Six Sigma Pizza Line

QM 602 Lean Six Sigma · Walsh College · Fall 2025

Six Sigma on a pizza line

Control charts, Pareto analysis, DPMO and process capability for a pizza station case study, recomputed live in your browser from her QM 602 workbook.

ExcelX̄-R control chartsPareto analysisDPMO & sigmaCp / CpkDMAIC

Live demo

Every number below is calculated in the page from the workbook's raw readings and counts. Edit the inputs and the charts recompute.

Crust thickness: X̄ and R control charts

30 subgroups of 5 readings (mm), constants for n = 5: A2 0.577, D3 0, D4 2.114.

Readings (mm)

Subgroup valueBeyond a control limitRun of 8 on one side of the centre lineCentre line (dashed: UCL / LCL)

Order-taking errors: Pareto

Cumulative share printed on each bar.

Vital few (top causes reaching 75% of errors)Remaining causes

DPMO and sigma calculator

Defaults are the workbook's DPMO sheet: 445 defects in 1,500 orders, 6 opportunities per order.

Z is NORM.S.INV(yield), the formula in her workbook. Six Sigma tables quote the sigma level as Z + 1.5 (the conventional long-term shift), shown alongside. The Pareto sheets log 890 errors, exactly twice the DPMO sheet's 445, so 890 over 3,000 orders gives the same rate.

Process capability: Cp and Cpk

Histogram of the individual crust readings against the spec limits, with the fitted normal curve.

Readings per 0.05 mm binNormal fitSpec limits

Results

Improve phase figures from the workbook: the proposed future-state value stream and the root-cause priority scores.

Lead time by step, current vs proposed

Current stateProposed future state

Root-cause priority score

Score = frequency × impact ÷ difficulty, from the Root_Cause_Matrix sheet.

How it works

The case study followed DMAIC. She applied the same method in a paired research paper with Elizabeth Hoffmann on DMAIC for IT helpdesk ticket processing.

  1. Define and measure. Logged order-taking errors by type and ranked them in a Pareto, for all days and for Friday alone.
  2. Quantify the defect rate. Converted defects, units and opportunities into DPO, DPMO, yield and a Z value with NORM.S.INV.
  3. Chart the crust process. Took 30 subgroups of 5 thickness readings, then computed X̄̄, R̄ and X̄/R limits with A2, D3 and D4 for n = 5.
  4. Test capability. Estimated sigma as R̄/d2 and compared the process with the 4.25 to 5.75 mm spec to get Cp and Cpk.
  5. Improve and control. Mapped wastes with DOWNTIME, redesigned the value stream (lead time and takt), and set a control plan with c-chart and X̄-R triggers.

Data

First 10 of 30 subgroups from the "Crust Xbar-R Data" sheet. X̄ and R are recomputed in the page.