Abstract
Statistical process control is a method of monitoring product in its development process using statistical techniques with the presumption that the products produced under identical process condition shall not always be alike with respect to some quality characteristic(s). However, if the observed variations are within the tolerable limits statistical process control (SPC) methods would pass them for acceptance. This philosophy is adopted to decide the reliability and quality of a product by defining some quality measures and proposing a probability model for the quality measurements. The well known Dagum distribution(DD) is considered to propose a product reliability based on non-homogenous Poisson process (NHPP). Its mean value function is taken as a quality characteristic and SPC limits for it are developed. These control limits are exemplified to a live failure data to detect the out of control signals for the quality of the product based on the failure data and compared with Exponential distribution(ED).
Highlights
Life time data generally contain the failure times of sample products or interfailure times or number of failures experienced in a given time
If the observed variations are within the tolerable limits statistical process control (SPC) methods would pass them for acceptance
The well known Dagum distribution(DD) is considered to propose a product reliability based on non-homogenous Poisson process (NHPP)
Summary
Life time data generally contain the failure times of sample products or interfailure times or number of failures experienced in a given time. An NHPP designed to study the failure process of a product can be constructed as a Poisson process with mean value function based on the cumulative distribution function of a continuous positive valued random variable With this backdrop, we consider the well known Dagum distribution (DD) as F(t) to generate a growth model based Non Homogenous Poisson Process (NHPP). We consider the well known Dagum distribution (DD) as F(t) to generate a growth model based Non Homogenous Poisson Process (NHPP) For such a model we developed the statistically admissible control limits for the mean value function and demonstrate the same how a graphical procedure called a statistical process control (SPC) chart based on the mean value function would help in detecting out of control signals for the product quality.
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