IndPenSim-Golden-APC — Golden batch and multiway PCA

+------------------------------------------------------------------------------
| Program Name:         step_batch.py
| Program Version:      2026-09-10 18:41:38
| Date:                 2026-09-11
| Time:                 08:51:00
| Input 1 - Raw CSV:    indpensim_process.csv  (100 batches, 23 tags)
| Input 2 - Glossary:   indpensim_schema.csv
| Input 3 - Time stamp: aligned onto 100 points of batch progress
+------------------------------------------------------------------------------

In short. 100 batches were compared against a golden batch built from 20 of them. 71 sit more than 10 sigma away at their worst point, and 10 of the 10 batches with a recorded fault were caught.

1. The input data

Where it came from

Three steps, so any number in this report can be traced back to the file it was downloaded from. The links open the file or its folder on this machine.

What	File
1. Raw data, as downloaded	100_Batches_IndPenSim_V3.csv 2.6 GB the original, kept on the drive and never edited /Volumes/YN-4T/WIP/CTRL-Designer/B-CDL-Data-Analysis/A-Raw-Data/IndPenSim	open the folder
2. Program that converted it	make_indpensim.py 8 kB run this again to rebuild the analysis file /Users/yahyanazer/Dropbox/__C_2026_Work/CTRL-Designer/B-CDL-Data-Analysis/B-Engines	open the folder
3. Data used for this analysis	indpensim_process.csv 19 MB what the numbers in this report were computed from /Users/yahyanazer/Dropbox/__C_2026_Work/CTRL-Designer/B-CDL-Data-Analysis/A-Raw-Data/IndPenSim	open the folder
Batch list	indpensim_batches.csv 5 kB /Users/yahyanazer/Dropbox/__C_2026_Work/CTRL-Designer/B-CDL-Data-Analysis/A-Raw-Data/IndPenSim	open the folder
Glossary	indpensim_schema.csv 1 kB /Users/yahyanazer/Dropbox/__C_2026_Work/CTRL-Designer/B-CDL-Data-Analysis/A-Raw-Data/IndPenSim	open the folder
Data sheet	data-source.md 8 kB what the dataset is, its licence, and its known quirks /Users/yahyanazer/Dropbox/__C_2026_Work/CTRL-Designer/B-CDL-Data-Analysis/A-Raw-Data/IndPenSim	open the folder

What it holds

Batches	100
Tags used	23
Batch length	167 to 290 h (median 230 h)
Alignment	every batch stretched onto 100 points of 0–100% progress, because they run to different lengths
Corridor	mean ± 3 sigma of the reference batches

How the batches were run

Strategy	Batches	Mean length	Mean yield
APC with Raman	30	225 h	3,484,283 kg
faulty	10	230 h	2,600,203 kg
operator controlled	30	229 h	2,833,113 kg
recipe driven	30	229 h	2,912,750 kg

Left out of the analysis: agitator_rpm (constant in every batch), paa_conc_offline (offline, 98% blank), nh3_conc_offline (offline, 98% blank), penicillin_offline (offline, 98% blank), biomass_offline (offline, 98% blank), nh3_shots (constant in every batch), viscosity_offline (offline, 98% blank).

2. The golden batch

Built from 20 reference batches. At every one of the 100 points of progress it holds a mean and a spread for each of the 23 tags. Those 20 batches sit on average 1.1% outside their own corridor, which is the noise floor of the method — nothing can score better than that.

The corridor for every tag is drawn in section 6. Here is what the whole set looks like measured against it:

the same as a picture (for printing)

One point per batch. T² across is movement inside the pattern the good batches share; SPE up is what the model cannot explain at all. Both on log scales.

3. Every batch against the golden batch

Each batch is placed by its worst single point — how far from the golden batch it ever got, in sigma. That is the plain reading of "stays within ± so many sigma". The sustained figure beside it is the 99.9th percentile, which ignores one bad sample and says where the batch really lived.

	Band	Batches	How far	Which
1	Near the golden batch — within 2 sigma	0	none
2	Similar — 2 to 5 sigma a normal batch: it wandered, but never far	21 0 with a recorded fault	worst point 2–4 sigma sustained 4 sigma (median)	Batch 61 - APC with Raman, Batch 62 - APC with Raman, Batch 63 - APC with Raman, Batch 64 - APC with Raman, Batch 65 - APC with Raman, Batch 66 - APC with Raman, Batch 67 - APC with Raman, Batch 68 - APC with Raman, Batch 69 - APC with Raman, Batch 70 - APC with Raman, Batch 71 - APC with Raman, Batch 72 - APC with Raman, Batch 73 - APC with Raman, Batch 74 - APC with Raman, Batch 75 - APC with Raman, Batch 76 - APC with Raman, Batch 77 - APC with Raman, Batch 78 - APC with Raman, Batch 79 - APC with Raman, Batch 80 - APC with Raman, Batch 86 - APC with Raman
3	Outside — 5 to 10 sigma clearly different from the golden batch at some point	8 0 with a recorded fault	worst point 7–9 sigma sustained 8 sigma (median)	Batch 8 - recipe driven, Batch 12 - recipe driven, Batch 16 - recipe driven, Batch 22 - recipe driven, Batch 26 - recipe driven, Batch 82 - APC with Raman, Batch 84 - APC with Raman, Batch 88 - APC with Raman
4	Far from it — over 10 sigma a different batch altogether - something happened	71 10 with a recorded fault	worst point 36–1500 sigma sustained 236 sigma (median)	Batch 1 - recipe driven, Batch 2 - recipe driven, Batch 3 - recipe driven, Batch 4 - recipe driven, Batch 5 - recipe driven, Batch 6 - recipe driven, Batch 7 - recipe driven, Batch 9 - recipe driven, Batch 10 - recipe driven, Batch 11 - recipe driven, Batch 13 - recipe driven, Batch 14 - recipe driven, Batch 15 - recipe driven, Batch 17 - recipe driven, Batch 18 - recipe driven, Batch 19 - recipe driven, Batch 20 - recipe driven, Batch 21 - recipe driven, Batch 23 - recipe driven, Batch 24 - recipe driven, Batch 25 - recipe driven, Batch 27 - recipe driven …

