Reliability
Are you on the path to product consistency and quality? Let JMP guide you as you look at life distributions, competing failure causes and accelerated life testing. With JMP, you can quickly model and understand expected lifetimes for products and parts.
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Find out about trends in the statistical assessment of product reliability in this article by renowned quality expert, William Q. Meeker.
In any manufacturing endeavor – whether the product is semiconductors, light bulbs, automobiles, shoes, medical devices, jet engines or any other type of durable goods – product reliability strongly influences business success. A product that functions as intended throughout its anticipated life cycle yields happy customers who will provide repeat business as well as referrals to friends. Dependable products also reduce warranty costs, which can otherwise quickly eat away at profit margins.
Product failure, or “field catastrophe,” diminishes consumer trust, tarnishing the brand, the company’s reputation and the likelihood that customers will return.
Preventing failure and improving warranty performance are two of the most important reasons for using proven techniques to understand the reliability of your products. JMP software sets itself apart by integrating robust statistical analysis with dynamic data visualization that lets users immediately spot trends and outliers in huge data sets. Manufacturers improve reliability by pinpointing defects in materials or processes and determining how to correct them.
The first step in enhancing reliability is to determine the likelihood of failure as a product ages. This requires collecting data about product failures and using that data to find an appropriate distributional model for the lifetime of the product. Selecting the correct distribution is critically important for sound, accurate reliability estimates. The Life Distribution platform introduced in JMP 8 combines an interactive graphical interface with statistical criteria to automatically find the best fit to the data. The platform can handle left, right or mixed censoring. To analyze competing causes of failures, the Life Distribution platform allows you to select the best distribution for each cause and improvement prediction by interactively removing individual causes.
Need to know how products will perform in the field? Accelerated lifetime testing simulates a product’s entire lifecycle by introducing a stress-accelerating factor, like high temperatures or voltage. Then the Fit Life by X platform introduced in JMP 8 helps you quickly understand how the product will perform over its expected lifetime under normal operating conditions. In addition, you can use Fit Life by X to compare group life data – from different suppliers or manufacturing plants, for example – to compare their expected performance.
- Life Distribution
- Competing Causes
- Accelerated Life Testing
- More Techniques
The Life Distribution platform gives engineers greater choices and flexibility in finding the best fit for their data compared to traditional options. This platform, introduced in JMP 8, allows users to examine a nonparametric distribution as well as 15 parametric distributions. The parametric distributions that can be fit by the platform include the Weibull, lognormal, Fréchet, smallest and largest extreme value, the three parameter Weibull, and the generalized gamma distribution.
What is this? Life Distribution’s interactive probability plot allows comparison of non-negative and negative distribution properties of lifetime events. The plot at left is a non-parametric (Kaplan-Meier) graph of the failure probability. The Distribution Profiler graphs at right are interactive plots of the cumulative density function (CDF) to predict the probability that product failure will have occurred by a given time.
What is it for? The probability plot can be used to identify the distribution that best fits the data. Once a distributional model is selected, predictions and extrapolations can be made for various time periods to estimate failure probabilities. In addition to the CDF, interactive Quantile, Hazard and Probability Density Function (PDF) profilers are provided.
What can it do? In this example, a white goods manufacturer analyzes data collected from testing a random sample of washing machines filled with abnormally large loads of laundry and turned continuously for 135 days. When the machines failed, the manufacturer recorded the time of failure. The data points and dashed lines show a nonparametric fit to the failure times collected. The graph also displays two distributional models that have been fit to this data, and which often describe reliability data: Weibull and Smallest Extreme Value (SEV). The Weibull model (green line) is clearly better for predicting machine life because it follows the data points more closely.
Most products have multiple ways they can fail. Use the Competing Causes module in the Life Distribution platform to model each failure mode individually. Life Distribution rolls up all the individual models into an overall series reliability model that can be used to describe the field performance of your product. You can use the Omit Causes feature to conduct tradeoff analyses to identify which failure mode you should resolve first to offer the most improvement for your customers.
