Hardy Zaragoza

SPC stands for Statistical Process Control.

In the manufacturing industry, a poor product—defined as not meeting spec— is often the result of a poor process.

SPC is a statistical method of quality control that collects and analyzes data from product and process measurements.

The goal is to determine what falls within vs outside of the process capability leading to preventive or corrective actions when needed.

SPC is part of the five Core Tools for effective quality management with APQP, PPAP, FMEA, and MSA being the other core tools.

In the manufacturing industry, the cost of poor quality (COPQ) measures cost associated with process and product failures.

The best manufacturers have a COPQ score around 1% whereas subpar manufacturers have a score of 5% or higher, which means subpar manufacturers are 5X more likely to pay in scrap, rework, defect, retesting, and recall costs compared to the leaders in the sector.

SPC statistically evaluates a process that is efficient, cost-effective, and able to improve.

Most importantly, it is a method of prevention, which saves more time and money than detecting the problem downstream.

All manufacturing processes produce variability. It’s a natural part of the process.

The SPC investigates data from process and product measurements to determine whether the variation is acceptable or not.

Variation in manufacturing has two classes:

About 85% of variations are common cause, while around 15% are special cause.

But how do we define what is common or special cause variation?

As long as the data is within ±3 standard deviations from the mean, it represents 99.73% of acceptable values (common cause variation). Anything outside the ±3 standard deviations from the mean is unacceptable (special cause variation).

For example, a normal commute to work might take 30 minutes plus/minus 10 minutes.

The 30 minutes is the mean with the ± 10 minutes representing the acceptable deviation range.

If we were to plot a whole month’s worth of commute data, then nearly all data should fall between 20 to 40 minutes for commuting to work aka common cause variation.

However, if there is one day where the commute time was 1 hour and 5 minutes, it’s beyond our acceptable range and we have to find out why. The reason? An accident that created a long traffic jam aka special cause variation.

The goal of the SPC is to eliminate special cause variations.

There are 14 quality control tools used in SPC. Seven are quality control tools and the other seven are supplemental tools.

Quality Control Tools:

Supplemental Tools:

The most popular SPC tool is the control chart.

A control chart graphically represents the gathered data with predetermined control limits. Think of the control chart as a bell curve laid sideways in order to see the time sequence of data points.

The control limits, as explained above in the variation section, are ±3 standard deviations from the mean.

Anything that falls within that range between the upper control limit (UCL) and the lower control limit (LCL) is acceptable.

Anything outside that range is unacceptable and defined as special cause variation as shown below.

It’s important to know that control limits are different from specification limits. Control limits represent the voice of the process (what’s feasible) while specification limits represent the voice of the customer (what’s expected). Ideally, control limits should fall within spec limits.

Selection of the right control chart depends on the type of data: variable (continuous) or attribute (discrete). Variable data is preferred when available.

Control charts for variable data:

Control charts for attribute data:

After all data is plotted on the control chart, it should fall between the control limits.

Examples of common cause variation include:

Anything outside the control limits is a special cause and must be addressed.

Examples of special cause variation include:

However, there can be situations where all data points are within control limits but still potentially be “out of control.”

Common cause variation data points should be within control limits but also randomly plotted. If a discernable pattern can be noticed, then further investigation is needed.

Examples of within control limits but out of control process includes:

SPC collects and produces valuable data for immediate but also long-term improvements.

Most data is viewed as pass/fail and often discarded. But in a century of Big Data & AI, data is the new oil.

A model-based definition (MBD) introduces data back into the ecosystem for improved designs, improved parts, and improved operations done quicker, cheaper, and more efficiently.

MBD is a growing industry practice of having the 3D CAD model be the “single source of truth.”

This means the CAD model along with semantic product and manufacturing information (PMI) can make data collection for APQP, MSA, PPAP, and SPC more robust and faster in real-time as the digital thread head towards Industry 4.0 practices.

Most importantly, advanced analytics and deep learning has the power to elevate SPC workflows to the next level as the manufacturing industry leans into digital and data technologies.

Contact us and we'll glad to help answer questions about SPC and improving process capability.

Lend-Lease is the only way other than combat to get rid of unwanted planes What you get from lend-lease is Army/Navy/Air experience(when the

Square footage with 3 sides is calculated. The area of a triangle can be found using a formula that uses the side of the triangle with the highest height drawn to it from its opposite side.