A batch holds 23 tags x 100 points = 2,300 readings. The largest of that many draws from a normal distribution is about 3.5 sigma by chance alone, so the first band is expected to be thinly populated or empty even for perfect batches. Change the edges in the window if you want bands that split your own data more usefully.

4. What caused the deviation

The 71 batches beyond 10 sigma, worst first. "Worst tag" is the single tag furthest from the golden batch, and "at" is where in the batch that happened.

Batch	Fault recorded	Worst point	Worst tag	at	first left	time outside
91	faulty	yes	1500 sigma	substrate_conc	100%	2%	26.5%
99	faulty	yes	1263 sigma	substrate_conc	100%	2%	23.4%
45	operator controlled	no	1253 sigma	substrate_conc	100%	1%	23.7%
33	operator controlled	no	1132 sigma	substrate_conc	100%	2%	17.4%
9	recipe driven	no	1093 sigma	substrate_conc	100%	2%	17.9%
95	faulty	yes	1012 sigma	substrate_conc	100%	10%	21.6%
100	faulty	yes	950 sigma	substrate_conc	100%	0%	14.7%
30	recipe driven	no	938 sigma	substrate_conc	100%	1%	12.4%
94	faulty	yes	923 sigma	substrate_conc	100%	9%	19.3%
25	recipe driven	no	857 sigma	substrate_conc	100%	1%	16.5%
51	operator controlled	no	853 sigma	substrate_conc	100%	0%	14.7%
43	operator controlled	no	811 sigma	substrate_conc	100%	4%	8.9%
92	faulty	yes	806 sigma	acid_flow_rate	75%	10%	5.0%
18	recipe driven	no	801 sigma	substrate_conc	100%	6%	8.8%
3	recipe driven	no	739 sigma	substrate_conc	100%	1%	17.6%
41	operator controlled	no	716 sigma	acid_flow_rate	96%	2%	3.8%
44	operator controlled	no	663 sigma	substrate_conc	100%	5%	9.9%
59	operator controlled	no	652 sigma	acid_flow_rate	85%	7%	9.0%
97	faulty	yes	615 sigma	acid_flow_rate	77%	9%	6.8%
10	recipe driven	no	589 sigma	acid_flow_rate	84%	13%	4.0%
34	operator controlled	no	589 sigma	acid_flow_rate	84%	8%	8.0%
28	recipe driven	no	589 sigma	acid_flow_rate	84%	13%	3.4%
4	recipe driven	no	589 sigma	acid_flow_rate	84%	13%	7.0%
40	operator controlled	no	589 sigma	acid_flow_rate	84%	13%	6.4%
6	recipe driven	no	589 sigma	acid_flow_rate	84%	13%	5.1%
96	faulty	yes	589 sigma	acid_flow_rate	84%	6%	4.8%
54	operator controlled	no	589 sigma	acid_flow_rate	84%	6%	6.2%
24	recipe driven	no	564 sigma	substrate_conc	100%	6%	5.5%
42	operator controlled	no	542 sigma	acid_flow_rate	84%	0%	7.2%
60	operator controlled	no	541 sigma	acid_flow_rate	84%	6%	6.3%
36	operator controlled	no	541 sigma	acid_flow_rate	84%	13%	12.7%
39	operator controlled	no	533 sigma	acid_flow_rate	99%	13%	5.3%
47	operator controlled	no	530 sigma	substrate_conc	100%	12%	5.7%
37	operator controlled	no	478 sigma	acid_flow_rate	92%	7%	5.2%
19	recipe driven	no	473 sigma	acid_flow_rate	93%	8%	4.3%
49	operator controlled	no	469 sigma	substrate_conc	100%	6%	7.1%
93	faulty	yes	364 sigma	acid_flow_rate	1%	1%	3.4%
50	operator controlled	no	362 sigma	substrate_conc	100%	7%	5.2%
35	operator controlled	no	330 sigma	acid_flow_rate	1%	1%	5.5%
21	recipe driven	no	309 sigma	acid_flow_rate	93%	0%	4.1%
56	operator controlled	no	266 sigma	substrate_conc	100%	0%	4.7%
52	operator controlled	no	246 sigma	acid_flow_rate	92%	13%	4.4%
38	operator controlled	no	220 sigma	substrate_conc	100%	1%	4.6%
58	operator controlled	no	199 sigma	substrate_conc	100%	0%	5.2%
7	recipe driven	no	174 sigma	acid_flow_rate	91%	13%	3.1%
32	operator controlled	no	169 sigma	sugar_feed_rate	96%	13%	7.5%
5	recipe driven	no	164 sigma	acid_flow_rate	14%	2%	6.5%
31	operator controlled	no	161 sigma	acid_flow_rate	10%	2%	6.9%
83	APC with Raman	no	97 sigma	acid_flow_rate	63%	2%	1.9%
53	operator controlled	no	96 sigma	sugar_feed_rate	96%	0%	7.5%
48	operator controlled	no	96 sigma	sugar_feed_rate	96%	5%	7.2%
55	operator controlled	no	96 sigma	sugar_feed_rate	96%	13%	3.6%
98	faulty	yes	90 sigma	ph	69%	13%	1.7%
23	recipe driven	no	88 sigma	acid_flow_rate	50%	2%	7.2%
20	recipe driven	no	87 sigma	acid_flow_rate	66%	0%	2.2%
2	recipe driven	no	87 sigma	acid_flow_rate	66%	12%	1.3%
17	recipe driven	no	81 sigma	acid_flow_rate	54%	2%	4.1%
14	recipe driven	no	78 sigma	acid_flow_rate	6%	6%	1.1%
27	recipe driven	no	72 sigma	heat_water_flow	43%	12%	5.6%
15	recipe driven	no	68 sigma	acid_flow_rate	50%	1%	9.2%
89	APC with Raman	no	64 sigma	acid_flow_rate	67%	34%	0.9%
57	operator controlled	no	63 sigma	heat_water_flow	34%	13%	2.9%
13	recipe driven	no	60 sigma	heat_water_flow	13%	8%	2.5%
29	recipe driven	no	57 sigma	water_injection	18%	1%	14.6%
11	recipe driven	no	46 sigma	dumped_broth_flow	95%	7%	2.7%
1	recipe driven	no	46 sigma	dumped_broth_flow	58%	0%	2.2%
85	APC with Raman	no	46 sigma	dumped_broth_flow	50%	1%	1.3%
81	APC with Raman	no	46 sigma	dumped_broth_flow	60%	7%	1.1%
87	APC with Raman	no	46 sigma	dumped_broth_flow	46%	0%	1.0%
90	APC with Raman	no	41 sigma	heat_water_flow	19%	5%	0.1%
46	operator controlled	no	36 sigma	sugar_feed_rate	52%	13%	2.5%

