Formula solver index — formula.expert

Capital Recovery Factor

\mathit{CRF} = \frac{i\,(1+i)^{n}}{(1+i)^{n} - 1}

Industrial EngineeringMoney & BusinessFraction of a capital sum that must be recovered each year to repay it with interest over n years. Multiply a first cost by CRF and you get its annual equivalent.

Defects Per Million Opportunities (DPMO)

\mathit{DPMO} = \frac{D}{U \times O} \times 10^{6}

Industrial EngineeringDefect rate on a scale that makes very good processes comparable: defects found, divided by the units inspected times the chances to go wrong on each unit, scaled to a million.

Economic Order Quantity (Wilson EOQ)

Q = \sqrt{\frac{2\,D\,S}{H}}

Industrial EngineeringMoney & BusinessOrder size that minimises the sum of ordering cost and holding cost: the square root of twice the annual demand times the cost per order, divided by the annual cost of holding one unit.

Equivalent Annual Cost

\mathit{EAC} = P\,\frac{i\,(1+i)^{n}}{(1+i)^{n} - 1} + M

Industrial EngineeringMoney & BusinessTotal yearly cost of owning and running an asset: the capital cost spread over its life at interest, plus the annual operating cost. The right way to compare a cheap machine that lasts five years with an expensive one that lasts fifteen.

Inventory Turnover Ratio

T = \frac{\mathit{COGS}}{\bar{I}}

Industrial EngineeringMoney & BusinessHow many times a year the stockroom empties and refills: cost of goods sold divided by the average value of inventory on hand.

Line Balancing Efficiency

E = \frac{\sum t_i}{N\,C}

Industrial EngineeringFraction of paid station time that is actually working: total task time divided by the stations you staffed times the cycle time. What is left over is balance delay.

Little's Law (Work in Process)

\mathit{WIP} = \mathit{TH} \times \mathit{CT}

Industrial EngineeringThe most general law in operations: the work sitting in a system equals the rate it flows through times how long each job stays. True for any stable system, whatever the arrival pattern.

Machine Utilisation

U = \frac{T_o}{T_a}

Industrial EngineeringShare of the time a machine was actually running: operating time divided by the time it was available to run. The answer depends entirely on which hours you count as available.

Net Present Value of a Uniform Annual Cash Flow

\mathit{NPV} = A\,\frac{1 - (1+i)^{-n}}{i} - C_0

Industrial EngineeringMoney & BusinessWorth of a project today when it costs C0 up front and returns the same net amount every year for n years: the discounted value of the series, less what it cost to start.

Overall Equipment Effectiveness (OEE)

\mathit{OEE} = A \times P \times Q

Industrial EngineeringThe single number total productive maintenance is built on: availability times performance times quality. Three losses multiplied, never averaged.

Process Capability (Cp)

C_p = \frac{\mathit{USL} - \mathit{LSL}}{6\sigma}

Industrial EngineeringHow the tolerance band compares with the spread of the process: the width of the specification divided by six standard deviations. Says nothing about whether the process is centred.

Process Capability Index (Cpk)

C_{pk} = \min\!\left(\frac{\mathit{USL} - \mu}{3\sigma},\ \frac{\mu - \mathit{LSL}}{3\sigma}\right)

Industrial EngineeringCapability measured to the nearer specification limit, so an off-centre process is penalised: the smaller of the two one-sided indices. Cpk can never exceed Cp, and equals it only when the process is perfectly centred.

Reorder Point

R = d\,L

Industrial EngineeringStock level that should trigger the next order: the quantity consumed during the supplier's lead time, so the last unit leaves the shelf as the replacement arrives.

Rolled Throughput Yield

\mathit{RTY} = y^{\,n}

Industrial EngineeringFraction of units that pass every step of an n-step process with no rework, when each step has the same first-pass yield: the yield raised to the number of steps.

Safety Stock (Statistical Buffer)

\mathit{SS} = z\,\sigma_d\,\sqrt{L}

Industrial EngineeringBuffer that absorbs demand variability over the lead time: a service-level z value times the standard deviation of daily demand times the square root of the lead time in days.

Standard Time from a Time Study

T_s = T_o\,R\,(1 + A)

Industrial EngineeringTurns a stopwatch reading into an allowed time: observed time, adjusted for how fast the operator was working, then padded for rest, personal needs and unavoidable delay.

Takt Time

T_t = \frac{T_a}{D}

Industrial EngineeringThe pace the customer sets: available production time in a period divided by the units the customer wants in that period. One unit must leave the line every takt.

Theoretical Minimum Number of Stations

N_{\min} = \frac{\sum t_i}{C}

Industrial EngineeringFewest workstations a line could possibly need: total work content divided by the cycle time. Round the answer UP to the next whole station — the fraction cannot be staffed.

Wright's Learning Curve (Unit Time)

T_n = T_1\,n^{\,\log b / \log 2}

Industrial EngineeringTime to build the nth unit when every doubling of cumulative output cuts the time to a fraction b of what it was: the aircraft-industry curve that still prices first-of-a-kind work.

X-bar Chart Upper Control Limit

\mathit{UCL} = \bar{\bar{x}} + A_2 \bar{R}

Industrial EngineeringUpper control limit of an X-bar chart, built from the average range rather than a computed sigma: grand average plus the tabulated A2 factor times the average range. The lower limit is the same product subtracted.