Process capability

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Nov 13 2023

Process Capability Indices

Within the quality profession, a capable process is one with a high C_{p_k}. In the field, it is not quite so simple. My colleague Joerg Muenzing recently shared concerns about the process capability indices:

“Many manufacturers that I know struggle with incapable processes. Intellectually, people understand the concept of capability, but are unable to effectively apply it to an entire process. A single-figure measure for the entire chain would be ideal to better understand and manage it. The challenge is that the chain consists of processes with measurable characteristics, like thickness, substitute characteristics, like leak current to infer dryness, and also visual inspection results like blemishes or scratches.

They know that C_{p_k} < 1 is bad, and scrap shrinks the bottom line, but not much more. At the same time, customers like large Automotive OEMs demand from their suppliers a C_{p_k} > 1.33 for manual and “uncritical” characteristics, and C_{p_k} >1.66 or even >2.00 for critical characteristics.

What would be useful without being ‘too wrong’?”

Let’s take a closer look.

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By • Data science • 5 • Tags: , , , ,

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Dec 1 2022

About Digital Twins

Some hosts showed digital twins during the Van of Nerds tour de France last September, but none mentioned the cyber-physical systems touted as a key component in Industry 4.0. Furthermore, we also found that the meaning of digital twin had drifted away from detailed simulations of physics and chemistry as part of a cyber-physical system for process control.

Instead, a digital twin is now an animation of part movements and machine status in a line for production control. This has effectively disabled discussions of digital twins in the context of cyber-physical systems, which matters in stabilizing and establishing capability for high-technology processes like additive manufacturing.

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By • Van of Nerds • 3 • Tags: , , , ,

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Nov 7 2022

Analyzing Variation with Histograms, KDE, and the Bootstrap

Assume you have a dataset that is a clean sample of a measured variable. It could be a critical dimension of a product, delivery lead times from a supplier, or environmental characteristics like temperature and humidity. How do you make it talk about the variable’s distribution? This post explores this challenge in the simple case of 1-dimensional data. I have used methods from histograms to KDE and the Bootstrap, varying in vintage from the 1890s to the 1980s:

Timeline of tools used in this post

Other methods were surely invented for the same purpose between 1895 and 1960 or since 1979, that I don’t know about or haven’t used. Readers are welcome to point them out.

The ones discussed here are not black boxes, automatically producing answers from a stream of data. All require a human to tune the settings of the tools. And this human needs to know the back story of the data.

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By • Data science • 2 • Tags: , , ,

Apr 22 2010

Lean is about simultaneously improving all dimensions of performance, including quality

This is in response to Mike Micklewright‘s question on Why Is Quality So Rarely Central In Lean?:

“I see so many internal Lean “experts” using “Lean” as a means to increase efficiencies and productivity, and therefore, reduce costs.  They still do not see the connection to quality.  They see quality and the reduction of variation in significant product characteristics as something that is outside of the Lean scope and something that should be handled by the quality folks independently of the lean effort.  What a shame!  If you agree with this observation, why does this exist and what can we do to change this perception?”

Following is my response:

Quality not central to Lean? Says who? Lean is about simultaneously improving all dimensions of performance, including quality. Quality professionals frequently miss this, because what they learned primarily addresses process capability issues that are central only in high technology, where, if your process is mature, your product is obsolete. This is the context where statistical approaches like Six Sigma make a difference.

Modern machine tools, on the other hand, can easily hold required tolerances, and most quality problems are not due to lack of process capability. They are instead due to discrete failure of the equipment or human error. The main issue with discrete equipment failures is to detect them quickly so that they affect few parts and can be diagnosed before their trail is cold. With one-piece flow, defects are detected immediately instead of being buried in WIP, and this is why conversion from batch production to one-piece flow typically yields large improvements in quality.

The next step, which Dennis alluded to, is having machines stop as soon as they start producing defectives, but this still leaves human error, and that is addressed by mistake-proofing. Beyond these approaches, there is also management to prevent the deterioration over time, and plan responses to potential new problems.

This is a hierarchy of approaches. Actual numbers vary, but, in orders of magnitude, statistical tools will get you from 30% defectives to 3%, one-piece flow to 0.3%, mistake-proofing to 15ppm, and I know of one case of a Toyota supplier achieving <1ppm on some parts.

By • Management • 0 • Tags: , , , , , ,