The milder bands

Similar — 2 to 5 sigma — 21 batches, 0 with a recorded fault. Furthest tag most often: heat_water_flow (7), acid_flow_rate (4), dumped_broth_flow (3). The worst point typically falls at 57% of the batch.
Outside — 5 to 10 sigma — 8 batches, 0 with a recorded fault. Furthest tag most often: paa_flow (5), heat_water_flow (2), cool_water_flow (1). The worst point typically falls at 15% of the batch. paa_flow is the furthest tag in 5 of these 8 batches. When one tag leads across a whole band of otherwise normal batches, the corridor is too tight for that tag rather than the batches being wrong — it swings more than the 3 sigma corridor allows even when nothing is amiss.

Batch by batch

Each chart holds every tag of that batch on one axis, measured in sigma from the golden batch. The green line at zero is the golden trajectory, the dashed red lines are the ±3 sigma corridor. The tags driving the batch are bold, the rest are faint behind them so you can still see whether the whole batch moved or only a few tags.

1. Batch 91 - faulty does not look like a golden batchseverity 10
faulty · a fault IS recorded for this batch · first left the corridor at 2% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 1500 sigma above the golden batch at 100% of the way through; 22 of 23 tags leave the corridor at some point; the first departure is at 2%, almost from the start; a large share of the batch sits outside, so this batch did not recover.

The numbers. SPE 55576720 against a limit of 381 (145714.1x); T² 99 against a limit of 18 (5.5x); 26.5% of the batch sits outside the golden corridor.

Driven by: substrate_conc (97%), acid_flow_rate (3%), aeration_rate (0%), dumped_broth_flow (0%), head_pressure (0%)

2. Batch 99 - faulty does not look like a golden batchseverity 10
faulty · a fault IS recorded for this batch · first left the corridor at 2% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 1263 sigma above the golden batch at 100% of the way through; 23 of 23 tags leave the corridor at some point; the first departure is at 2%, almost from the start; a large share of the batch sits outside, so this batch did not recover.

The numbers. SPE 38063050 against a limit of 381 (99795.8x); T² 61 against a limit of 18 (3.4x); 23.4% of the batch sits outside the golden corridor.

Driven by: substrate_conc (98%), acid_flow_rate (2%), heat_water_flow (0%), aeration_rate (0%), head_pressure (0%)

3. Batch 45 - operator controlled does not look like a golden batchseverity 10
operator controlled · no fault recorded for this batch · first left the corridor at 1% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 1253 sigma above the golden batch at 100% of the way through; 21 of 23 tags leave the corridor at some point; the first departure is at 1%, almost from the start; a large share of the batch sits outside, so this batch did not recover.

The numbers. SPE 25132546 against a limit of 381 (65893.9x); T² 39 against a limit of 18 (2.2x); 23.7% of the batch sits outside the golden corridor.

Driven by: substrate_conc (99%), acid_flow_rate (1%), sugar_feed_rate (0%), aeration_rate (0%), water_injection (0%)

4. Batch 95 - faulty does not look like a golden batchseverity 10
faulty · a fault IS recorded for this batch · first left the corridor at 10% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 1012 sigma above the golden batch at 100% of the way through; 19 of 23 tags leave the corridor at some point; the first departure is at 10%, early in the batch; a large share of the batch sits outside, so this batch did not recover.

