Your Reliability Engineering Professional Development Site
A listing in reverse chronological order of articles by:
The prior article, https://accendoreliability.com/measurement-system-bias/, focused on defining and calculating a point estimate of gage bias. A method was presented to determine if the bias was statistically significant. If significant, the bias would be applied to the data as a correction factor.
This article discusses gage bias linearity over a measurement range.
Root Cause Analysis is different than “problem solving.” It is highly visible with money on the table. How can you approach it? How can you be successful? This video gives some fundamentals of my approach. [Read more…]
Conflict is a normal part of living. Do you consider it a positive or a negative? Communication helps, but so does the perspective that you take. This video discusses it from a New Product Development and from a sports point of view. [Read more…]
(Reproduced from the article “Death of a Reliability Engineer” by Dev Raheja, Reliability Review, Vol. 30, March 2010 with permission)
When I first wrote the article in March 1990, I implied an ‘F’ grade to reliability engineers. Now almost 20 years later, I would give them a “E’. Yes, there is a little improvement but nothing you can write to your mother about.
The MTBF cancer was wide spread and is still wide spread in the DoD. The only reason I upgraded the reliability engineer from F to E is because the MTBF in some industries is no longer used such as in the automotive industry. They use the failure rates instead to hide their shame.
Failure rate is just the reciprocal of MTBF. Good job! Same old corn flakes with a new product name! [Read more…]
When doing training, some will focus only on the tools. However, in our approach we focus on 3 things. It is the people, process and tools. In that order. If you would like to improve your systems and tool usage, we can create a plan to execute with you. And we can make it a reality. [Read more…]
By prepopulating the highest priority functions, along with other selected information, the FMEA team can focus their efforts on the most important functions, and minimize in-meeting time. This is the last step in FMEA preparation. However, there are specific limitations to FMEA prepopulation that must be understood and adhered to.
“Give me six hours to chop down a tree and I will spend the first four sharpening the axe.”
Abraham Lincoln
In my prior article, Measurement Systems, the total variation in the measurement data was partitioned into part variation (PV), assessor variation (AV), and equipment variation (EV). GR&R is the square root of the sum of the squares of AV and EV. If the ratio of GRR/TV is less than 10%, then the measurement system variation was acceptable.
In addition to variation, data bias needs to be considered. This bias is created by systematic measurement errors.
Recall that a frequency histogram shows that measurement data is spread about a center value. During calibration, a gage is used to measure a known reference standard that is traceable to a national standard. When the measurements are repeated, the data will show some variation. When the data shows a bell shape about a center, the average is a good indicator of the center. The difference between the average and the reference is called bias, calculated as
$$BIAS = \bar{X}-X_{ref}$$
(1)
This can be easily illustrated. Consider the case where a standard gage block with a reference value of 10 (units) was measured 30 times by a single appraiser and the values recorded. The average of the measurements should be about 10, however the data statistics show a sample average of 10.23 and sample standard deviation of 0.4635. To visualize the data, Minitab was used to create a histogram of the data with normal distribution. Then, the reference value of 10 and the data average of 10.23 were added to the chart.
Figure 1
Using equation 1, the gage bias is 0.23, but this could be caused sampling errors. Note that 10 and 10.23 are both contained within the spread of the data. So how can the significance of the bias be determined?
With this data set, bias was positive, but in other situations, the bias could be negative. Any significance test should consider both cases.
Hypothesis testing can be used to determine the significance. In hypothesis testing, there is a null hypothesis $-H_O-$ and an alternative hypothesis $-H_A-$. For this analysis, the null hypothesis is that the bias = 0. The alternate hypothesis is that the bias is significantly different than 0. In hypothesis testing, this is expressed as:
$$H_O: \mu=0$$
$$H_A: \mu\neq0$$
(2)
The sample average $-\bar{X}-$ is normally distributed about the population mean $-\mu-$ and is approximately normally distributed with a variance of $-\sigma-$. We don’t know $-\mu-$ and $-\sigma-$, but know the sample size N = 30, the sample average $-\bar{X}=10.23-$, and the sample standard deviation $-s=0.4635-$.
The sample average $-\bar{X}-$ follows a t-distribution. If $-H_O-$ is true, then the t-statistic is
$$t=\frac{\bar{X}-\mu}{\sigma/\sqrt{N}}=\frac{10.23-10}{0.4635/sqrt{30}}=2.718$$
(3)
Using a table of t-values and a 90% confidence interval, the critical t-value is 1.70. The sample t-value was 2.718, so the null hypothesis $-H_O-$ is rejected. This leaves us with the alternate hypothesis $-H_A-$. One would be justified to apply a correction factor of -0.23 to the data collected by the gage.
Linearity describes the bias over the gage measurement range. It is discussed in Measurement System Gage Linearity. Stability is the change in bias as the gage ages. This will be discussed in a future article and a link provided here.
Using a single reference standard, gage bias is relatively easy to determine. Hypothesis tests on the data can be used to determine if the bias is statistically significant. If not significant, then the gage correction factor can be 0. If the bias is significant, the bias can be used as a gage correction factor.
If you want to engage me on this or other topics, please contact me. We can discuss your problem/concerns and determine how I can help solve your analysis, design, and manufacturing problems.
I have worked in Quality, Reliability, Applied Statistics, and Data Analytics for over 30 years in design engineering and manufacturing. At Wayne State University, I taught at the graduate level. I also provided Minitab seminars to corporate clients, write articles, and have presented and written papers at SAE, ISSAT, and ASQ.
Dennis Craggs, Consultant
Quality, Reliability and Analytics Services
dlcraggs@me.com
(810) 964-1529
The QFD concept is widely known, yet appears to be used infrequently. Too time consuming for the value, but it is a “good idea.” There are several schools of thought, and certainly practical approaches for implementation that can provide needed business solutions. This video introduces the topic. If you want help with implementation, or with training – contact us to obtain the break throughs available. [Read more…]
When an objective requires a tool to be used, that is idea. Certain projects can greatly benefit from use of Monte Carlo analysis. This in depth knowledge can create solutions where it is not readily apparent. If you are considering going this far, we can help you decide if the value is worthwhile. And we can help you apply it in a simple yet powerful way. [Read more…]
Statistical Process Control is about addressing business needs. It is not about charts. It is not even about control. It is about focused learning and taking action. Our successful implementation history means that we can help you too! [Read more…]
“. . . not everything that can be counted counts” Albert Einstein
A key, but often missed, step in FMEA preparation is to identify and prioritize the functions that relate to the item being analyzed. These become candidate functions to be brought into the FMEA.
A recent call to us asked about “Understanding Variation.” What does that really mean? We explore the topic with you in this video. [Read more…]
DOE is often seen as a manufacturing tool, or at least as a technical tool. However, any process with inputs and outputs can be improved with this tool. This video talks about 3 areas, including a focus on a running DOE which found a surprising medical issue. [Read more…]
What is numerical optimization? What are the limits of the approach? It can be used while trying to obtain robust design, but constraints need to be understood. [Read more…]
Tom Izzo has often talked about the difference between winning games and winning championships. Observing him, I believe I understand his comment better now. [Read more…]