# Fab SPC Xbar-R Chart Worksheet > Source: https://netray.co/tools/fab-spc-xbar-r-chart-worksheet > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Enter subgroups of five readings, such as film thickness or CD, and get subgroup mean, range and Xbar-R control limits. ## Category quality ## Industry Semiconductors ## Audience - Process engineer - Equipment engineer - Quality engineer - Fab technician ## Tool **Kind:** worksheet **Mode:** editable **Columns:** #### Subgroup / lot **Key:** sg **Type:** text #### Site 1 **Key:** x1 **Type:** number **Unit:** nm #### Site 2 **Key:** x2 **Type:** number **Unit:** nm #### Site 3 **Key:** x3 **Type:** number **Unit:** nm #### Site 4 **Key:** x4 **Type:** number **Unit:** nm #### Site 5 **Key:** x5 **Type:** number **Unit:** nm #### Mean (Xbar) **Key:** xbar **Type:** number **Expr:** (x1 + x2 + x3 + x4 + x5) / 5 **Format:** decimal #### Range (R) **Key:** rng **Type:** number **Expr:** max(max(max(x1, x2), max(x3, x4)), x5) - min(min(min(x1, x2), min(x3, x4)), x5) **Format:** decimal **Rows:** **Sg:** LOT-0412 W03 **X1:** 100.2 **X2:** 99.8 **X3:** 100.5 **X4:** 99.6 **X5:** 100.1 **Sg:** LOT-0413 W05 **X1:** 100.8 **X2:** 100.3 **X3:** 100.9 **X4:** 100 **X5:** 100.4 **Sg:** LOT-0414 W02 **X1:** 99.7 **X2:** 100.1 **X3:** 99.9 **X4:** 100.4 **X5:** 100 **Sg:** LOT-0415 W11 **X1:** 100.6 **X2:** 100.2 **X3:** 99.9 **X4:** 100.7 **X5:** 100.3 **Sg:** LOT-0416 W08 **X1:** 99.9 **X2:** 100 **X3:** 100.4 **X4:** 99.5 **X5:** 100.2 **Sg:** LOT-0417 W14 **X1:** 100.3 **X2:** 100.7 **X3:** 100.1 **X4:** 100.5 **X5:** 99.8 **Totals:** #### Average of subgroup means (Xbar-bar) **Key:** xbar **Agg:** avg **Format:** decimal #### Average range (R-bar) **Key:** rng **Agg:** avg **Format:** decimal **Summary:** #### Xbar UCL **Key:** ucl_x **Expr:** avg_xbar + 0.577 * avg_rng **Format:** decimal **Primary:** true **Description:** Xbar-bar + A2 x R-bar, A2 = 0.577 for n = 5. #### Xbar LCL **Key:** lcl_x **Expr:** avg_xbar - 0.577 * avg_rng **Format:** decimal **Primary:** true **Description:** Xbar-bar - A2 x R-bar. #### R chart UCL **Key:** ucl_r **Expr:** 2.114 * avg_rng **Format:** decimal **Description:** D4 x R-bar, D4 = 2.114 for n = 5. #### R chart LCL **Key:** lcl_r **Expr:** 0 * avg_rng **Format:** decimal **Description:** D3 is 0 for subgroup sizes below 7. #### Estimated within sigma (R-bar / d2) **Key:** sigma_hat **Expr:** avg_rng / 2.326 **Format:** decimal **Description:** d2 = 2.326 for n = 5. **Notes:** Constants are for subgroup size n = 5 (A2 0.577, D3 0, D4 2.114, d2 2.326). Use at least 20 to 25 subgroups before trusting limits, and recompute after a process change. Sort or plot the means and ranges against the limits to look for points outside limits and runs. ## Content **Intro:** Xbar-R charts are the workhorse of fab SPC for film thickness, CD, sheet resistance and overlay. This worksheet turns subgroups of five site readings into subgroup means, ranges and control limits you can chart or paste into your SPC system. **Sections:** #### How to use the worksheet **Body:** Each row is one subgroup, for example five sites on one wafer or one reading from each of five wafers in a lot. Replace the sample rows with your data, keeping five readings per row. The sheet computes the mean and range of every row, then the average of those means (Xbar-bar) and the average range (R-bar). The summary gives Xbar limits, R chart limits and the within subgroup sigma. Export to Excel to plot the points against the limits, or compare each row manually to find out of control points. #### The method **Body:** Xbar-R charts track the process center with subgroup means and the spread with subgroup ranges. Control limits are three sigma estimates built from R-bar using tabulated constants. For n = 5 the Xbar limits are Xbar-bar plus or minus 0.577 x R-bar, the R chart upper limit is 2.114 x R-bar, and sigma is estimated as R-bar divided by 2.326. Control limits describe what the process does, not what the customer wants, so keep them separate from spec limits. **Bullets:** - Check the R chart first: if spread is unstable, Xbar limits are not valid - Rational subgroups should capture short term variation only - Recalculate limits after a verified process change #### Common mistakes **Body:** Frequent errors include using spec limits as control limits, mixing tools or chambers in one subgroup, computing limits from too few points and recomputing limits every time a point goes out. Another is using site to site variation as the subgroup when the real risk is lot to lot drift, which makes the limits too wide. Agree on what a subgroup represents before collecting data, then link out of control actions to your OCAP. **Cta:** Netray can pull measurement data from your MES or database into a private SPC view with alerts, without moving data off your network. **Faq:** #### Why subgroups of five? **Answer:** Five is common in fabs because five-site measurement maps are standard and the Xbar-R constants are well known. The worksheet uses n = 5 constants, so enter exactly five readings per row. #### How many subgroups do I need? **Answer:** Use at least 20 to 25 subgroups from a stable period to set limits. Fewer points give unreliable limits. After that, hold the limits and only recompute after a verified process change. #### Are control limits the same as spec limits? **Answer:** No. Control limits come from process variation and show when the process changed. Spec limits come from design and customer needs. A process can be in control and still out of spec. #### Should I use Xbar-S instead? **Answer:** For subgroup sizes above about 8 to 10, Xbar-S is more efficient. For n = 5 the range method is fine and simpler to check by hand. ## Search terms SPC worksheet, xbar r chart excel, fab SPC template, control chart worksheet, semiconductor SPC, xbar and r chart calculator, control limits calculator, SPC for wafer fab --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json