The numbers. SPE 22134388 against a limit of 381 (58033.2x); T² 64 against a limit of 18 (3.6x); 21.6% of the batch sits outside the golden corridor.

Driven by: substrate_conc (95%), acid_flow_rate (4%), sugar_feed_rate (1%), dumped_broth_flow (0%), heat_water_flow (0%)

5. Batch 100 - faulty does not look like a golden batchseverity 10
faulty · a fault IS recorded for this batch · first left the corridor at 0% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 950 sigma above the golden batch at 100% of the way through; 15 of 23 tags leave the corridor at some point; the first departure is at 0%, almost from the start.

The numbers. SPE 21871792 against a limit of 381 (57344.7x); T² 22 against a limit of 18 (1.2x); 14.7% of the batch sits outside the golden corridor.

Driven by: substrate_conc (96%), acid_flow_rate (4%), co2_offgas (0%), heat_water_flow (0%), o2_offgas (0%)

6. Batch 9 - recipe driven does not look like a golden batchseverity 10
recipe driven · no fault recorded for this batch · first left the corridor at 2% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 1093 sigma above the golden batch at 100% of the way through; 22 of 23 tags leave the corridor at some point; the first departure is at 2%, almost from the start; a large share of the batch sits outside, so this batch did not recover.

The numbers. SPE 21376420 against a limit of 381 (56045.9x); T² 42 against a limit of 18 (2.3x); 17.9% of the batch sits outside the golden corridor.

Driven by: substrate_conc (99%), acid_flow_rate (1%), head_pressure (0%), aeration_rate (0%), dumped_broth_flow (0%)

7. Batch 94 - faulty does not look like a golden batchseverity 10
faulty · a fault IS recorded for this batch · first left the corridor at 9% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 923 sigma above the golden batch at 100% of the way through; 15 of 23 tags leave the corridor at some point; the first departure is at 9%, almost from the start; a large share of the batch sits outside, so this batch did not recover.

The numbers. SPE 17032606 against a limit of 381 (44657.0x); T² 52 against a limit of 18 (2.9x); 19.3% of the batch sits outside the golden corridor.

Driven by: substrate_conc (91%), acid_flow_rate (9%), temperature (0%), co2_offgas (0%), heat_water_flow (0%)

8. Batch 33 - operator controlled does not look like a golden batchseverity 10
operator controlled · no fault recorded for this batch · first left the corridor at 2% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 1132 sigma above the golden batch at 100% of the way through; 20 of 23 tags leave the corridor at some point; the first departure is at 2%, almost from the start; a large share of the batch sits outside, so this batch did not recover.

The numbers. SPE 15775811 against a limit of 381 (41361.9x); T² 19 against a limit of 18 (1.1x); 17.4% of the batch sits outside the golden corridor.

Driven by: substrate_conc (93%), acid_flow_rate (7%), sugar_feed_rate (0%), aeration_rate (0%), head_pressure (0%)

9. Batch 30 - recipe driven does not look like a golden batchseverity 10
recipe driven · no fault recorded for this batch · first left the corridor at 1% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 938 sigma above the golden batch at 100% of the way through; 14 of 23 tags leave the corridor at some point; the first departure is at 1%, almost from the start.

The numbers. SPE 14441737 against a limit of 381 (37864.1x); T² 25 against a limit of 18 (1.4x); 12.4% of the batch sits outside the golden corridor.

Driven by: substrate_conc (95%), acid_flow_rate (5%), paa_flow (0%), penicillin_conc (0%), heat_water_flow (0%)

10. Batch 51 - operator controlled does not look like a golden batchseverity 10
operator controlled · no fault recorded for this batch · first left the corridor at 0% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 853 sigma above the golden batch at 100% of the way through; 16 of 23 tags leave the corridor at some point; the first departure is at 0%, almost from the start.

The numbers. SPE 11337651 against a limit of 381 (29725.7x); T² 19 against a limit of 18 (1.1x); 14.7% of the batch sits outside the golden corridor.

Driven by: substrate_conc (89%), acid_flow_rate (11%), sugar_feed_rate (0%), paa_flow (0%), penicillin_conc (0%)

11. Batch 25 - recipe driven does not look like a golden batchseverity 10
recipe driven · no fault recorded for this batch · first left the corridor at 1% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 857 sigma above the golden batch at 100% of the way through; 21 of 23 tags leave the corridor at some point; the first departure is at 1%, almost from the start; a large share of the batch sits outside, so this batch did not recover.

The numbers. SPE 10093403 against a limit of 381 (26463.4x); T² 30 against a limit of 18 (1.6x); 16.5% of the batch sits outside the golden corridor.

Driven by: substrate_conc (93%), acid_flow_rate (7%), water_injection (0%), aeration_rate (0%), head_pressure (0%)

12. Batch 18 - recipe driven does not look like a golden batchseverity 10
recipe driven · no fault recorded for this batch · first left the corridor at 6% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 801 sigma above the golden batch at 100% of the way through; 12 of 23 tags leave the corridor at some point; the first departure is at 6%, almost from the start.

The numbers. SPE 9446301 against a limit of 381 (24766.8x); 8.8% of the batch sits outside the golden corridor.

Driven by: substrate_conc (95%), acid_flow_rate (5%), heat_water_flow (0%), paa_flow (0%), penicillin_conc (0%)

13. Batch 43 - operator controlled does not look like a golden batchseverity 10
operator controlled · no fault recorded for this batch · first left the corridor at 4% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 811 sigma above the golden batch at 100% of the way through; 13 of 23 tags leave the corridor at some point; the first departure is at 4%, almost from the start.

