Control Charts for Monitoring Field Failure Data

Abstract

One responsibility of the reliability engineer is to monitor failure trends for fielded units to confirm that pre-production life testing results remain valid. This research suggests an approach that is computationally simple and can be used with a small number of failures per observation period. The approach is based on converting failure time data from fielded units to normal distribution data, using simple logarithmic or power transformations. Appropriate normalizing transformations for the classic life distributions (exponential, lognormal, and Weibull) are identified from the literature. Samples of size 500 field failure times are generated for seven different lifetime distributions (normal, lognormal, exponential, and four Weibulls of various shapes). Various control charts are then tested under three sampling schemes (individual, fixed, and random) and three system reliability degradations (large step, small step, and linear decrease in mean time between failures (MTBF)). The results of these tests are converted to performance measures of time to first out-of-control signal and persistence of signal after out-of-control status begins. Three of the wellknown Western Electric sensitizing rules are used to recognize the assignable cause signals. Based on this testing, theX-chart with fixed sample size is the best overall for field failure monitoring, although the individual chart was better for the transformed exponential and another highly-skewed Weibull. As expected, the linear decrease in MTBF is the most difficult change for any of the charts to detect.

MaxEWMA Control Chart for a Weibull Process with Individual Measurements

“…It should be noted that the inverse erf transformation method is based on the conversion of a normal distributed variable into a uniform one and then the conversion of this one into a Weibull one Method 1Batson et al studied the individuals and MR control charts using the power transformation method for a Weibull process. That is, y 1 = x 0.2777 β and , where μ 1,0 = E ( y 1 ) = Γ(1.2777) θ 0.2777 β , , and Γ(⋅) = gamma function.…”

“…Batson et al studied the individual and moving range (I‐MR) control charts using the power transformation method to transform the Weibull data to a normal distribution. Chen and Cheng investigated the effect of non‐normality on the control limits of the chart.…”

Simultaneous optimization of [Xbar] control chart and age-based preventive maintenance policies under an economic objective

“…Over the past 25-30 years quality improvement methodologies have spawned increased industrial productivity in the range of 15-25% (Cassady and Nachlas, 1998;Rahim, 2005, 2006;Batson et al, 2006;Zhang et al, 2006), and in 1988 alone, the combined services of the United States spent approximately $10 billion 0740-817X C 2008 "IIE" on programmed depot maintenance (Joint Logistics Commanders, 1988).…”

Bayesian monitoring to detect a shift in process mean

“…• refining control chart methods to be more efficient, to interact with more types of information, and to produce better diagnostics, as in Batson et al 2 , Chakhunashvili and Bergman 3 , Cheng and Thaga 4 , Guh 5 , Nichols and Padgett 6 , Perry et al 7,8 , Trip and Wieringa 9 , Wu et al 10 , and Ye et al 11 ; • developing methods for integrating statistical process control with engineering process control, as in Del Castillo 12 , Jiang et al 13 , Nembhard and Chen 14 , Runger et al 15 , and Yang and Sheu 16 ; • developing monitoring methods for non-stationary and/or auto-correlated data, as in Nembhard and Changpetch 17 , Nembhard and Valverde-Ventura 18 , Noorossana and Vaghefi 19 , Shepherd et al 20 , and Triantafyllopoulos 21 ; • synthesizing theory and practice, as in Barone et al 22 , Nikolaidis et al 23 , and Stoumbos and Reynolds 24 ;…”