Orthogonal Array
An orthogonal array is a structured experimental design table where, for any chosen set of t columns, every possible level combination appears an equal number of times. Formally, it is an N × k array with s levels and strength t, meaning each t-tuple occurs exactly λ times in every N × t subarray. This balance lets researchers estimate factor effects without bias using a fraction of the full factorial combinations.
On a manufacturing line or in a warehouse, an orthogonal array is a disciplined test matrix for process improvement. Instead of trying every combination of settings, planners select a balanced subset of runs that covers the factor space efficiently. Typical factors include barcode scan method, receiving batch size, putaway location class, cycle-count frequency, slotting rule, or replenishment trigger. Because each factor level is distributed evenly across the array, analysts can estimate main effects with minimal confounding and then use ANOVA to identify which variables materially affect throughput, inventory accuracy, lead time, or scrap. The method is especially valuable when process changes are expensive, disruptive, or slow to execute, such as altering WMS parameters or shop-floor kitting rules. It works best when interactions are limited or when only a few interactions matter enough to assign to array columns, allowing a reduced but statistically valid experiment.
What property makes an orthogonal array statistically useful?
Its balance and orthogonality: every t-factor combination occurs equally often, so factor effects can be estimated without systematic bias from the other columns.
Why is an orthogonal array classified as a fractional factorial design?
Because it tests only a carefully chosen subset of all possible factor combinations while preserving enough structure to estimate main effects and selected interactions.
When is it appropriate to use orthogonal arrays in industrial improvement work?
When there are multiple controllable variables, exhaustive testing is too costly, and the number of important interactions is limited or known in advance.