Chartwell Assesment

Percentage change

The difference between a new value and an old value, expressed as a percent of the old value.

Reverse percentage

Working backward from a final value and a known percent change to find the original value.

Ratio

A comparison of two quantities showing how many times one contains the other.

Proportion

An equation stating two ratios are equal, used to scale quantities up or down.

Rate

A quantity measured per unit of something else, usually per unit time.

Weighted average

An average where some values count more than others based on an assigned weight, rather than each value counting equally.

Mean

The sum of all values divided by the number of values.

Median

The middle value in a data set when values are sorted from smallest to largest.

Mode

The value that appears most frequently in a data set.

Standard deviation

A measure of how spread out data is around the mean.

Variance

The average of the squared differences from the mean.

Independent events

Two events where the outcome of one does not affect the probability of the other. Their probabilities multiply: P(A and B) = P(A) × P(B).

Mutually exclusive events

Two events that cannot both happen at the same time. Their probabilities add: P(A or B) = P(A) + P(B).

Complement probability

The probability that an event does NOT happen: P(not A) = 1 − P(A).

At least one probability

A common trick: P(at least one occurs) = 1 − P(none occur).

Expected value

The long-run average outcome of a probabilistic event, calculated as the sum of each outcome multiplied by its probability: E = Σ(probability × outcome).

Combination

A selection of items where order does NOT matter.

Permutation

An arrangement of items where order DOES matter.

Percentile

The value below which a given percentage of data falls.

Dimensional analysis

Tracking units through a calculation to convert between unit systems and to catch setup errors.

Order of magnitude

A rough, quick calculation used to sanity-check whether a precise answer is reasonable.

Throughput

The rate at which a process produces completed output, usually measured in units per unit time.

Bottleneck/limiting step

The slowest step in a multi-step process; it caps the maximum throughput of the entire line, regardless of how fast other steps run.

Yield

The percentage of input that becomes good, usable output for a process or given step.

Cumulative yield

The combined yield across multiple sequential steps, found by multiplying each step's yield together.

Availability OEE

The percentage of scheduled time a machine or line is actually running (excludes downtime, changeovers, breakdowns).

Performance OEE

How fast a process runs compared to its designed/ideal speed, expressed as a percentage.

Quality OEE

The percentage of output that meets specifications in a line or process.

Overall Equipment Effectiveness OEE

A composite metric equal to Availability × Performance × Quality; measures how effectively equipment is used.

Utilization

The percentage of total available capacity that is actually being used.

Cycle time

The time it takes to complete one unit or one cycle of a process step.

Takt time

The maximum allowable time per unit to meet customer demand, calculated as available production time divided by customer demand.

Downtime

Time a machine or line is not producing due to breakdowns, changeovers, maintenance, or stoppages.

Scrap

Output that fails quality standards and is discarded rather than sold or reworked.

Rework

Output that fails quality standards but can be corrected and brought back up to spec, at additional cost/time.

Contribution margin

Revenue per unit minus variable cost per unit; used to estimate the profit impact of gaining or losing units of output.

Theory of constraints

The principle that a process's overall output is limited by its single bottleneck step, so improving any non-bottleneck step does not increase total throughput.

Capacity

The maximum possible output a process or machine could produce under ideal conditions.

Serial process

A process where units pass through steps in sequence, one after another, so each step depends on the output of the one before it.

Effective rate

A step's realistic production rate after accounting for availability and yield losses, not just its nominal/rated speed.

Defect rate

The percentage or fraction of output that does not meet quality standards.

Mass balance

An accounting of material flow through a process where total input must equal total output plus any accumulation or loss.

Energy balance

An accounting of energy flow through a process, based on the principle that energy in equals energy out plus any losses or storage.

Lead Time

The amount of time required to complete a process from start to finish, including order preparation and delivery.

Nominal rate

The designed rate of a process or machine.

Payback period

The time required for an investment to generate enough cash flow to recover its initial cost.