What is this? An interactive probability plot allows comparison of the series system distribution of failures with the individual failure modes. All the features available for distribution fitting seen in the Life Distribution example can be used in the Competing Causes analysis option.
What is it for? Many products, systems, or components have more than one failure mode or cause of failures. It is important to distinguish among different causes of failure for such units to understand how to improve product reliability and quality.
What does it do? The manufacturer of a mechanical device wants to improve warranty performance. The company has experienced a high level of failures, and repair staff have found multiple failure modes. Using the Competing Causes feature of the Life Distribution platform, a cause combination plot is shown with the overall Series System Failure (black line) and individual failure modes (colored lines). In this case, all the failure modes are modeled with a Fréchet distribution; however, each individual cause can be fit with a separate distribution. Once the correct distributions are selected, either manually or automatically, product lifetime estimates for various failure combinations are made using the interactive profilers. The platform can be used for Pareto analysis to determine system improvement potential by evaluating lifetime performance as the causes are omitted. This allows an engineer to quickly determine which failure cause should be corrected first to gain the most improvement to the system’s overall reliability.
Need to know your product’s reliability over a period of months or years, but only have days or weeks to run a reliability test? Use the Fit Life By X platform to model the results of accelerated life tests to get information you need as quickly as possible.
Fit Life by X lets you model the relationship between an event and the factor of interest, using transformations for common acceleration methods, including Arrhenius, voltage, linear, log, logit, location, and location and scale.
The report below is the result of a custom data transformation. It is used to compare various distributional models at the same factor level or a single distribution across various factor levels.
JMP also can shows you density curves and quantile lines for as many as four different distributions for the lifetime event and the accelerating factor. The scatterplot below shows two highlighted distributions.
What is this? A scatterplot with nonparametric density contours and marginal distributions.
What is it for? It shows where the data is most dense, with each contour line in the curved shape enclosing 5 percent of the data.
What can it do? For example, the manufacturer of computer processors can analyze the relationship between the speed of a chip and any factor that engineers can control, such as standby current, to improve quality and profit margins. Using this scatterplot, the manufacturer can identify abnormal chips – the ones represented by points lying farthest from the curved shape – and see that reducing standby current helps increase the speed of chips.
JMP includes other reliability testing techniques as well.
Recurrence Analysis analyzes event times like the other Reliability and Survival platforms, but the events can recur several times for each unit. Typically, these events occur when a unit breaks down, is repaired and returns to service. The unit is tracked until it is taken out of service. Recurrence analysis also can be used to analyze data from continuing treatments of a long-term disease, such as the recurrence of tumors in patients receiving treatment for bladder cancer. The goal of the analysis is to obtain the mean cumulative function (MCF), which shows the total cost per unit as a function of time. “Cost” can describe either the number of repairs or the actual financial charges associated with the repairs.
Fit Parametric Survival is a regression platform that fits a survival distribution scaled to a linear model. The distributions available are Weibull, lognormal, exponential, Fréchet and loglogistic. The regression uses an iterative maximum likelihood method. Accelerated failure models can be fit here if there is more than one stress variable.
Fit Proportional Hazards is a regression platform that uses the Cox proportional hazards method to fit a linear model. Proportional hazards models are popular regression models for survival data with covariates. See Cox (1972). This model is semiparametric; the linear model is estimated, but the form of the hazard function is not. Time-varying covariates are not supported.
Survival calculates estimates of survival functions using the product-limit (Kaplan-Meier) method for one or more groups of either right-censored or complete data. (Complete data have no censored values.) This platform gives an overlay plot of the estimated survival function for each group and for the whole sample. JMP also computes the log rank and Wilcoxon statistics to test homogeneity between groups. Diagnostic plots and fitting options are available for exponential, Weibull, and lognormal survival distributions. This is a popular platform for those interested in evaluating survival versus failure data, as in medical and research disciplines.
