6*Standard Deviation-Pessimistic Time). To calculate Optimistic Time given Standard Deviation, you need Standard Deviation (σ) & Pessimistic Time (t_p). With our tool, you need to enter the respective value for Standard Deviation & Pessimistic Time and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Optimistic Time?

In this formula, Optimistic Time uses Standard Deviation & Pessimistic Time. We can use 1 other way(s) to calculate the same, which is/are as follows -

Optimistic Time = (6*Mean Time)-(4*Most Likely Time)-Pessimistic Time

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