The numbers. SPE 8874244 against a limit of 381 (23267.0x); 8.9% of the batch sits outside the golden corridor.

Driven by: substrate_conc (93%), acid_flow_rate (6%), sugar_feed_rate (1%), heat_water_flow (0%), paa_flow (0%)

14. Batch 3 - recipe driven does not look like a golden batchseverity 10
recipe driven · no fault recorded for this batch · first left the corridor at 1% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 739 sigma above the golden batch at 100% of the way through; 23 of 23 tags leave the corridor at some point; the first departure is at 1%, almost from the start; a large share of the batch sits outside, so this batch did not recover.

The numbers. SPE 6203700 against a limit of 381 (16265.2x); T² 20 against a limit of 18 (1.1x); 17.6% of the batch sits outside the golden corridor.

Driven by: substrate_conc (85%), acid_flow_rate (14%), aeration_rate (0%), water_injection (0%), head_pressure (0%)

15. Batch 44 - operator controlled does not look like a golden batchseverity 10
operator controlled · no fault recorded for this batch · first left the corridor at 5% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 663 sigma above the golden batch at 100% of the way through; 12 of 23 tags leave the corridor at some point; the first departure is at 5%, almost from the start.

The numbers. SPE 5591929 against a limit of 381 (14661.2x); T² 21 against a limit of 18 (1.2x); 9.9% of the batch sits outside the golden corridor.

Driven by: substrate_conc (90%), acid_flow_rate (10%), sugar_feed_rate (0%), paa_flow (0%), penicillin_conc (0%)

16. Batch 92 - faulty does not look like a golden batchseverity 10
faulty · a fault IS recorded for this batch · first left the corridor at 10% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 597 sigma above the golden batch at 100% of the way through; 12 of 23 tags leave the corridor at some point; the first departure is at 10%, early in the batch.

The numbers. SPE 5154621 against a limit of 381 (13514.7x); 5.0% of the batch sits outside the golden corridor.

Driven by: substrate_conc (77%), acid_flow_rate (23%), ph (0%), paa_flow (0%), oxygen_uptake (0%)

17. Batch 34 - operator controlled does not look like a golden batchseverity 10
operator controlled · no fault recorded for this batch · first left the corridor at 8% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 556 sigma above the golden batch at 100% of the way through; 12 of 23 tags leave the corridor at some point; the first departure is at 8%, almost from the start.

The numbers. SPE 5064372 against a limit of 381 (13278.1x); 8.0% of the batch sits outside the golden corridor.

Driven by: substrate_conc (89%), acid_flow_rate (10%), sugar_feed_rate (1%), paa_flow (0%), penicillin_conc (0%)

18. Batch 6 - recipe driven does not look like a golden batchseverity 10
recipe driven · no fault recorded for this batch · first left the corridor at 13% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 572 sigma above the golden batch at 100% of the way through; 11 of 23 tags leave the corridor at some point; the first departure is at 13%, early in the batch.

The numbers. SPE 4366606 against a limit of 381 (11448.6x); 5.1% of the batch sits outside the golden corridor.

Driven by: substrate_conc (88%), acid_flow_rate (12%), paa_flow (0%), heat_water_flow (0%), cool_water_flow (0%)

19. Batch 10 - recipe driven does not look like a golden batchseverity 10
recipe driven · no fault recorded for this batch · first left the corridor at 13% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 546 sigma above the golden batch at 100% of the way through; 8 of 23 tags leave the corridor at some point; the first departure is at 13%, early in the batch.

The numbers. SPE 3899527 against a limit of 381 (10224.0x); 4.0% of the batch sits outside the golden corridor.

Driven by: substrate_conc (87%), acid_flow_rate (13%), paa_flow (0%), penicillin_conc (0%), oxygen_uptake (0%)

20. Batch 4 - recipe driven does not look like a golden batchseverity 10
recipe driven · no fault recorded for this batch · first left the corridor at 13% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 559 sigma above the golden batch at 100% of the way through; 12 of 23 tags leave the corridor at some point; the first departure is at 13%, early in the batch.

The numbers. SPE 3842857 against a limit of 381 (10075.4x); 7.0% of the batch sits outside the golden corridor.

Driven by: substrate_conc (86%), acid_flow_rate (14%), paa_flow (0%), oxygen_uptake (0%), o2_offgas (0%)

21. Batch 42 - operator controlled does not look like a golden batchseverity 10
operator controlled · no fault recorded for this batch · first left the corridor at 0% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 525 sigma above the golden batch at 100% of the way through; 14 of 23 tags leave the corridor at some point; the first departure is at 0%, almost from the start.

The numbers. SPE 3703452 against a limit of 381 (9709.9x); 7.2% of the batch sits outside the golden corridor.

Driven by: substrate_conc (86%), acid_flow_rate (13%), sugar_feed_rate (1%), heat_water_flow (0%), paa_flow (0%)

22. Batch 24 - recipe driven does not look like a golden batchseverity 10
recipe driven · no fault recorded for this batch · first left the corridor at 6% of the way through

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What the chart shows. substrate_conc carries most of it, running 564 sigma above the golden batch at 100% of the way through; 12 of 23 tags leave the corridor at some point; the first departure is at 6%, almost from the start.

The numbers. SPE 3543513 against a limit of 381 (9290.6x); 5.5% of the batch sits outside the golden corridor.

