Work Sampling and Six Sigma: DMAIC Integration

Work sampling can supply state and time-utilization data to DMAIC: define, measure, analyze, improve and control. It does not replace measurement of defects, cycle times or customer requirements. Choose a technique for the decision variable rather than assumed superiority over sensors or existing records.

Define: ask a measurable question

A useful objective could be reducing material waits on one line while maintaining quality and safety. Define population, period, resource, categories and the intended outcome. A time share spent waiting differs from each wait's duration, lead time or units-per-hour productivity.

A pilot can suggest where to investigate but does not confirm a cause. If 35 of 100 simulated readings show waiting, report 35/100 with uncertainty; do not turn that share into an exact annual description or a saving.

Measure: design and classification quality

For a proportion under approximately independent binomial sampling, plan n=ceil(z²p₀(1−p₀)/e²). With z=1.96, p₀=0.30 and e=0.03:

n=ceil(3.8416×0.30×0.70/0.0009)=ceil(896.3733)=897.

With p₀=0.5 and e=0.05, it would be 385. DMAIC does not prescribe a universal 2–3% margin: agree decision-relevant precision. Each shift's interval needs its own data; a sufficient total does not ensure adequate segment precision.

Check coverage of shifts, days, products and areas. When readings are clustered in rounds, examine dependence and weights before applying independent-sample formulas.

Repeatability and reproducibility

For attribute classification, examine whether the same observer consistently classifies the same situations (repeatability), whether observers agree (reproducibility), and agreement with a defensible reference where one exists. Include frequent, rare and ambiguous states. A 95% agreement figure alone does not validate every system: prevalence and category-specific errors matter.

Instrument linearity for quantitative measures is not equivalent to comparing the beginning and end of a shift. The latter concerns drift or fatigue. Attribute assessment must fit the data; do not transplant continuous-measurement Gage R&R without adaptation.

Analyze: association is not causation

For two independent proportions under H₀:p₁=p₂:

z=(p̂₁−p̂₂)/√(p̂(1−p̂)(1/n₁+1/n₂)),
where p̂=(x₁+x₂)/(n₁+n₂).

The test requires appropriate assumptions and counts; sparse data need suitable methods. A small p-value does not measure economic importance or establish the source of a difference. Consider multiplicity and prespecification when comparing many shifts, categories and days.

Contingency tables may show association between day and state, not establish a root cause. Examine product mix, staffing, maintenance and demand.

A Pareto chart ranks categories using an explicit denominator. If 32%, 18% and 12% are shares of delays, they total 62% of delays, not the shift. Necessary activity does not become avoidable because it ranks highly.

Improve: a reproducible simulated example

Assume independent, comparable before/after samples:

Period	Readings	Material waiting	Proportion
Before	385	108	28.05%
After	385	42	10.91%

The reduction is 17.14 percentage points, approximately 61.1% relative to baseline. The pooled two-sided test gives z≈6.01 and p<0.001 under the stated assumptions. An unpooled normal 95% interval for the difference is approximately 11.68–22.61 percentage points.

This establishes a difference in the simulated data, not that kanban is its sole cause. Before/after comparisons may be confounded by load, seasonality or other changes. Where feasible, randomized experiments or suitable comparative designs improve causal estimation. Sampling existing shifts does not turn an observational study into a DOE.

A lower waiting percentage also does not automatically mean more output or monetary savings. Check bottlenecks, demand, paid hours and costs that can actually change.

Control: follow-up without invented software capabilities

Specify the monitored variable, timing, sample, owner and response to incidents. Fifty weekly readings may be an illustrative budget, not a sample guaranteeing sensitivity to every change.

For a p-chart, use p̄=Σxᵢ/Σnᵢ and subgroup limits max(0,p̄−3√(p̄(1−p̄)/nᵢ)) and min(1,p̄+3√(p̄(1−p̄)/nᵢ)). These are control limits, not a confidence interval for the mean or a business target. Assess independence, baseline stability and rational subgrouping. An outlying point requests investigation; it does not identify a cause or invalidate the whole study.

WorkSamp supports visit preparation and recording and provides Wilson intervals in advanced reports. Do not assume automatic p-charts, SPC alerts, Minitab integration or ERP dashboards. Check pending local records before treating synchronization as confirmed.

Use Cronometras for element-duration analysis; Induly supplies working-time context. The ASETEMYT directory lists methods and time-study resources.