How many square feet is there? How many square feet is a 12x12 room?

A room that is 12 feet wide by 12 feet long has a total of 144 square feet of square footage. To find the square footage, you need to divide the width by the length.

How is square footage calculated? The area should be calculated as square feet.

If you're measuring a square or rectangular area, you can use the length by the width as the area's area.

How do I find the third side of a triangle?

How is the square footage calculated?

Add the lengths of the parallel sides. Then add this number to the height of the area. If you divide by two, you can find the square footage of the trapezoid.

How do you find the third side of a triangle?

If you know the length of the other two sides of the triangle, you can use the Pythagorean Theorem to find the hypotenuse of a right triangle. You can find c if you know the lengths of a and b.

How to find the sides of the triangle?

A 200 square foot room is large.

A 200 square foot space is about the same size as a one car garage. The average car could fit into a small spot with a small amount of flexibility.

How many square feet is a tile? The tile is 2' by 2' or 24' by 24' and the total square foot is 2' by 2' feet.

The total square foot is 2 feet by 2 feet, which is 4 square feet.

The square foot is 10 12.

The width of the floor or ceiling area should be divided by the area.

What is the calculation of square footage?

To find square footage, divide the length measurement in feet by the width measurement in feet. If you're calculating a much smaller space, like a doll's house, the area is expressed in square feet or square inches.

How do you find the length of a square foot? To get square footage, you divide the length in feet by the width. 6 feet long by 3 feet wide is 18 square feet. Just divide to convert back.

If you know the area is 20 square feet and the length is 5 feet, the width must be 4 feet.

The price per square foot is calculated by dividing the price of the house by the square footage of the house. The price per square foot is the amount of money spent on a house.

How do you find the length of a right triangle? Right triangles and the Pythagorean theorem are related.

The Ticknock walk is one of my favourite Dublin Mountains walks.

Aside from on the many occasions that I arrive to the main car park and find the place absolutely swamped, but more on getting parking below!

The Ticknock hike is a moderate, 1.5 to 2.5 hour walk, depending on pace and how long you linger at the top to soak up the views.

In the guide below, you’ll find an easy-to-follow breakdown of the trails along with everything you need to know about the Ticknock Fairy Castle Loop.

The Ticknock walk is fairly straight-forward, once you have a good sense of 1, the car park situation and 2, the trail. Here’s some handy info to get you up-to-speed:

You’ll find Ticknock Hill in the Dublin Mountains. It’s around 3 km south-west of Sandyford, and a handy half-hour bus journey (the 44B) or drive from the centre of Dublin.

The main Ticknock car park (here on maps) can be an absolute disaster at the weekend. If you’re parking here, arrive early. An alternative entrance is the Kilmashogue Forest Car Park (here on maps).

From what I can tell online (this could be wrong), the opening hours for the Ticknock car park are 06:00 to 22:00 during the summer months and 07:00 to 17:00 from the start of November. Again, I can’t find anywhere to confirm this online, so keep that in mind.

The Ticknock Fairy Castle Loop is the most popular trail here. To do it from the main car parK, just follow the green way-markers. If you start at Kilmashogue, follow the yellow way-markers and then join the green as soon as you see them (find an overview of the trails below).

If you start the walk from the main Ticknock car park, allow 1.5 to 2 hours. If you start it from Kilmashogue, allow 2 to 2.5 hours. There’s a lot of incline on this walk and a moderate level of fitness is needed.

Ticknock Hill offers a glorious 10km of mountain and forest walks for those looking to stretch the legs and soak up views of Dublin City, the Wicklow Mountains and beyond.

Ticknock Forest is home to a huge number of trails, and it’s a popular destination for walkers, runners and mountain-bikers!

At the summit of Two Rock Mountain, you’ll find the Fairy Castle – a Neolithic passage tomb measuring 27 metres in diameter by 3 metres in height.

It’s believed that an entrance to the tomb was visible in the 1940s but, do to parts of the exterior collapsing, it’s no longer visible.

If you’re doing the Ticknock hike for the first time, the summit of Three Rock Mountain is a good spot to stop off.

You’ll find some big boulders here (near the transmitters) that make a fine little seat. You’ll have views out over Dublin City right in front of you.