Driven by: substrate_conc (87%), acid_flow_rate (13%), paa_flow (0%), oxygen_uptake (0%), penicillin_conc (0%)

23. Batch 40 - operator controlled does not look like a golden batchseverity 10
operator controlled · no fault recorded for this batch · first left the corridor at 13% of the way through

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What the chart shows. substrate_conc carries most of it, running 522 sigma above the golden batch at 100% of the way through; 9 of 23 tags leave the corridor at some point; the first departure is at 13%, early in the batch.

The numbers. SPE 3180412 against a limit of 381 (8338.6x); 6.4% of the batch sits outside the golden corridor.

Driven by: substrate_conc (83%), acid_flow_rate (16%), sugar_feed_rate (0%), paa_flow (0%), penicillin_conc (0%)

24. Batch 36 - operator controlled does not look like a golden batchseverity 10
operator controlled · no fault recorded for this batch · first left the corridor at 13% of the way through

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What the chart shows. substrate_conc carries most of it, running 434 sigma above the golden batch at 100% of the way through; 13 of 23 tags leave the corridor at some point; the first departure is at 13%, early in the batch.

The numbers. SPE 2949482 against a limit of 381 (7733.1x); 12.7% of the batch sits outside the golden corridor.

Driven by: substrate_conc (82%), acid_flow_rate (16%), sugar_feed_rate (2%), paa_flow (0%), penicillin_conc (0%)

25. Batch 47 - operator controlled does not look like a golden batchseverity 10
operator controlled · no fault recorded for this batch · first left the corridor at 12% of the way through

the same as a picture (for printing)

What the chart shows. substrate_conc carries most of it, running 530 sigma above the golden batch at 100% of the way through; 14 of 23 tags leave the corridor at some point; the first departure is at 12%, early in the batch.

The numbers. SPE 2410682 against a limit of 381 (6320.5x); 5.7% of the batch sits outside the golden corridor.

Driven by: substrate_conc (93%), acid_flow_rate (6%), sugar_feed_rate (1%), heat_water_flow (0%), dumped_broth_flow (0%)

5. How each way of running the plant behaves

Each curve is one batch: how far it sits from the golden batch at that point of its progress, taken across all 23 tags at once. The bold line is the middle batch of the group. All four charts share the same scale, so they can be read against each other.

Way of running it	Batches	Typical distance from golden	Worst batch	Mean yield	Beyond 10 sigma
recipe driven	30	1.05 sigma	1093 sigma	2,912,750 kg	25 of 30
operator controlled	30	1.35 sigma	1253 sigma	2,833,113 kg	30 of 30
APC with Raman	30	0.66 sigma	97 sigma	3,484,283 kg	6 of 30
faulty	10	12.51 sigma	1500 sigma	2,600,203 kg	10 of 10

The four side by side

Only the middle batch of each group, so the four are directly comparable.

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recipe driven — 30 batches

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operator controlled — 30 batches

