Statistical Process Control Charts Based on the Exponentiated Janardan Distribution for Skewed Lifetime Data
Karupaiah K, Zhang L and Platonova LE
Published on: 2026-05-01
Abstract
Statistical process control techniques are widely used for monitoring process quality; however, traditional control charts are mainly based on the assumption of normality, which is often violated in practice. This study proposes a control chart based on the Exponentiated Janardan Distribution to effectively monitor skewed and non-normal lifetime data. The fundamental properties of the distribution, including the survival function, hazard function, and moments, are derived and utilized for constructing control limits. A numerical illustration is presented to demonstrate the applicability of the proposed control chart. The resulting control chart successfully detects out-of-control signals, highlighting its sensitivity to process shifts. The truncation of the lower control limit further supports its suitability for lifetime data analysis. The proposed control chart provides a flexible and robust alternative to conventional normal-based charts and is applicable in quality control, reliability engineering, and healthcare monitoring.
Keywords
Exponentiated Janardan distribution; Statistical quality control; Control charts statistical process control; Gamma transformationIntroduction
Control charts are widely recognized as the most effective tools in Statistical Process Monitoring (SPM) for enhancing the quality and productivity of manufacturing processes. In recent years, their application has extended beyond manufacturing to monitor processes in non-manufacturing sectors such as healthcare [1] and meteorology [2].
A typical control chart consists of three horizontal lines: a central line (CL) representing the average value of a stable process, and two control limits-the upper control limit (UCL) and lower control limit (LCL). When the process is in control, nearly all data points fall within these limits. Control charts can monitor both variable and attribute characteristics.
Most control chart methodologies assume that the quality characteristic follows a normal distribution. However, in many practical situations, the distribution is unknown or non-normal. This has led to considerable research on control charts for non-normal distributions from [3-7].
In this article, we propose a control chart scheme for time-truncated life tests using the exponentiated half logistic distribution. Shanker, [7] introduced the Janardan distribution, building on the work of [8] who explored the one-parameter Lindley distribution [9]. They established the cumulative distribution function (CDF) and probability density function (PDF) for the Janardan distribution alongside key statistical properties such as mode, moments, failure rate, mean residual life, stochastic orderings, and parameter estimation. Their findings revealed that the Janardan distribution fits certain life data more closely than the Lindley distribution.
There is growing interest in developing skewed distributions for Statistical Quality Control (SQC) methods. For instance, Betul and Yazici explored the Burr distribution [10], and Chan and Cui [5] developed control chart constants for X- and R-charts that adjust based on the distribution’s skewness.
While parameter estimation and hypothesis testing for the three-parameter exponentiated Janardan distribution are well documented, research on associated control charts remains limited. Ramalhoto and Morais [11] developed a control chart for monitoring its scale parameter, and Surucu and Sazak [12] introduced a scheme based on moments. More recently, Mukherjee, McCracken, and Chakraborti [13] proposed several control charts and monitoring schemes for both location and scale parameters of this distribution.
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