The first Ticknock walk is the one from the main car park. Now, if you’ve never been here before, the car park has a lower section and then a higher section.

Personally, I try and avoid the upper section of the Ticknock car park as it gets wedged up there at times and can be tricky to get out of.

You can start this walk up through Ticknock Forest from the main car park (here it is on Google Maps). This is a well-signposted trail, just make sure to follow the GREEN arrows.

Follow the arrows up through Ticknock Forest to Three Rock Mountain and then continue on to the Fairy Castle. You’ll take a right after this and continue down towards the rifle range and then back to the car park.

This version of the Ticknock hike is moderate enough and it should prove to be reasonably handy for those with a half-decent level of fitness.

If you stick to the trail and don’t venture off into Ticknock Forest, you’ll be able to walk along a well-kept tarmac path for the most part.

This trail stretches for 5.5km and it takes roughly 1.5 – 2 hours in total to complete (with time spent admiring the views).

I’ve done the main Ticknock Forest Walk 5 or 6 times over the years. It wasn’t until last weekend that we parked at Kilmashogue Forest and walked from there.

This is a brilliant walk and (as you can see in the map above) it takes you up to the Fairy Castle and around to Three Rock (there’s some mighty views from both spots).

The only downside is that it isn’t a looped walk, so you have to retrace your steps to get back to the car park.

Start in this car park (you can’t miss the beginning of the trail). It’s a steep aul slog for a good chunk of this trail, but there’s plenty of places to stop and soak up the views.

There’s only one section of this trail that can cause confusion, and that’s when you come to a fork in the road – take the path to the right (it’s the one going up) and keep strolling.

Soon after the trail will join up with the Fairy Castle Loop (see above where the yellow dots collide with the green).

This Ticknock walk, similar to the Howth Cliff Path walk, is reasonably strenuous at the beginning, as there’s a good bit of incline walking. However, if you have moderate fitness levels you’ll be fine.

We did this walk last weekend and it took us roughly 2 hours in total (that includes time spent sat up at Three Rock admiring the view.

There’s an almost endless number of walks in Dublin to tackle after you’ve conquered the Ticknock walk.

Below, you’ll find 3 of our favourites, from hill walks with mighty views to forest walks where, if you start early, you’ll dodge the crowds.

If you were feeling particularly ambitious/energetic, you could take on the Cruagh Woods Walk straight after the Ticknock walk. Doubling up on these woods walks sounds a bit mad but they’re right next to each other and the Cruagh Woods offer some gorgeous views.

Tibradden Woods is another great shout for a forest walk, and it’s a handy spin from Ticknock Forest. The trail here stretches for around 2.5km and it’ll take you roughly 2 hours to complete it, depending on pace.

The Carrickgollogan Forest walk is another of the more popular Dublin Mountains walks, and it includes the very unique chimney that you can see above. If you’ve had your fill of forests, Bohernabreena Reservoir (30-minutes drive) is well worth a visit.

We’ve had a lot of questions over the years asking about everything from ‘Which is the handiest car park for the Ticknock hike?’ to ‘Is the Ticknock Walk buggy friendly?’.

In the section below, we’ve popped in the most FAQs that we’ve received. If you have a question that we haven’t tackled, ask away in the comments section below.

The walk from the ‘main’ car park will take you 1.5 – 2 hours. The walk from the second (quieter) car park mentioned above should take 1.5 to 2.5 hours, depending on pace.

If you visit at peak times on the weekend, yes! However, the car park at Kilmashogue Forest is a good alternative and you can join the main Ticknock walk from here.

Let us consider "the standard foundations of mathematics" the first order set theory ZFC.

It has model that using partial functions: (see article WILLIAM M. FARMER, JOSHUA D. GUTTMAN: A Set Theory with Support for Partial Functions )

Let's define value of the function the following way: $"f(x)" := (\iota y: \langle x,y\rangle \in f)$ (here $f$ and $x$ are object variables, and iota is THE definite description operator :) ).

Without a doubt, the following sequence is valid:

$(\langle x,y\rangle \in f) \Rightarrow (f(x)=y)$

My claim is that the opposite implication is also valid:

$(f(x)=y) \Rightarrow (\langle x,y\rangle \in f)$