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APC with Raman — 30 batches

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faulty — 10 batches

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6. Every batch, ranked

label	batch	strategy	band	max_z	sustained_z	worst_tag	worst_at_pct	outside_pct	first_outside_pct	T2	SPE	yield_total_kg
Batch 91 - faulty	91	faulty	far from it (over 10 sigma)	1500	1429	substrate_conc	100	26.52	2	99.06	5.558e+07	2.597e+06
Batch 45 - operator controlled	45	operator controlled	far from it (over 10 sigma)	1253	1168	substrate_conc	100	23.74	1	38.98	2.513e+07	2.828e+06
Batch 99 - faulty	99	faulty	far from it (over 10 sigma)	1263	1231	substrate_conc	100	23.39	2	61.21	3.806e+07	8.908e+05
Batch 95 - faulty	95	faulty	far from it (over 10 sigma)	1012	1004	substrate_conc	100	21.61	10.1	64.03	2.213e+07	1.954e+06
Batch 94 - faulty	94	faulty	far from it (over 10 sigma)	923.4	884.5	substrate_conc	100	19.3	9.1	51.82	1.703e+07	3.584e+06
Batch 9 - recipe driven	9	recipe driven	far from it (over 10 sigma)	1093	1044	substrate_conc	100	17.87	2	41.82	2.138e+07	4.083e+06
Batch 3 - recipe driven	3	recipe driven	far from it (over 10 sigma)	738.6	670.3	substrate_conc	100	17.65	1	19.65	6.204e+06	2.675e+06
Batch 33 - operator controlled	33	operator controlled	far from it (over 10 sigma)	1132	1031	substrate_conc	100	17.43	2	19.28	1.578e+07	3.294e+06
Batch 25 - recipe driven	25	recipe driven	far from it (over 10 sigma)	857.2	787.6	substrate_conc	100	16.48	1	29.62	1.009e+07	3.717e+06
Batch 51 - operator controlled	51	operator controlled	far from it (over 10 sigma)	852.9	814.6	substrate_conc	100	14.74	0	19.18	1.134e+07	2.918e+06
Batch 100 - faulty	100	faulty	far from it (over 10 sigma)	949.8	926.9	substrate_conc	100	14.65	0	22.5	2.187e+07	1.555e+06
Batch 29 - recipe driven	29	recipe driven	far from it (over 10 sigma)	57.4	53.9	water_injection	18.2	14.61	1	13.98	7.662e+04	1.842e+06
Batch 36 - operator controlled	36	operator controlled	far from it (over 10 sigma)	541.4	420	acid_flow_rate	83.8	12.65	13.1	17.01	2.949e+06	1.754e+06
Batch 30 - recipe driven	30	recipe driven	far from it (over 10 sigma)	937.6	895.1	substrate_conc	100	12.39	1	25.21	1.444e+07	3.539e+06
Batch 67 - APC with Raman	67	APC with Raman	similar (2-5 sigma)	4.4	4.4	head_pressure	89.9	10.91	2	18.01	0.9129	3.413e+06
Batch 44 - operator controlled	44	operator controlled	far from it (over 10 sigma)	663	612.6	substrate_conc	100	9.91	5.1	21	5.592e+06	1.474e+06
Batch 15 - recipe driven	15	recipe driven	far from it (over 10 sigma)	68.1	54.6	acid_flow_rate	49.5	9.22	1	14.35	2.018e+04	2.853e+06
Batch 59 - operator controlled	59	operator controlled	far from it (over 10 sigma)	651.7	236.2	acid_flow_rate	84.8	9	7.1	15.05	1.098e+06	2.91e+06
Batch 43 - operator controlled	43	operator controlled	far from it (over 10 sigma)	811	758.4	substrate_conc	100	8.87	4	6.064	8.874e+06	2.212e+06
Batch 18 - recipe driven	18	recipe driven	far from it (over 10 sigma)	801.3	761.3	substrate_conc	100	8.83	6.1	11.13	9.446e+06	2.014e+06
Batch 34 - operator controlled	34	operator controlled	far from it (over 10 sigma)	589.4	540	acid_flow_rate	83.8	8	8.1	6.676	5.064e+06	2.066e+06
Batch 53 - operator controlled	53	operator controlled	far from it (over 10 sigma)	96.4	96.4	sugar_feed_rate	96	7.52	0	18.53	5.848e+04	2.858e+06
Batch 32 - operator controlled	32	operator controlled	far from it (over 10 sigma)	168.7	168.7	sugar_feed_rate	96	7.52	13.1	17.71	1.837e+05	4.196e+06
Batch 42 - operator controlled	42	operator controlled	far from it (over 10 sigma)	541.5	506.2	acid_flow_rate	83.8	7.22	0	6.472	3.703e+06	2.358e+06
Batch 48 - operator controlled	48	operator controlled	far from it (over 10 sigma)	96.4	96.4	sugar_feed_rate	96	7.17	5.1	12.15	9.266e+04	3.265e+06
Batch 23 - recipe driven	23	recipe driven	far from it (over 10 sigma)	88.2	53.9	acid_flow_rate	49.5	7.17	2	9.588	5.328e+04	2.855e+06
Batch 49 - operator controlled	49	operator controlled	far from it (over 10 sigma)	468.8	435.1	substrate_conc	100	7.09	6.1	8.211	1.928e+06	2.597e+06
Batch 4 - recipe driven	4	recipe driven	far from it (over 10 sigma)	589.3	539.1	acid_flow_rate	83.8	6.96	13.1	14.85	3.843e+06	1.887e+06
Batch 31 - operator controlled	31	operator controlled	far from it (over 10 sigma)	160.7	60.3	acid_flow_rate	10.1	6.91	2	5.562	9.225e+04	1.89e+06
Batch 97 - faulty	97	faulty	far from it (over 10 sigma)	615.4	378.4	acid_flow_rate	76.8	6.83	9.1	12.15	1.977e+06	3.894e+06
Batch 5 - recipe driven	5	recipe driven	far from it (over 10 sigma)	164.1	48.7	acid_flow_rate	14.1	6.52	2	9.567	3.829e+04	3.563e+06
Batch 40 - operator controlled	40	operator controlled	far from it (over 10 sigma)	589.2	499.9	acid_flow_rate	83.8	6.39	13.1	3.375	3.18e+06	2.426e+06
Batch 60 - operator controlled	60	operator controlled	far from it (over 10 sigma)	541.4	272	acid_flow_rate	83.8	6.26	6.1	8.993	1.046e+06	3.802e+06
Batch 54 - operator controlled	54	operator controlled	far from it (over 10 sigma)	588.9	360.3	acid_flow_rate	83.8	6.17	6.1	2.876	1.48e+06	3.184e+06
Batch 47 - operator controlled	47	operator controlled	far from it (over 10 sigma)	530.3	488.8	substrate_conc	100	5.7	12.1	4.866	2.411e+06	2.586e+06
Batch 27 - recipe driven	27	recipe driven	far from it (over 10 sigma)	72.3	37.8	heat_water_flow	43.4	5.57	12.1	12.41	1.313e+04	2.176e+06
Batch 24 - recipe driven	24	recipe driven	far from it (over 10 sigma)	564.3	537.4	substrate_conc	100	5.52	6.1	10.07	3.544e+06	1.958e+06
Batch 35 - operator controlled	35	operator controlled	far from it (over 10 sigma)	330.3	100.3	acid_flow_rate	1	5.52	1	10.74	1.772e+05	3.538e+06
Batch 39 - operator controlled	39	operator controlled	far from it (over 10 sigma)	532.8	132.6	acid_flow_rate	99	5.3	13.1	79.5	5.318e+05	2.682e+06
Batch 58 - operator controlled	58	operator controlled	far from it (over 10 sigma)	199	180.3	substrate_conc	100	5.22	0	4.107	2.849e+05	2.758e+06

first 40 of 100 — the rest are in batch_scores.csv

7. The golden batch, tag by tag

The green band is where a good batch is expected to be at each point of its progress. The worst batches are drawn over it in red, and one reference batch in green for comparison. Drag to zoom, double-click to reset, click a name in the legend to hide it.

