spc statistical process control analysis

intent

use this skill when you need to monitor manufacturing production quality, assess process stability, identify anomalies, or compare data across multiple cycles. the skill generates control charts (xbar-r, xbar-s, i-mr, p, c, u), detects outliers using nelson rules, calculates process capability indices, and produces an html report with visualizations. run it whenever process data needs statistical analysis or trend comparison.

inputs

required:

• data source: excel file or raw numeric data (user uploads or provides inline). must contain measurements aligned to chosen chart type (subgrouped data for xbar-r/xbar-s, individual values for i-mr, defect counts for p/c/u).
• chart type: one of xbarr (xbar-r), xbars (xbar-s), imr (i-mr), p, c, or u. user specifies or you infer from data structure.

optional:

• usl (upper specification limit): numeric value for process capability analysis.
• lsl (lower specification limit): numeric value for process capability analysis.
• output path: custom html report filename. if omitted, auto-generated as spc_analysis_report_YYYYMMDD_HHMMSS.html.

external connections:

• none (script is self-contained).

dependencies:

• pandas >= 2.0.0
• numpy >= 1.24.0
• openpyxl >= 3.1.0
• script location: /workspace/projects/spc-analysis/scripts/spc_analysis.py

context requirements:

• data characteristic (e.g., "product a diameter", "temperature readings") must remain consistent within a conversation. if characteristic changes, start a new conversation.
• conversation history is used for multi-cycle comparisons. key summaries (mean, std dev, anomaly count, stability rating) are retained; detailed reports are stored as files.

procedure

1. receive and identify data

   • input: raw data file (excel) or inline measurements, user statement of what data represents.
   • action: determine data source type and quantity. validate data structure matches chosen or inferred chart type.
   • output: confirmed data shape, characteristic name, chart type candidate list.
   • edge case: if data is empty or all nulls, halt and ask user to resubmit.

2. confirm chart type

   • input: data structure (subgroups, individuals, or counts) and user preference (if stated).
   • action: map data type to chart option. for subgrouped continuous data (n >= 2 per subgroup), recommend xbarr or xbars. for individual continuous values, recommend imr. for defect counts or proportions, recommend c, u, or p.
   • decision: see decision points section.
   • output: final chart type selection.

3. invoke spc analysis script

   • input: data file path, chart type, optional usl/lsl.
   • action: call exec_shell with command:

     cd /workspace/projects/spc-analysis && python scripts/spc_analysis.py --input <data_file> --chart-type <type> [--output <report_path>] [--usl <value>] [--lsl <value>]
     

   • output: html report file (with embedded svg control chart, nelson rule violations, process capability metrics if usl/lsl provided).
   • edge case: if script timeout exceeds 60 seconds, notify user and suggest data subsetting.
   • edge case: if file not found, confirm path and retry.

4. parse and summarize report

   • input: generated html report.
   • action: extract key metrics (process mean, std dev, control limit violations, nelson flags, cpk if applicable). generate prose summary and improvement recommendations.
   • output: conversational summary in chat, with file link for full report download.

5. compare with history (if applicable)

   • input: current report metrics and prior summaries from conversation.
   • action: if prior analyses exist, compare mean, std dev, anomaly count, and stability rating. identify trends (mean shift, increased variation, new anomaly patterns).
   • decision: see decision points section.
   • output: trend narrative (e.g., "mean stable week-to-week; variance increased 15% in cycle 3").

6. present results

   • input: summary text, improvement suggestions, trend analysis.
   • action: display findings in chat. provide html report file for download. recommend next monitoring steps.
   • output: user-facing summary and downloadable report.

decision points

• chart type selection: if data has subgroups (n >= 2 per sample), ask user whether to use xbar-r (simpler, less data) or xbar-s (more sensitive to variation). if data is individual measurements, use imr. if data is defect counts on fixed sample size, use p or c. if defect counts on variable sample size, use u.

• specification limits: if user provides usl/lsl, rerun script with those flags to compute cpk (capability). if user does not provide limits, report only on stability and centering (no capability metrics).

• multi-cycle comparison: if conversation already contains a prior analysis summary for the same characteristic, extract and compare; else skip comparison. only compare last 3-5 cycles to avoid clutter; if older cycles are needed, suggest user copy key summaries to new conversation.

• data characteristic consistency: if user introduces new characteristic (e.g., switches from diameter to weight), warn user that analysis is cleaner if new characteristic is analyzed in a fresh conversation. if user insists on continuing, start new context but note the shift.

• anomaly interpretation: if nelson rules flag >= 2 violations, notify user of specific rules triggered and suggest investigation of root cause. if no violations, affirm stability.

• long conversation management: after 15-20 analyses, suggest opening new conversation and copying prior summaries to avoid token bloat.

output contract

• file type: html report with embedded svg control chart.
• file location: /workspace/projects/spc-analysis/ (working directory) or user-specified path.
• file naming: if --output omitted, auto-generated as spc_analysis_report_YYYYMMDD_HHMMSS.html. if --output provided without date, date prefix is added.
• contents: control chart visualization, control limits (lcl, ucl, centerline), data points, nelson rule violations (if any), process capability indices (cpk, ppk if usl/lsl provided), summary statistics (n, mean, std dev, min, max), recommendations.
• format: valid html5 with inline svg (no external image dependencies).
• encoding: utf-8.

outcome signal

• user can download the html report and open it in a browser to see the control chart.
• conversation contains a clear summary: "process is stable" or "X anomalies detected; check ".
• if comparison was performed, user sees trend statement: "mean shifted Y units week-to-week" or "variation reduced Z%".
• user receives next-step recommendations: "monitor subgroup 7 further", "investigate cause on day 5", "process ready for capability approval" or "reduce variation before certification".
• if anomalies are found, user can click report to see exact samples flagged.