aeration_rate

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sugar_feed_rate

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acid_flow_rate

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base_flow_rate

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cool_water_flow

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heat_water_flow

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water_injection

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head_pressure

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dumped_broth_flow

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substrate_conc

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dissolved_o2

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penicillin_conc

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vessel_volume

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vessel_weight

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ph

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temperature

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generated_heat

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co2_offgas

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paa_flow

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oil_flow

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oxygen_uptake

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o2_offgas

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carbon_evolution

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8. What this cannot tell you

Batches are aligned by percent complete. If a batch is slow because a phase ran long, alignment by phase or by an indicator variable would place it better.
The corridor is only as good as the reference batches. If a bad batch is in the reference set, its behaviour becomes normal.
The bands say how far a batch sat from the golden one. They do not say the deviation mattered: a batch inside the corridor throughout can still be poor if it is late, or if the yield is low for reasons no tag records.
"Worst tag" is where the deviation is largest, which is not always where it started. Use the per-batch charts above to see the order things moved in.

9. Comparing the ways of running the plant

APC with Raman produces the most and is also the most repeatable.
Across all 3 strategies the yields differ: one-way ANOVA F=9.91, p=1.3e-04; Kruskal-Wallis p=5.1e-04 without assuming normality. The spreads differ too: Levene p=5.6e-05.
The 10 faulty batches are excluded from every comparison below. They appear only in the last table, as the thing each strategy's golden batch is asked to detect.

9.1 What each way of running it produced

Way of running it	Batches	Mean yield (kg)	Spread (CV)	Worst batch	Best batch	Mean hours	kg per hour
recipe driven	30	2,912,750	26.4%	1,842,400	4,083,100	228.8	12,917
operator controlled	30	2,833,113	24.0%	1,474,100	4,196,000	229.2	12,431
APC with Raman	30	3,484,283	8.8%	2,830,800	4,044,300	224.7	15,587

CV is the batch-to-batch spread as a percentage of the mean. In a regulated plant it often matters more than the mean, because it is what lets you promise a delivery date and pass a validation.

9.2 Is the difference real, or is it noise?

Comparison	Difference		Welch p	Mann-Whitney p	Cohen d	Significant
recipe driven vs operator controlled	+79,637 kg	+2.8%	6.7e-01	8.9e-01	+0.11	no
recipe driven vs APC with Raman	-571,533 kg	-16.4%	5.3e-04	1.1e-02	-0.98	yes
operator controlled vs APC with Raman	-651,170 kg	-18.7%	2.3e-05	4.4e-05	-1.23	yes

Two tests because one assumes normality and the other does not; they should agree. Cohen d is the size of the gap in standard deviations: 0.2 is small, 0.5 medium, 0.8 large. A difference can be statistically significant and still too small to act on, so read the size as well as the p-value.

9.3 The golden batch of each way of running it

One real batch per strategy, chosen on two criteria at once: high yield and close to that group's own mean trajectory. The highest-yielding batch is often a lucky outlier that ran unlike anything else, and the most typical batch is often mediocre. These are both.

Way of running it	Golden batch	Yield	Yield rank	Closeness rank
recipe driven	Batch 26 - recipe driven	3,886,800 kg	4 of 30	2 of 30
operator controlled	Batch 60 - operator controlled	3,802,300 kg	3 of 30	5 of 30
APC with Raman	Batch 79 - APC with Raman	3,825,600 kg	5 of 30	2 of 30

9.4 Does each way of running it actually look different?

A golden batch is built from one strategy, holding back some of its own batches, and every group is then scored against it. The figure is the median batch's typical distance, in sigma. The shaded cell on the diagonal is that strategy's own held-back batches — the fair self-comparison, and it should be the lowest number in its row.

Golden built from	recipe driven	operator controlled	APC with Raman	faulty
recipe driven	0.77	1.07	1.08	1.11
operator controlled	0.82	0.74	0.95	1.20
APC with Raman	1.05	1.35	0.66	12.51

Golden built from	Its own held-back batches	The other strategies	How much further	Fault detection power
recipe driven	0.77	1.07	1.40x	1.4x
operator controlled	0.74	0.89	1.20x	1.6x
APC with Raman	0.66	1.20	1.82x	19.0x

"How much further" says how distinctive that way of running the plant is. "Fault detection power" is how far the faulty batches sit compared with its own good ones — a tighter normal is a more sensitive detector, which is a reason to run a strategy quite separate from what it yields.

9.5 What this comparison cannot settle

Do not rank strategies by distance from the main golden batch in section 2. That golden is built from all the good batches, so it is a blend of every strategy, and each is being measured against an average that contains itself. Section 9.4 avoids that by giving each strategy its own golden.
These are the batches that were run, not a designed experiment. If the strategies were used in different periods, on different feedstock or by different crews, that difference is inside the numbers and cannot be separated out.
Yield is the only outcome recorded here. Cost, energy, operator effort and the price of the instrumentation are not, and a strategy that yields more can still lose on all four.
Sample size is 30 to 30 batches per strategy. Enough to see a large difference, not enough to see a small one.

Folder: /Volumes/YN-4T/WIP/CTRL-Designer/B-CDL-Data-Analysis/E-Batch/IndPenSim-Golden-APC